lst:=[[tan(d*x+c)^5*(a+I*a*tan(d*x+c)),x,6,-I*a*x-a*ln(cos(d*x+c))/d+I*a*tan(d*x+c)/d-1/2*a*tan(d*x+c)^2/d-1/3*I*a*tan(d*x+c)^3/d+1/4*a*tan(d*x+c)^4/d+1/5*I*a*tan(d*x+c)^5/d,1],
[tan(d*x+c)^4*(a+I*a*tan(d*x+c)),x,5,a*x-I*a*ln(cos(d*x+c))/d-a*tan(d*x+c)/d-1/2*I*a*tan(d*x+c)^2/d+1/3*a*tan(d*x+c)^3/d+1/4*I*a*tan(d*x+c)^4/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c)),x,4,I*a*x+a*ln(cos(d*x+c))/d-I*a*tan(d*x+c)/d+1/2*a*tan(d*x+c)^2/d+1/3*I*a*tan(d*x+c)^3/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c)),x,3,-a*x+I*a*ln(cos(d*x+c))/d+a*tan(d*x+c)/d+1/2*I*a*tan(d*x+c)^2/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c)),x,2,-I*a*x-a*ln(cos(d*x+c))/d+I*a*tan(d*x+c)/d,1],
[a+I*a*tan(d*x+c),x,2,a*x-I*a*ln(cos(d*x+c))/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c)),x,2,I*a*x+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c)),x,3,-a*x-a*cot(d*x+c)/d+I*a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c)),x,4,-I*a*x-I*a*cot(d*x+c)/d-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^4*(a+I*a*tan(d*x+c)),x,5,a*x+a*cot(d*x+c)/d-1/2*I*a*cot(d*x+c)^2/d-1/3*a*cot(d*x+c)^3/d-I*a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*(a+I*a*tan(d*x+c)),x,6,I*a*x+I*a*cot(d*x+c)/d+1/2*a*cot(d*x+c)^2/d-1/3*I*a*cot(d*x+c)^3/d-1/4*a*cot(d*x+c)^4/d+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^6*(a+I*a*tan(d*x+c)),x,7,-a*x-a*cot(d*x+c)/d+1/2*I*a*cot(d*x+c)^2/d+1/3*a*cot(d*x+c)^3/d-1/4*I*a*cot(d*x+c)^4/d-1/5*a*cot(d*x+c)^5/d+I*a*ln(sin(d*x+c))/d,1],
[tan(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x,6,2*a^2*x-2*I*a^2*ln(cos(d*x+c))/d-2*a^2*tan(d*x+c)/d-I*a^2*tan(d*x+c)^2/d+2/3*a^2*tan(d*x+c)^3/d+1/2*I*a^2*tan(d*x+c)^4/d-1/5*a^2*tan(d*x+c)^5/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x,5,2*I*a^2*x+2*a^2*ln(cos(d*x+c))/d-2*I*a^2*tan(d*x+c)/d+a^2*tan(d*x+c)^2/d+2/3*I*a^2*tan(d*x+c)^3/d-1/4*a^2*tan(d*x+c)^4/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x,3,-2*a^2*x+2*I*a^2*ln(cos(d*x+c))/d+a^2*tan(d*x+c)/d-1/3*I*(a+I*a*tan(d*x+c))^3/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^2,x,3,-2*I*a^2*x-2*a^2*ln(cos(d*x+c))/d+I*a^2*tan(d*x+c)/d+1/2*(a+I*a*tan(d*x+c))^2/d,1],
[(a+I*a*tan(d*x+c))^2,x,2,2*a^2*x-2*I*a^2*ln(cos(d*x+c))/d-a^2*tan(d*x+c)/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^2,x,3,2*I*a^2*x+a^2*ln(cos(d*x+c))/d+a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x,3,-2*a^2*x-a^2*cot(d*x+c)/d+2*I*a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x,4,-2*I*a^2*x-2*I*a^2*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)^2/d-2*a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x,5,2*a^2*x+2*a^2*cot(d*x+c)/d-I*a^2*cot(d*x+c)^2/d-1/3*a^2*cot(d*x+c)^3/d-2*I*a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x,6,2*I*a^2*x+2*I*a^2*cot(d*x+c)/d+a^2*cot(d*x+c)^2/d-2/3*I*a^2*cot(d*x+c)^3/d-1/4*a^2*cot(d*x+c)^4/d+2*a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x,7,-2*a^2*x-2*a^2*cot(d*x+c)/d+I*a^2*cot(d*x+c)^2/d+2/3*a^2*cot(d*x+c)^3/d-1/2*I*a^2*cot(d*x+c)^4/d-1/5*a^2*cot(d*x+c)^5/d+2*I*a^2*ln(sin(d*x+c))/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x,6,4*I*a^3*x+4*a^3*ln(cos(d*x+c))/d-4*I*a^3*tan(d*x+c)/d+2*a^3*tan(d*x+c)^2/d+4/3*I*a^3*tan(d*x+c)^3/d-11/20*a^3*tan(d*x+c)^4/d-1/5*tan(d*x+c)^4*(a^3+I*a^3*tan(d*x+c))/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x,4,-4*a^3*x+4*I*a^3*ln(cos(d*x+c))/d+2*a^3*tan(d*x+c)/d-1/2*I*a*(a+I*a*tan(d*x+c))^2/d-1/4*I*(a+I*a*tan(d*x+c))^4/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^3,x,4,-4*I*a^3*x-4*a^3*ln(cos(d*x+c))/d+2*I*a^3*tan(d*x+c)/d+1/2*a*(a+I*a*tan(d*x+c))^2/d+1/3*(a+I*a*tan(d*x+c))^3/d,1],
[(a+I*a*tan(d*x+c))^3,x,3,4*a^3*x-4*I*a^3*ln(cos(d*x+c))/d-2*a^3*tan(d*x+c)/d+1/2*I*a*(a+I*a*tan(d*x+c))^2/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^3,x,5,4*I*a^3*x+3*a^3*ln(cos(d*x+c))/d+a^3*ln(sin(d*x+c))/d-(a^3+I*a^3*tan(d*x+c))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x,5,-4*a^3*x+I*a^3*ln(cos(d*x+c))/d+3*I*a^3*ln(sin(d*x+c))/d-cot(d*x+c)*(a^3+I*a^3*tan(d*x+c))/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x,4,-4*I*a^3*x-2*I*a^3*cot(d*x+c)/d-4*a^3*ln(sin(d*x+c))/d-1/2*a*cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2/d,1],
[cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x,5,4*a^3*x+2*a^3*cot(d*x+c)/d-4*I*a^3*ln(sin(d*x+c))/d-1/2*I*a*cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2/d-1/3*cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3/d,1],
[cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x,6,4*I*a^3*x+4*I*a^3*cot(d*x+c)/d+2*a^3*cot(d*x+c)^2/d-3/4*I*a^3*cot(d*x+c)^3/d+4*a^3*ln(sin(d*x+c))/d-1/4*cot(d*x+c)^4*(a^3+I*a^3*tan(d*x+c))/d,1],
[cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x,7,-4*a^3*x-4*a^3*cot(d*x+c)/d+2*I*a^3*cot(d*x+c)^2/d+4/3*a^3*cot(d*x+c)^3/d-11/20*I*a^3*cot(d*x+c)^4/d+4*I*a^3*ln(sin(d*x+c))/d-1/5*cot(d*x+c)^5*(a^3+I*a^3*tan(d*x+c))/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x,7,8*I*a^4*x+8*a^4*ln(cos(d*x+c))/d-8*I*a^4*tan(d*x+c)/d+4*a^4*tan(d*x+c)^2/d+8/3*I*a^4*tan(d*x+c)^3/d-67/60*a^4*tan(d*x+c)^4/d-1/6*tan(d*x+c)^4*(a^2+I*a^2*tan(d*x+c))^2/d-7/15*tan(d*x+c)^4*(a^4+I*a^4*tan(d*x+c))/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x,5,-8*a^4*x+8*I*a^4*ln(cos(d*x+c))/d+4*a^4*tan(d*x+c)/d-1/3*I*a*(a+I*a*tan(d*x+c))^3/d-1/5*I*(a+I*a*tan(d*x+c))^5/a/d-I*(a^2+I*a^2*tan(d*x+c))^2/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^4,x,5,-8*I*a^4*x-8*a^4*ln(cos(d*x+c))/d+4*I*a^4*tan(d*x+c)/d+1/3*a*(a+I*a*tan(d*x+c))^3/d+1/4*(a+I*a*tan(d*x+c))^4/d+(a^2+I*a^2*tan(d*x+c))^2/d,1],
[(a+I*a*tan(d*x+c))^4,x,4,8*a^4*x-8*I*a^4*ln(cos(d*x+c))/d-4*a^4*tan(d*x+c)/d+1/3*I*a*(a+I*a*tan(d*x+c))^3/d+I*(a^2+I*a^2*tan(d*x+c))^2/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^4,x,6,8*I*a^4*x+7*a^4*ln(cos(d*x+c))/d+a^4*ln(sin(d*x+c))/d-1/2*(a^2+I*a^2*tan(d*x+c))^2/d-3*(a^4+I*a^4*tan(d*x+c))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x,5,-8*a^4*x+4*I*a^4*ln(cos(d*x+c))/d+4*I*a^4*ln(sin(d*x+c))/d-cot(d*x+c)*(a^2+I*a^2*tan(d*x+c))^2/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x,6,-8*I*a^4*x-a^4*ln(cos(d*x+c))/d-7*a^4*ln(sin(d*x+c))/d-1/2*cot(d*x+c)^2*(a^2+I*a^2*tan(d*x+c))^2/d-3*I*cot(d*x+c)*(a^4+I*a^4*tan(d*x+c))/d,1],
[cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4,x,5,8*a^4*x+4*a^4*cot(d*x+c)/d-8*I*a^4*ln(sin(d*x+c))/d-1/3*a*cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3/d-I*cot(d*x+c)^2*(a^2+I*a^2*tan(d*x+c))^2/d,1],
[cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x,6,8*I*a^4*x+4*I*a^4*cot(d*x+c)/d+8*a^4*ln(sin(d*x+c))/d-1/3*I*a*cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3/d-1/4*cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4/d+cot(d*x+c)^2*(a^2+I*a^2*tan(d*x+c))^2/d,1],
[cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4,x,7,-8*a^4*x-8*a^4*cot(d*x+c)/d+4*I*a^4*cot(d*x+c)^2/d+23/15*a^4*cot(d*x+c)^3/d+8*I*a^4*ln(sin(d*x+c))/d-1/5*cot(d*x+c)^5*(a^2+I*a^2*tan(d*x+c))^2/d-3/5*I*cot(d*x+c)^4*(a^4+I*a^4*tan(d*x+c))/d,1],
[cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x,8,-8*I*a^4*x-8*I*a^4*cot(d*x+c)/d-4*a^4*cot(d*x+c)^2/d+8/3*I*a^4*cot(d*x+c)^3/d+67/60*a^4*cot(d*x+c)^4/d-8*a^4*ln(sin(d*x+c))/d-1/6*cot(d*x+c)^6*(a^2+I*a^2*tan(d*x+c))^2/d-7/15*I*cot(d*x+c)^5*(a^4+I*a^4*tan(d*x+c))/d,1],
[tan(d*x+c)^6/(a+I*a*tan(d*x+c)),x,6,5/2*x/a+3*I*ln(cos(d*x+c))/a/d-5/2*tan(d*x+c)/a/d+3/2*I*tan(d*x+c)^2/a/d+5/6*tan(d*x+c)^3/a/d-3/4*I*tan(d*x+c)^4/a/d-1/2*tan(d*x+c)^5/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c)),x,5,-5/2*I*x/a+2*ln(cos(d*x+c))/a/d+5/2*I*tan(d*x+c)/a/d+tan(d*x+c)^2/a/d-5/6*I*tan(d*x+c)^3/a/d-1/2*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c)),x,4,-3/2*x/a-2*I*ln(cos(d*x+c))/a/d+3/2*tan(d*x+c)/a/d-I*tan(d*x+c)^2/a/d-1/2*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c)),x,3,3/2*I*x/a-ln(cos(d*x+c))/a/d-3/2*I*tan(d*x+c)/a/d-1/2*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c)),x,3,1/2*x/a+I*ln(cos(d*x+c))/a/d-1/2*I/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c)),x,2,-1/2*I*x/a-1/2/d/(a+I*a*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c)),x,2,1/2*x/a+1/2*I/d/(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c)),x,4,-1/2*I*x/a+ln(sin(d*x+c))/a/d+1/2/d/(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c)),x,4,-3/2*x/a-3/2*cot(d*x+c)/a/d-I*ln(sin(d*x+c))/a/d+1/2*cot(d*x+c)/d/(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^3/(a+I*a*tan(d*x+c)),x,5,3/2*I*x/a+3/2*I*cot(d*x+c)/a/d-cot(d*x+c)^2/a/d-2*ln(sin(d*x+c))/a/d+1/2*cot(d*x+c)^2/d/(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^4/(a+I*a*tan(d*x+c)),x,6,5/2*x/a+5/2*cot(d*x+c)/a/d+I*cot(d*x+c)^2/a/d-5/6*cot(d*x+c)^3/a/d+2*I*ln(sin(d*x+c))/a/d+1/2*cot(d*x+c)^3/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x,6,-25/4*x/a^2-6*I*ln(cos(d*x+c))/a^2/d+25/4*tan(d*x+c)/a^2/d-3*I*tan(d*x+c)^2/a^2/d-25/12*tan(d*x+c)^3/a^2/d+3/2*I*tan(d*x+c)^4/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^5/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x,5,15/4*I*x/a^2-4*ln(cos(d*x+c))/a^2/d-15/4*I*tan(d*x+c)/a^2/d-2*tan(d*x+c)^2/a^2/d+5/4*I*tan(d*x+c)^3/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x,4,9/4*x/a^2+2*I*ln(cos(d*x+c))/a^2/d-9/4*tan(d*x+c)/a^2/d+I*tan(d*x+c)^2/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x,6,-3/4*I*x/a^2+ln(cos(d*x+c))/a^2/d-3/4/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x,3,-1/4*x/a^2+3/4*I/a^2/d/(1+I*tan(d*x+c))-1/4*I/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^2,x,3,-1/4*I*x/a^2-1/4/d/(a+I*a*tan(d*x+c))^2+1/4/d/(a^2+I*a^2*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c))^2,x,3,1/4*x/a^2+1/4*I/d/(a+I*a*tan(d*x+c))^2+1/4*I/d/(a^2+I*a^2*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^2,x,4,-3/4*I*x/a^2+ln(sin(d*x+c))/a^2/d+3/4/a^2/d/(1+I*tan(d*x+c))+1/4/d/(a+I*a*tan(d*x+c))^2,1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x,5,-9/4*x/a^2-9/4*cot(d*x+c)/a^2/d-2*I*ln(sin(d*x+c))/a^2/d+cot(d*x+c)/a^2/d/(1+I*tan(d*x+c))+1/4*cot(d*x+c)/d/(a+I*a*tan(d*x+c))^2,1],
[cot(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x,6,15/4*I*x/a^2+15/4*I*cot(d*x+c)/a^2/d-2*cot(d*x+c)^2/a^2/d-4*ln(sin(d*x+c))/a^2/d+5/4*cot(d*x+c)^2/a^2/d/(1+I*tan(d*x+c))+1/4*cot(d*x+c)^2/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x,6,55/8*x/a^3+7*I*ln(cos(d*x+c))/a^3/d-55/8*tan(d*x+c)/a^3/d+7/2*I*tan(d*x+c)^2/a^3/d-1/6*tan(d*x+c)^5/d/(a+I*a*tan(d*x+c))^3+13/24*I*tan(d*x+c)^4/a/d/(a+I*a*tan(d*x+c))^2+55/24*tan(d*x+c)^3/d/(a^3+I*a^3*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x,5,-25/8*I*x/a^3+3*ln(cos(d*x+c))/a^3/d+25/8*I*tan(d*x+c)/a^3/d-1/6*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^3+11/24*I*tan(d*x+c)^3/a/d/(a+I*a*tan(d*x+c))^2+3/2*tan(d*x+c)^2/d/(a^3+I*a^3*tan(d*x+c)),1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x,7,-7/8*x/a^3-I*ln(cos(d*x+c))/a^3/d-1/6*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^3+3/8*I*tan(d*x+c)^2/a/d/(a+I*a*tan(d*x+c))^2+7/8*I/d/(a^3+I*a^3*tan(d*x+c)),1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x,4,1/8*I*x/a^3+3/8/a^3/d/(1+I*tan(d*x+c))+1/6*I*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^3-1/8/a/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x,4,-1/8*x/a^3-1/6*I/d/(a+I*a*tan(d*x+c))^3+3/8*I/a/d/(a+I*a*tan(d*x+c))^2-1/8*I/d/(a^3+I*a^3*tan(d*x+c)),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^3,x,4,-1/8*I*x/a^3-1/6/d/(a+I*a*tan(d*x+c))^3+1/8/a/d/(a+I*a*tan(d*x+c))^2+1/8/d/(a^3+I*a^3*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c))^3,x,4,1/8*x/a^3+1/6*I/d/(a+I*a*tan(d*x+c))^3+1/8*I/a/d/(a+I*a*tan(d*x+c))^2+1/8*I/d/(a^3+I*a^3*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^3,x,5,-7/8*I*x/a^3+ln(sin(d*x+c))/a^3/d+1/6/d/(a+I*a*tan(d*x+c))^3+3/8/a/d/(a+I*a*tan(d*x+c))^2+7/8/d/(a^3+I*a^3*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x,6,-25/8*x/a^3-25/8*cot(d*x+c)/a^3/d-3*I*ln(sin(d*x+c))/a^3/d+1/6*cot(d*x+c)/d/(a+I*a*tan(d*x+c))^3+11/24*cot(d*x+c)/a/d/(a+I*a*tan(d*x+c))^2+3/2*cot(d*x+c)/d/(a^3+I*a^3*tan(d*x+c)),1],
[tan(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x,6,-65/16*x/a^4-4*I*ln(cos(d*x+c))/a^4/d+65/16*tan(d*x+c)/a^4/d-2*I*tan(d*x+c)^2/a^4/d/(1+I*tan(d*x+c))+31/48*tan(d*x+c)^3/a^4/d/(1+I*tan(d*x+c))^2-1/8*tan(d*x+c)^5/d/(a+I*a*tan(d*x+c))^4+7/24*I*tan(d*x+c)^4/a/d/(a+I*a*tan(d*x+c))^3,1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x,8,15/16*I*x/a^4-ln(cos(d*x+c))/a^4/d+15/16/a^4/d/(1+I*tan(d*x+c))+7/16*tan(d*x+c)^2/a^4/d/(1+I*tan(d*x+c))^2-1/8*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^4+1/4*I*tan(d*x+c)^3/a/d/(a+I*a*tan(d*x+c))^3,1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x,5,1/16*x/a^4-3/16*I/a^4/d/(1+I*tan(d*x+c))+1/8*I*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^4+1/12*tan(d*x+c)^3/a/d/(a+I*a*tan(d*x+c))^3+1/16*I/d/(a^2+I*a^2*tan(d*x+c))^2,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x,5,1/16*I*x/a^4+3/16/a^4/d/(1+I*tan(d*x+c))+1/8*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^4+1/12*I*tan(d*x+c)^3/a/d/(a+I*a*tan(d*x+c))^3-1/16/d/(a^2+I*a^2*tan(d*x+c))^2,1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x,5,-1/16*x/a^4-1/8*I/d/(a+I*a*tan(d*x+c))^4+1/4*I/a/d/(a+I*a*tan(d*x+c))^3-1/16*I/d/(a^2+I*a^2*tan(d*x+c))^2-1/16*I/d/(a^4+I*a^4*tan(d*x+c)),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^4,x,5,-1/16*I*x/a^4-1/8/d/(a+I*a*tan(d*x+c))^4+1/12/a/d/(a+I*a*tan(d*x+c))^3+1/16/d/(a^2+I*a^2*tan(d*x+c))^2+1/16/d/(a^4+I*a^4*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c))^4,x,5,1/16*x/a^4+1/8*I/d/(a+I*a*tan(d*x+c))^4+1/12*I/a/d/(a+I*a*tan(d*x+c))^3+1/16*I/d/(a^2+I*a^2*tan(d*x+c))^2+1/16*I/d/(a^4+I*a^4*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^4,x,6,-15/16*I*x/a^4+ln(sin(d*x+c))/a^4/d+7/16/a^4/d/(1+I*tan(d*x+c))^2+15/16/a^4/d/(1+I*tan(d*x+c))+1/8/d/(a+I*a*tan(d*x+c))^4+1/4/a/d/(a+I*a*tan(d*x+c))^3,1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x,7,-65/16*x/a^4-65/16*cot(d*x+c)/a^4/d-4*I*ln(sin(d*x+c))/a^4/d+31/48*cot(d*x+c)/a^4/d/(1+I*tan(d*x+c))^2+2*cot(d*x+c)/a^4/d/(1+I*tan(d*x+c))+1/8*cot(d*x+c)/d/(a+I*a*tan(d*x+c))^4+7/24*cot(d*x+c)/a/d/(a+I*a*tan(d*x+c))^3,1],
[tan(d*x+c)^4*sqrt(a+I*a*tan(d*x+c)),x,6,-I*sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+8/35*I*sqrt(a+I*a*tan(d*x+c))/d-2/35*I*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d+2/7*tan(d*x+c)^3*sqrt(a+I*a*tan(d*x+c))/d+62/105*I*(a+I*a*tan(d*x+c))^(3/2)/a/d,1],
[tan(d*x+c)^3*sqrt(a+I*a*tan(d*x+c)),x,5,sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-8/5*sqrt(a+I*a*tan(d*x+c))/d+2/5*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d-2/15*(a+I*a*tan(d*x+c))^(3/2)/a/d,1],
[tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c)),x,3,I*sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-2/3*I*(a+I*a*tan(d*x+c))^(3/2)/a/d,1],
[tan(d*x+c)*sqrt(a+I*a*tan(d*x+c)),x,3,-sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+2*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(a+I*a*tan(d*x+c)),x,2,-I*sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d,1],
[cot(d*x+c)*sqrt(a+I*a*tan(d*x+c)),x,6,-2*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d,1],
[cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c)),x,8,-I*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+I*sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^3*sqrt(a+I*a*tan(d*x+c)),x,8,7/4*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d-sqrt(2)*sqrt(a)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-1/4*I*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d-1/2*cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x,7,2*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+2/7*I*a^2*tan(d*x+c)^3/d/sqrt(a+I*a*tan(d*x+c))-2/7*a^2*tan(d*x+c)^4/d/sqrt(a+I*a*tan(d*x+c))-64/35*a*sqrt(a+I*a*tan(d*x+c))/d+16/35*a*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d-76/105*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x,4,2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-2*I*a*sqrt(a+I*a*tan(d*x+c))/d-2/5*I*(a+I*a*tan(d*x+c))^(5/2)/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x,4,-2*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+2*a*sqrt(a+I*a*tan(d*x+c))/d+2/3*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[(a+I*a*tan(d*x+c))^(3/2),x,3,-2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+2*I*a*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x,6,-2*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+2*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x,8,-3*I*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-I*a^2/d/sqrt(a+I*a*tan(d*x+c))-a^2*cot(d*x+c)/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x,9,11/4*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d-2*sqrt(2)*a^(3/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-1/2*I*a^2*cot(d*x+c)/d/sqrt(a+I*a*tan(d*x+c))-1/2*a^2*cot(d*x+c)^2/d/sqrt(a+I*a*tan(d*x+c))-5/4*I*a*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x,7,4*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-368/105*a^2*sqrt(a+I*a*tan(d*x+c))/d+92/105*a^2*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d+38/63*I*a^2*tan(d*x+c)^3*sqrt(a+I*a*tan(d*x+c))/d-2/9*a^2*tan(d*x+c)^4*sqrt(a+I*a*tan(d*x+c))/d-472/315*a*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x,5,4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-4*I*a^2*sqrt(a+I*a*tan(d*x+c))/d-2/3*I*a*(a+I*a*tan(d*x+c))^(3/2)/d-2/7*I*(a+I*a*tan(d*x+c))^(7/2)/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x,5,-4*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+4*a^2*sqrt(a+I*a*tan(d*x+c))/d+2/3*a*(a+I*a*tan(d*x+c))^(3/2)/d+2/5*(a+I*a*tan(d*x+c))^(5/2)/d,1],
[(a+I*a*tan(d*x+c))^(5/2),x,4,-4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+4*I*a^2*sqrt(a+I*a*tan(d*x+c))/d+2/3*I*a*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x,7,-2*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+4*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-2*a^2*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x,7,-5*I*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d+4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-a^2*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x,8,23/4*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d-4*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d-9/4*I*a^2*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d-1/2*a^2*cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x,9,45/8*I*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/d-4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+19/8*a^2*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/d-13/12*I*a^2*cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/d-1/3*a^2*cot(d*x+c)^3*sqrt(a+I*a*tan(d*x+c))/d,1],
[(a+I*a*tan(d*x+c))^(7/2),x,5,-8*I*sqrt(2)*a^(7/2)*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/d+8*I*a^3*sqrt(a+I*a*tan(d*x+c))/d+4/3*I*a^2*(a+I*a*tan(d*x+c))^(3/2)/d+2/5*I*a*(a+I*a*tan(d*x+c))^(5/2)/d,1],
[tan(d*x+c)^5/sqrt(a+I*a*tan(d*x+c)),x,7,-arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d-tan(d*x+c)^4/d/sqrt(a+I*a*tan(d*x+c))-188/35*sqrt(a+I*a*tan(d*x+c))/a/d+47/35*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/a/d-9/7*I*tan(d*x+c)^3*sqrt(a+I*a*tan(d*x+c))/a/d+223/105*(a+I*a*tan(d*x+c))^(3/2)/a^2/d,1],
[tan(d*x+c)^4/sqrt(a+I*a*tan(d*x+c)),x,6,-I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d-tan(d*x+c)^3/d/sqrt(a+I*a*tan(d*x+c))+28/5*I*sqrt(a+I*a*tan(d*x+c))/a/d-7/5*I*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/a/d-23/15*I*(a+I*a*tan(d*x+c))^(3/2)/a^2/d,1],
[tan(d*x+c)^3/sqrt(a+I*a*tan(d*x+c)),x,5,arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d-tan(d*x+c)^2/d/sqrt(a+I*a*tan(d*x+c))+4*sqrt(a+I*a*tan(d*x+c))/a/d-5/3*(a+I*a*tan(d*x+c))^(3/2)/a^2/d,1],
[tan(d*x+c)^2/sqrt(a+I*a*tan(d*x+c)),x,4,I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d-I/d/sqrt(a+I*a*tan(d*x+c))-2*I*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[tan(d*x+c)/sqrt(a+I*a*tan(d*x+c)),x,3,-arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d-1/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(a+I*a*tan(d*x+c)),x,3,-I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d+I/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)/sqrt(a+I*a*tan(d*x+c)),x,7,-2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/sqrt(a)/d+arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d+1/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^2/sqrt(a+I*a*tan(d*x+c)),x,8,I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/sqrt(a)/d+I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d+cot(d*x+c)/d/sqrt(a+I*a*tan(d*x+c))-2*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[cot(d*x+c)^3/sqrt(a+I*a*tan(d*x+c)),x,9,11/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/sqrt(a)/d-arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/sqrt(a)/d+cot(d*x+c)^2/d/sqrt(a+I*a*tan(d*x+c))+7/4*I*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/a/d-3/2*cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x,7,-1/2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d-1/3*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^(3/2)+19/6*I*tan(d*x+c)^3/a/d/sqrt(a+I*a*tan(d*x+c))+78/5*sqrt(a+I*a*tan(d*x+c))/a^2/d-39/10*tan(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/a^2/d-151/30*(a+I*a*tan(d*x+c))^(3/2)/a^3/d,1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x,6,-1/2*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d-1/3*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^(3/2)+5/2*I*tan(d*x+c)^2/a/d/sqrt(a+I*a*tan(d*x+c))-10*I*sqrt(a+I*a*tan(d*x+c))/a^2/d+7/2*I*(a+I*a*tan(d*x+c))^(3/2)/a^3/d,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x,5,1/2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d-1/3*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(3/2)-11/6/a/d/sqrt(a+I*a*tan(d*x+c))-7/3*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x,4,1/2*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d-1/3*I/d/(a+I*a*tan(d*x+c))^(3/2)+3/2*I/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x,4,-1/2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d-1/3/d/(a+I*a*tan(d*x+c))^(3/2)+1/2/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c))^(3/2),x,4,-1/2*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d+1/3*I/d/(a+I*a*tan(d*x+c))^(3/2)+1/2*I/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x,8,-2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/a^(3/2)/d+1/2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d+1/3/d/(a+I*a*tan(d*x+c))^(3/2)+3/2/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x,9,3*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/a^(3/2)/d+1/2*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d+1/3*cot(d*x+c)/d/(a+I*a*tan(d*x+c))^(3/2)+13/6*cot(d*x+c)/a/d/sqrt(a+I*a*tan(d*x+c))-7/2*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x,10,23/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/a^(3/2)/d-1/2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(3/2)/d+1/3*cot(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(3/2)+17/6*cot(d*x+c)^2/a/d/sqrt(a+I*a*tan(d*x+c))+21/4*I*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/a^2/d-11/3*cot(d*x+c)^2*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x,7,-1/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5*tan(d*x+c)^4/d/(a+I*a*tan(d*x+c))^(5/2)+7/10*I*tan(d*x+c)^3/a/d/(a+I*a*tan(d*x+c))^(3/2)+89/20*tan(d*x+c)^2/a^2/d/sqrt(a+I*a*tan(d*x+c))-89/5*sqrt(a+I*a*tan(d*x+c))/a^3/d+361/60*(a+I*a*tan(d*x+c))^(3/2)/a^4/d,1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x,6,-1/4*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^(5/2)+17/30*I*tan(d*x+c)^2/a/d/(a+I*a*tan(d*x+c))^(3/2)+151/60*I/a^2/d/sqrt(a+I*a*tan(d*x+c))+83/30*I*sqrt(a+I*a*tan(d*x+c))/a^3/d,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x,5,1/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(5/2)-13/30/a/d/(a+I*a*tan(d*x+c))^(3/2)+31/20/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x,5,1/4*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5*I/d/(a+I*a*tan(d*x+c))^(5/2)+1/2*I/a/d/(a+I*a*tan(d*x+c))^(3/2)-1/4*I/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x,5,-1/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5/d/(a+I*a*tan(d*x+c))^(5/2)+1/6/a/d/(a+I*a*tan(d*x+c))^(3/2)+1/4/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/(a+I*a*tan(d*x+c))^(5/2),x,5,-1/4*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d+1/5*I/d/(a+I*a*tan(d*x+c))^(5/2)+1/6*I/a/d/(a+I*a*tan(d*x+c))^(3/2)+1/4*I/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x,9,-2*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/a^(5/2)/d+1/4*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d+1/5/d/(a+I*a*tan(d*x+c))^(5/2)+1/2/a/d/(a+I*a*tan(d*x+c))^(3/2)+7/4/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x,10,5*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(a))/a^(5/2)/d+1/4*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d+1/5*cot(d*x+c)/d/(a+I*a*tan(d*x+c))^(5/2)+19/30*cot(d*x+c)/a/d/(a+I*a*tan(d*x+c))^(3/2)+41/12*cot(d*x+c)/a^2/d/sqrt(a+I*a*tan(d*x+c))-21/4*cot(d*x+c)*sqrt(a+I*a*tan(d*x+c))/a^3/d,1],
[1/(a+I*a*tan(d*x+c))^(7/2),x,6,-1/8*I*arctanh(sqrt(a+I*a*tan(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(7/2)/d+1/7*I/d/(a+I*a*tan(d*x+c))^(7/2)+1/10*I/a/d/(a+I*a*tan(d*x+c))^(5/2)+1/12*I/a^2/d/(a+I*a*tan(d*x+c))^(3/2)+1/8*I/a^3/d/sqrt(a+I*a*tan(d*x+c)),1],
[(d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e)),x,5,-2*(-1)^(3/4)*a*d^(5/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f-2*I*a*d^2*sqrt(d*tan(f*x+e))/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f+2/5*I*a*(d*tan(f*x+e))^(5/2)/f,1],
[(d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e)),x,4,2*(-1)^(1/4)*a*d^(3/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+2*a*d*sqrt(d*tan(f*x+e))/f+2/3*I*a*(d*tan(f*x+e))^(3/2)/f,1],
[sqrt(d*tan(f*x+e))*(a+I*a*tan(f*x+e)),x,3,2*(-1)^(3/4)*a*sqrt(d)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+2*I*a*sqrt(d*tan(f*x+e))/f,1],
[(a+I*a*tan(f*x+e))/sqrt(d*tan(f*x+e)),x,2,-2*(-1)^(1/4)*a*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f,1],
[(a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x,3,-2*(-1)^(3/4)*a*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f-2*a/d/f/sqrt(d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x,4,2*(-1)^(1/4)*a*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f-2/3*a/d/f/(d*tan(f*x+e))^(3/2)-2*I*a/d^2/f/sqrt(d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x,5,2*(-1)^(3/4)*a*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(7/2)/f-2/5*a/d/f/(d*tan(f*x+e))^(5/2)-2/3*I*a/d^2/f/(d*tan(f*x+e))^(3/2)+2*a/d^3/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)*(a-I*a*tan(f*x+e)),x,5,2*(-1)^(3/4)*a*d^(5/2)*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+2*I*a*d^2*sqrt(d*tan(f*x+e))/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f-2/5*I*a*(d*tan(f*x+e))^(5/2)/f,1],
[(d*tan(f*x+e))^(3/2)*(a-I*a*tan(f*x+e)),x,4,2*(-1)^(1/4)*a*d^(3/2)*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+2*a*d*sqrt(d*tan(f*x+e))/f-2/3*I*a*(d*tan(f*x+e))^(3/2)/f,1],
[sqrt(d*tan(f*x+e))*(a-I*a*tan(f*x+e)),x,3,-2*(-1)^(3/4)*a*sqrt(d)*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f-2*I*a*sqrt(d*tan(f*x+e))/f,1],
[(a-I*a*tan(f*x+e))/sqrt(d*tan(f*x+e)),x,2,-2*(-1)^(1/4)*a*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f,1],
[(a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x,3,2*(-1)^(3/4)*a*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f-2*a/d/f/sqrt(d*tan(f*x+e)),1],
[(a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x,4,2*(-1)^(1/4)*a*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f-2/3*a/d/f/(d*tan(f*x+e))^(3/2)+2*I*a/d^2/f/sqrt(d*tan(f*x+e)),1],
[(a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x,5,-2*(-1)^(3/4)*a*arctanh((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(7/2)/f-2/5*a/d/f/(d*tan(f*x+e))^(5/2)+2/3*I*a/d^2/f/(d*tan(f*x+e))^(3/2)+2*a/d^3/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^2,x,6,-4*(-1)^(3/4)*a^2*d^(5/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f-4*I*a^2*d^2*sqrt(d*tan(f*x+e))/f+4/3*a^2*d*(d*tan(f*x+e))^(3/2)/f+4/5*I*a^2*(d*tan(f*x+e))^(5/2)/f-2/7*a^2*(d*tan(f*x+e))^(7/2)/d/f,1],
[(d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^2,x,5,4*(-1)^(1/4)*a^2*d^(3/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+4*a^2*d*sqrt(d*tan(f*x+e))/f+4/3*I*a^2*(d*tan(f*x+e))^(3/2)/f-2/5*a^2*(d*tan(f*x+e))^(5/2)/d/f,1],
[sqrt(d*tan(f*x+e))*(a+I*a*tan(f*x+e))^2,x,4,4*(-1)^(3/4)*a^2*sqrt(d)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+4*I*a^2*sqrt(d*tan(f*x+e))/f-2/3*a^2*(d*tan(f*x+e))^(3/2)/d/f,1],
[(a+I*a*tan(f*x+e))^2/sqrt(d*tan(f*x+e)),x,3,-4*(-1)^(1/4)*a^2*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f-2*a^2*sqrt(d*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x,3,-4*(-1)^(3/4)*a^2*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f-2*a^2/d/f/sqrt(d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x,4,4*(-1)^(1/4)*a^2*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f-2/3*a^2/d/f/(d*tan(f*x+e))^(3/2)-4*I*a^2/d^2/f/sqrt(d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(7/2),x,5,4*(-1)^(3/4)*a^2*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(7/2)/f-2/5*a^2/d/f/(d*tan(f*x+e))^(5/2)-4/3*I*a^2/d^2/f/(d*tan(f*x+e))^(3/2)+4*a^2/d^3/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^3,x,7,-8*(-1)^(3/4)*a^3*d^(5/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f-8*I*a^3*d^2*sqrt(d*tan(f*x+e))/f+8/3*a^3*d*(d*tan(f*x+e))^(3/2)/f+8/5*I*a^3*(d*tan(f*x+e))^(5/2)/f-40/63*a^3*(d*tan(f*x+e))^(7/2)/d/f-2/9*(d*tan(f*x+e))^(7/2)*(a^3+I*a^3*tan(f*x+e))/d/f,1],
[(d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^3,x,6,8*(-1)^(1/4)*a^3*d^(3/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+8*a^3*d*sqrt(d*tan(f*x+e))/f+8/3*I*a^3*(d*tan(f*x+e))^(3/2)/f-32/35*a^3*(d*tan(f*x+e))^(5/2)/d/f-2/7*(d*tan(f*x+e))^(5/2)*(a^3+I*a^3*tan(f*x+e))/d/f,1],
[sqrt(d*tan(f*x+e))*(a+I*a*tan(f*x+e))^3,x,5,8*(-1)^(3/4)*a^3*sqrt(d)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/f+8*I*a^3*sqrt(d*tan(f*x+e))/f-8/5*a^3*(d*tan(f*x+e))^(3/2)/d/f-2/5*(d*tan(f*x+e))^(3/2)*(a^3+I*a^3*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^3/sqrt(d*tan(f*x+e)),x,4,-8*(-1)^(1/4)*a^3*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f-16/3*a^3*sqrt(d*tan(f*x+e))/d/f-2/3*sqrt(d*tan(f*x+e))*(a^3+I*a^3*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x,4,-8*(-1)^(3/4)*a^3*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f-2*(a^3+I*a^3*tan(f*x+e))/d/f/sqrt(d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x,4,8*(-1)^(1/4)*a^3*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f-16/3*I*a^3/d^2/f/sqrt(d*tan(f*x+e))-2/3*(a^3+I*a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(3/2),1],
[(a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x,5,8*(-1)^(3/4)*a^3*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(7/2)/f-8/5*I*a^3/d^2/f/(d*tan(f*x+e))^(3/2)+8*a^3/d^3/f/sqrt(d*tan(f*x+e))-2/5*(a^3+I*a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x,6,-8*(-1)^(1/4)*a^3*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(9/2)/f-32/35*I*a^3/d^2/f/(d*tan(f*x+e))^(5/2)+8/3*a^3/d^3/f/(d*tan(f*x+e))^(3/2)+8*I*a^3/d^4/f/sqrt(d*tan(f*x+e))-2/7*(a^3+I*a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(7/2),1],
[(d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x,12,(5/4-7/4*I)*d^(7/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f+(-5/4+7/4*I)*d^(7/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f-(5/4+7/4*I)*d^(7/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/f+5/2*d^3*sqrt(d*tan(f*x+e))/a/f-7/6*I*d^2*(d*tan(f*x+e))^(3/2)/a/f-1/2*d*(d*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x,11,(-3/4-5/4*I)*d^(5/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f+(3/4+5/4*I)*d^(5/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f+(-3/4+5/4*I)*d^(5/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/f-5/2*I*d^2*sqrt(d*tan(f*x+e))/a/f-1/2*d*(d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x,10,(-1/4+3/4*I)*d^(3/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f+(1/4-3/4*I)*d^(3/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/f+(1/4+3/4*I)*d^(3/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/f-1/2*d*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e)),1],
[sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,3,1/2*(-1)^(3/4)*sqrt(d)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/a/f+1/2*I*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e)),1],
[1/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,10,(-3/4+1/4*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/sqrt(d)/f+(3/4-1/4*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/sqrt(d)/f+(3/4+1/4*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/sqrt(d)/f+1/2*sqrt(d*tan(f*x+e))/d/f/(a+I*a*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x,11,(5/4+3/4*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/d^(3/2)/f-(5/4+3/4*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/d^(3/2)/f+(5/4-3/4*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/d^(3/2)/f-5/2/a/d/f/sqrt(d*tan(f*x+e))+1/2/d/f/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x,12,(7/4-5/4*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/d^(5/2)/f+(-7/4+5/4*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a/d^(5/2)/f-(7/4+5/4*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a/d^(5/2)/f-7/6/a/d/f/(d*tan(f*x+e))^(3/2)+5/2*I/a/d^2/f/sqrt(d*tan(f*x+e))+1/2/d/f/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x,13,(-49/16-45/16*I)*d^(9/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(49/16+45/16*I)*d^(9/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(-49/16+45/16*I)*d^(9/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f-45/8*I*d^4*sqrt(d*tan(f*x+e))/a^2/f-49/24*d^3*(d*tan(f*x+e))^(3/2)/a^2/f+9/8*I*d^2*(d*tan(f*x+e))^(5/2)/a^2/f/(1+I*tan(f*x+e))-1/4*d*(d*tan(f*x+e))^(7/2)/f/(a+I*a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x,12,(-25/16+21/16*I)*d^(7/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(25/16-21/16*I)*d^(7/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(25/16+21/16*I)*d^(7/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f-25/8*d^3*sqrt(d*tan(f*x+e))/a^2/f+7/8*I*d^2*(d*tan(f*x+e))^(3/2)/a^2/f/(1+I*tan(f*x+e))-1/4*d*(d*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x,11,(9/16+5/16*I)*d^(5/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-(9/16+5/16*I)*d^(5/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(9/16-5/16*I)*d^(5/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f+5/8*I*d^2*sqrt(d*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))-1/4*d*(d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x,11,(1/16+3/16*I)*d^(3/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-(1/16+3/16*I)*d^(3/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(-1/16+3/16*I)*d^(3/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f+3/8*d*sqrt(d*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))-1/4*d*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^2,1],
[sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,11,(-1/16+3/16*I)*sqrt(d)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+(1/16-3/16*I)*sqrt(d)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-(1/16+3/16*I)*sqrt(d)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f+1/8*I*sqrt(d*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))+1/4*I*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^2,1],
[1/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,11,(-9/16+5/16*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/sqrt(d)/f+(9/16-5/16*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/sqrt(d)/f+(9/16+5/16*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/sqrt(d)/f+5/8*sqrt(d*tan(f*x+e))/a^2/d/f/(1+I*tan(f*x+e))+1/4*sqrt(d*tan(f*x+e))/d/f/(a+I*a*tan(f*x+e))^2,1],
[1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x,12,(25/16+21/16*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(3/2)/f-(25/16+21/16*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(3/2)/f+(25/16-21/16*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/d^(3/2)/f-25/8/a^2/d/f/sqrt(d*tan(f*x+e))+7/8/a^2/d/f/(1+I*tan(f*x+e))/sqrt(d*tan(f*x+e))+1/4/d/f/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,1],
[1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x,13,(49/16-45/16*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(5/2)/f+(-49/16+45/16*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(5/2)/f-(49/16+45/16*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/d^(5/2)/f-49/24/a^2/d/f/(d*tan(f*x+e))^(3/2)+9/8/a^2/d/f/(1+I*tan(f*x+e))/(d*tan(f*x+e))^(3/2)+45/8*I/a^2/d^2/f/sqrt(d*tan(f*x+e))+1/4/d/f/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x,13,(7/4+15/8*I)*d^(9/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f-(7/4+15/8*I)*d^(9/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f+(7/4-15/8*I)*d^(9/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/f+15/4*I*d^4*sqrt(d*tan(f*x+e))/a^3/f-1/6*d*(d*tan(f*x+e))^(7/2)/f/(a+I*a*tan(f*x+e))^3+5/12*I*d^2*(d*tan(f*x+e))^(5/2)/a/f/(a+I*a*tan(f*x+e))^2+7/6*d^3*(d*tan(f*x+e))^(3/2)/f/(a^3+I*a^3*tan(f*x+e)),1],
[(d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x,12,(5/16-7/16*I)*d^(7/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f+(-5/16+7/16*I)*d^(7/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f-(5/16+7/16*I)*d^(7/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/f-1/6*d*(d*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^3+1/3*I*d^2*(d*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^2+5/8*d^3*sqrt(d*tan(f*x+e))/f/(a^3+I*a^3*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x,15,1/8*d^(5/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f-1/8*d^(5/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f+1/8*d^(5/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/f-1/6*d*(d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^3+1/4*I*d^2*sqrt(d*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^2-1/4*I*d^2*sqrt(d*tan(f*x+e))/f/(a^3+I*a^3*tan(f*x+e)),1],
[(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x,7,1/8*(-1)^(1/4)*d^(3/2)*arctan((-1)^(3/4)*sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f-1/6*d*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^3+1/6*d*sqrt(d*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^2+1/8*d*sqrt(d*tan(f*x+e))/f/(a^3+I*a^3*tan(f*x+e)),1],
[sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,13,1/8*I*sqrt(d)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f-1/8*I*sqrt(d)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/f-1/8*I*sqrt(d)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/f+1/6*I*sqrt(d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^3+1/12*I*sqrt(d*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^2,1],
[1/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,12,(-7/16+5/16*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/sqrt(d)/f+(7/16-5/16*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/sqrt(d)/f+(7/16+5/16*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/sqrt(d)/f+1/6*sqrt(d*tan(f*x+e))/d/f/(a+I*a*tan(f*x+e))^3+1/3*sqrt(d*tan(f*x+e))/a/d/f/(a+I*a*tan(f*x+e))^2+5/8*sqrt(d*tan(f*x+e))/d/f/(a^3+I*a^3*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x,13,(15/8+7/4*I)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/d^(3/2)/f-(15/8+7/4*I)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^3/d^(3/2)/f+(15/8-7/4*I)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^3/d^(3/2)/f-15/4/a^3/d/f/sqrt(d*tan(f*x+e))+1/6/d/f/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3+5/12/a/d/f/sqrt(d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2+7/6/d/f/sqrt(d*tan(f*x+e))/(a^3+I*a^3*tan(f*x+e)),1],
[tan(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c)),x,8,7/4*(-1)^(3/4)*sqrt(a)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-1/4*I*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d+1/2*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c)),x,8,-(-1)^(1/4)*sqrt(a)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(-1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c)),x,6,-2*(-1)^(3/4)*sqrt(a)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-(1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d,1],
[sqrt(a+I*a*tan(d*x+c))/sqrt(tan(d*x+c)),x,2,(1-I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d,1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(3/2),x,3,(1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(5/2),x,5,(-1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/3*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)-2/3*I*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(7/2),x,6,(-1-I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/5*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(5/2)-2/15*I*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)+26/15*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x,10,23/8*(-1)^(3/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+1/3*I*a^2*tan(d*x+c)^(5/2)/d/sqrt(a+I*a*tan(d*x+c))-1/3*a^2*tan(d*x+c)^(7/2)/d/sqrt(a+I*a*tan(d*x+c))-9/8*I*a*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d+7/12*a*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x,9,-11/4*(-1)^(1/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(-2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+1/2*I*a^2*tan(d*x+c)^(3/2)/d/sqrt(a+I*a*tan(d*x+c))-1/2*a^2*tan(d*x+c)^(5/2)/d/sqrt(a+I*a*tan(d*x+c))+5/4*a*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*(a+I*a*tan(d*x+c))^(3/2),x,8,-3*(-1)^(3/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-(2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+I*a^2*sqrt(tan(d*x+c))/d/sqrt(a+I*a*tan(d*x+c))-a^2*tan(d*x+c)^(3/2)/d/sqrt(a+I*a*tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/sqrt(tan(d*x+c)),x,6,2*(-1)^(1/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(2-2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d,1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x,3,(2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2*a*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x,4,(-2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2*I*a*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c))-2/3*(a+I*a*tan(d*x+c))^(3/2)/d/tan(d*x+c)^(3/2),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x,7,(-2-2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/5*a^2/d/tan(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c))-2/5*I*a^2/d/tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-4/5*I*a*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)+12/5*a*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x,8,(2-2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/7*a^2/d/tan(d*x+c)^(7/2)/sqrt(a+I*a*tan(d*x+c))-2/7*I*a^2/d/tan(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c))-16/35*I*a*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(5/2)+76/105*a*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)+268/105*I*a*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x,10,363/64*(-1)^(3/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-149/64*I*a^2*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d+107/96*a^2*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d+17/24*I*a^2*tan(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c))/d-1/4*a^2*tan(d*x+c)^(7/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x,9,-45/8*(-1)^(1/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(-4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+19/8*a^2*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d+13/12*I*a^2*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d-1/3*a^2*tan(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*(a+I*a*tan(d*x+c))^(5/2),x,8,-23/4*(-1)^(3/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+9/4*I*a^2*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-1/2*a^2*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[(a+I*a*tan(d*x+c))^(5/2)/sqrt(tan(d*x+c)),x,7,5*(-1)^(1/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-a^2*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[(a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x,7,2*(-1)^(3/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x,4,(-4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-4*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c))-2/3*a*(a+I*a*tan(d*x+c))^(3/2)/d/tan(d*x+c)^(3/2),1],
[(a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x,5,(-4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d+4*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c))-2/3*I*a*(a+I*a*tan(d*x+c))^(3/2)/d/tan(d*x+c)^(3/2)-2/5*(a+I*a*tan(d*x+c))^(5/2)/d/tan(d*x+c)^(5/2),1],
[(a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x,7,(4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/7*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(7/2)-6/7*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(5/2)+32/21*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)+104/21*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x,8,(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/d-2/9*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(9/2)-38/63*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(7/2)+92/105*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(5/2)+472/315*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/tan(d*x+c)^(3/2)-1576/315*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/sqrt(a+I*a*tan(d*x+c)),x,9,11/4*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+(1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d-tan(d*x+c)^(5/2)/d/sqrt(a+I*a*tan(d*x+c))+7/4*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a/d-3/2*I*tan(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[tan(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c)),x,8,-(-1)^(3/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+(1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d-tan(d*x+c)^(3/2)/d/sqrt(a+I*a*tan(d*x+c))-2*I*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c)),x,7,-2*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+(-1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d-sqrt(tan(d*x+c))/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)),x,3,(-1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+I*sqrt(tan(d*x+c))/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)),x,4,(1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+sqrt(tan(d*x+c))/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c)),x,5,(1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+1/d/sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c))-3*sqrt(a+I*a*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c)),x,6,(-1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+1/d/tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-5/3*sqrt(a+I*a*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)+7/3*I*sqrt(a+I*a*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(7/2)/sqrt(a+I*a*tan(d*x+c)),x,7,(-1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/sqrt(a)/d+1/d/tan(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c))-7/5*sqrt(a+I*a*tan(d*x+c))/a/d/tan(d*x+c)^(5/2)+23/15*I*sqrt(a+I*a*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)+61/15*sqrt(a+I*a*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x,9,-3*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+(1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d-1/3*tan(d*x+c)^(5/2)/d/(a+I*a*tan(d*x+c))^(3/2)+13/6*I*tan(d*x+c)^(3/2)/a/d/sqrt(a+I*a*tan(d*x+c))-7/2*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x,8,2*(-1)^(3/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+(1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d-1/3*tan(d*x+c)^(3/2)/d/(a+I*a*tan(d*x+c))^(3/2)+3/2*I*sqrt(tan(d*x+c))/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x,4,(-1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+1/3*I*tan(d*x+c)^(3/2)/d/(a+I*a*tan(d*x+c))^(3/2)+1/2*sqrt(tan(d*x+c))/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x,4,(-1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+1/3*tan(d*x+c)^(3/2)/d/(a+I*a*tan(d*x+c))^(3/2)+1/2*I*sqrt(tan(d*x+c))/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x,5,(1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+1/3*sqrt(tan(d*x+c))/d/(a+I*a*tan(d*x+c))^(3/2)+7/6*sqrt(tan(d*x+c))/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x,6,(1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+1/3/d/sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2)+11/6/a/d/sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c))-25/6*sqrt(a+I*a*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x,7,(-1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(3/2)/d+1/3/d/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+5/2/a/d/tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-7/2*sqrt(a+I*a*tan(d*x+c))/a^2/d/tan(d*x+c)^(3/2)+13/2*I*sqrt(a+I*a*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x,10,5*(-1)^(3/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d-(1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d-1/5*tan(d*x+c)^(7/2)/d/(a+I*a*tan(d*x+c))^(5/2)+19/30*I*tan(d*x+c)^(5/2)/a/d/(a+I*a*tan(d*x+c))^(3/2)+41/12*tan(d*x+c)^(3/2)/a^2/d/sqrt(a+I*a*tan(d*x+c))+21/4*I*sqrt(tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^3/d,1],
[tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x,9,2*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+(1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d-1/5*tan(d*x+c)^(5/2)/d/(a+I*a*tan(d*x+c))^(5/2)+1/2*I*tan(d*x+c)^(3/2)/a/d/(a+I*a*tan(d*x+c))^(3/2)+7/4*sqrt(tan(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x,5,(1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5*I*tan(d*x+c)^(5/2)/d/(a+I*a*tan(d*x+c))^(5/2)+1/6*tan(d*x+c)^(3/2)/a/d/(a+I*a*tan(d*x+c))^(3/2)-1/4*I*sqrt(tan(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x,5,(-1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5*tan(d*x+c)^(5/2)/d/(a+I*a*tan(d*x+c))^(5/2)+1/6*I*tan(d*x+c)^(3/2)/a/d/(a+I*a*tan(d*x+c))^(3/2)+1/4*sqrt(tan(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x,6,(-1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5*I*sqrt(tan(d*x+c))/d/(a+I*a*tan(d*x+c))^(5/2)+1/10*I*sqrt(tan(d*x+c))/a/d/(a+I*a*tan(d*x+c))^(3/2)-1/20*I*sqrt(tan(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x,6,(1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5*sqrt(tan(d*x+c))/d/(a+I*a*tan(d*x+c))^(5/2)+13/30*sqrt(tan(d*x+c))/a/d/(a+I*a*tan(d*x+c))^(3/2)+67/60*sqrt(tan(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x,7,(1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5/d/sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2)+17/30/a/d/sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2)+151/60/a^2/d/sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c))-317/60*sqrt(a+I*a*tan(d*x+c))/a^3/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x,8,(-1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))/a^(5/2)/d+1/5/d/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2)+7/10/a/d/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+89/20/a^2/d/tan(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-361/60*sqrt(a+I*a*tan(d*x+c))/a^3/d/tan(d*x+c)^(3/2)+707/60*I*sqrt(a+I*a*tan(d*x+c))/a^3/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c)),x,25,7/12*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d-7/12*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d-5/2*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d-7/6*arctan(tan(d*x+c)^(1/3))/a/d-5/6*I*ln(1+tan(d*x+c)^(2/3))/a/d+7/8*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-7/8*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d+5/12*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d+7/2*tan(d*x+c)^(1/3)/a/d-5/4*I*tan(d*x+c)^(4/3)/a/d-1/2*tan(d*x+c)^(7/3)/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c)),x,24,-5/12*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d+5/12*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d-2*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d+5/6*arctan(tan(d*x+c)^(1/3))/a/d+2/3*I*ln(1+tan(d*x+c)^(2/3))/a/d+5/8*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-5/8*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-1/3*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d-2*I*tan(d*x+c)^(2/3)/a/d-1/2*tan(d*x+c)^(5/3)/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),x,23,-1/12*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d+1/12*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d+I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d+1/6*arctan(tan(d*x+c)^(1/3))/a/d+1/3*I*ln(1+tan(d*x+c)^(2/3))/a/d-1/8*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d+1/8*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-1/6*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d-1/2*tan(d*x+c)^(1/3)/d/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),x,23,-1/12*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d+1/12*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d+1/2*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d+1/6*arctan(tan(d*x+c)^(1/3))/a/d-1/6*I*ln(1+tan(d*x+c)^(2/3))/a/d+1/8*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-1/8*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d+1/12*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d+1/2*I*tan(d*x+c)^(2/3)/d/(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c)),x,23,1/12*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d-1/12*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d-arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d-1/6*I*arctan(tan(d*x+c)^(1/3))/a/d+1/3*ln(1+tan(d*x+c)^(2/3))/a/d-1/8*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d+1/8*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-1/6*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d+1/2*tan(d*x+c)^(2/3)/d/(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c)),x,24,5/12*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d-5/12*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d+2*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d-5/6*I*arctan(tan(d*x+c)^(1/3))/a/d+2/3*ln(1+tan(d*x+c)^(2/3))/a/d+5/8*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-5/8*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-1/3*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d-2/a/d/tan(d*x+c)^(2/3)+1/2/d/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c)),x,25,-7/12*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a/d+7/12*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a/d+5/2*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a/d+7/6*I*arctan(tan(d*x+c)^(1/3))/a/d-5/6*ln(1+tan(d*x+c)^(2/3))/a/d+7/8*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d-7/8*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a/d+5/12*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a/d-5/4/a/d/tan(d*x+c)^(4/3)+7/2*I/a/d/tan(d*x+c)^(1/3)+1/2/d/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(14/3)/(a+I*a*tan(d*x+c))^2,x,26,-121/72*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d+121/72*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d-14/3*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d+121/36*arctan(tan(d*x+c)^(1/3))/a^2/d+14/9*I*ln(1+tan(d*x+c)^(2/3))/a^2/d+121/48*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-121/48*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-7/9*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d-14/3*I*tan(d*x+c)^(2/3)/a^2/d-121/60*tan(d*x+c)^(5/3)/a^2/d+7/6*I*tan(d*x+c)^(8/3)/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^(11/3)/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c))^2,x,25,-49/72*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d+49/72*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+5/3*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d+49/36*arctan(tan(d*x+c)^(1/3))/a^2/d+5/9*I*ln(1+tan(d*x+c)^(2/3))/a^2/d-49/48*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+49/48*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-5/18*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d-49/12*tan(d*x+c)^(1/3)/a^2/d+5/6*I*tan(d*x+c)^(4/3)/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^(7/3)/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c))^2,x,24,25/72*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d-25/72*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+2/3*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d-25/36*arctan(tan(d*x+c)^(1/3))/a^2/d-2/9*I*ln(1+tan(d*x+c)^(2/3))/a^2/d-25/48*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+25/48*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+1/9*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d+2/3*I*tan(d*x+c)^(2/3)/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^(5/3)/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,x,24,1/72*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d-1/72*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+1/3*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d-1/36*arctan(tan(d*x+c)^(1/3))/a^2/d+1/9*I*ln(1+tan(d*x+c)^(2/3))/a^2/d+1/48*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-1/48*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-1/18*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d+1/3*tan(d*x+c)^(1/3)/a^2/d/(1+I*tan(d*x+c))-1/4*tan(d*x+c)^(1/3)/d/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,x,24,-1/72*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d+1/72*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+1/3*I*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d+1/36*arctan(tan(d*x+c)^(1/3))/a^2/d-1/9*I*ln(1+tan(d*x+c)^(2/3))/a^2/d+1/48*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-1/48*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+1/18*I*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d+1/3*I*tan(d*x+c)^(2/3)/a^2/d/(1+I*tan(d*x+c))+1/4*tan(d*x+c)^(5/3)/d/(a+I*a*tan(d*x+c))^2,1],
[1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^2,x,24,7/72*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d-7/72*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d-2/3*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d-7/36*I*arctan(tan(d*x+c)^(1/3))/a^2/d+2/9*ln(1+tan(d*x+c)^(2/3))/a^2/d-7/48*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+7/48*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-1/9*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d+7/12*tan(d*x+c)^(2/3)/a^2/d/(1+I*tan(d*x+c))+1/4*tan(d*x+c)^(2/3)/d/(a+I*a*tan(d*x+c))^2,1],
[1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c))^2,x,25,55/72*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d-55/72*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+8/3*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d-55/36*I*arctan(tan(d*x+c)^(1/3))/a^2/d+8/9*ln(1+tan(d*x+c)^(2/3))/a^2/d+55/48*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-55/48*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-4/9*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d-8/3/a^2/d/tan(d*x+c)^(2/3)+11/12/a^2/d/(1+I*tan(d*x+c))/tan(d*x+c)^(2/3)+1/4/d/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,1],
[1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c))^2,x,26,-91/72*I*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/a^2/d+91/72*I*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/a^2/d+25/6*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/sqrt(3)/a^2/d+91/36*I*arctan(tan(d*x+c)^(1/3))/a^2/d-25/18*ln(1+tan(d*x+c)^(2/3))/a^2/d+91/48*I*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d-91/48*I*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/sqrt(3)/a^2/d+25/36*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/a^2/d-25/12/a^2/d/tan(d*x+c)^(4/3)+13/12/a^2/d/(1+I*tan(d*x+c))/tan(d*x+c)^(4/3)+91/12*I/a^2/d/tan(d*x+c)^(1/3)+1/4/d/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,1],
[tan(d*x+c)^(4/3)*sqrt(a+I*a*tan(d*x+c)),x,3,3/7*a*AppellF1(7/3,1/2,1,10/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(7/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)*sqrt(a+I*a*tan(d*x+c)),x,3,3/5*a*AppellF1(5/3,1/2,1,8/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(5/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(1/3)*sqrt(a+I*a*tan(d*x+c)),x,3,3/4*a*AppellF1(4/3,1/2,1,7/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(4/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(1/3),x,3,3/2*a*AppellF1(2/3,1/2,1,5/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(2/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(2/3),x,3,3*a*AppellF1(1/3,1/2,1,4/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(1/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[sqrt(a+I*a*tan(d*x+c))/tan(d*x+c)^(4/3),x,3,-3*a*AppellF1(-1/3,1/2,1,2/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))/d/tan(d*x+c)^(1/3)/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),x,3,3/7*a*AppellF1(7/3,-1/2,1,10/3,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(7/3)*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),x,3,3/5*a*AppellF1(5/3,-1/2,1,8/3,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(5/3)*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c)),1],
[tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),x,3,3/4*a*AppellF1(4/3,-1/2,1,7/3,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(4/3)*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),x,3,3/2*a*AppellF1(2/3,-1/2,1,5/3,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(2/3)*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),x,3,3*a*AppellF1(1/3,-1/2,1,4/3,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(1/3)*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),x,3,-3*a*AppellF1(-1/3,-1/2,1,2/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d/sqrt(1+I*tan(d*x+c))/tan(d*x+c)^(1/3),1],
[tan(d*x+c)^(4/3)/sqrt(a+I*a*tan(d*x+c)),x,3,3/7*AppellF1(7/3,3/2,1,10/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(7/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)/sqrt(a+I*a*tan(d*x+c)),x,3,3/5*AppellF1(5/3,3/2,1,8/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(5/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(1/3)/sqrt(a+I*a*tan(d*x+c)),x,3,3/4*AppellF1(4/3,3/2,1,7/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(4/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(1/3)/sqrt(a+I*a*tan(d*x+c)),x,3,3/2*AppellF1(2/3,3/2,1,5/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(2/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(2/3)/sqrt(a+I*a*tan(d*x+c)),x,3,3*AppellF1(1/3,3/2,1,4/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(1/3)/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(4/3)/sqrt(a+I*a*tan(d*x+c)),x,3,-3*AppellF1(-1/3,3/2,1,2/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))/d/tan(d*x+c)^(1/3)/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,3/7*AppellF1(7/3,5/2,1,10/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(7/3)/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,3/5*AppellF1(5/3,5/2,1,8/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(5/3)/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,3/4*AppellF1(4/3,5/2,1,7/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(4/3)/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,3/2*AppellF1(2/3,5/2,1,5/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(2/3)/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,3*AppellF1(1/3,5/2,1,4/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))*tan(d*x+c)^(1/3)/a/d/sqrt(a+I*a*tan(d*x+c)),1],
[1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x,3,-3*AppellF1(-1/3,5/2,1,2/3,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(1+I*tan(d*x+c))/a/d/tan(d*x+c)^(1/3)/sqrt(a+I*a*tan(d*x+c)),1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x,10,-1/4*I*a^(1/3)*x*2^(1/3)+1/2*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d-1/4*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d-3/4*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-18/7*(a+I*a*tan(d*x+c))^(1/3)/d+3/7*tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3)/d-3/28*(a+I*a*tan(d*x+c))^(4/3)/a/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x,8,1/4*a^(1/3)*x*2^(1/3)+1/2*I*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d-1/4*I*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d-3/4*I*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-3/4*I*(a+I*a*tan(d*x+c))^(4/3)/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x,8,1/4*I*a^(1/3)*x*2^(1/3)-1/2*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d+1/4*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d+3/4*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d+3*(a+I*a*tan(d*x+c))^(1/3)/d,1],
[(a+I*a*tan(d*x+c))^(1/3),x,7,-1/4*a^(1/3)*x*2^(1/3)-1/2*I*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d+1/4*I*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d+3/4*I*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x,15,-1/4*I*a^(1/3)*x*2^(1/3)-sqrt(3)*a^(1/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+1/2*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d-1/4*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d-1/2*a^(1/3)*ln(tan(d*x+c))/d+3/2*a^(1/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d-3/4*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x,16,1/4*a^(1/3)*x*2^(1/3)-I*a^(1/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/d+1/2*I*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d-1/4*I*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d-1/6*I*a^(1/3)*ln(tan(d*x+c))/d+1/2*I*a^(1/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d-3/4*I*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3)/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x,17,1/4*I*a^(1/3)*x*2^(1/3)+8/3*a^(1/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/d-1/2*sqrt(3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/d+1/4*a^(1/3)*ln(cos(d*x+c))*2^(1/3)/d+4/9*a^(1/3)*ln(tan(d*x+c))/d-4/3*a^(1/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d+3/4*a^(1/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-1/6*I*cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3)/d-1/2*cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3)/d,1],
[(a+I*a*tan(d*x+c))^(2/3),x,8,-1/4*a^(2/3)*x*2^(2/3)+1/2*I*sqrt(3)*a^(2/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/d+1/4*I*a^(2/3)*ln(cos(d*x+c))*2^(2/3)/d+3/4*I*a^(2/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/d,1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x,11,-1/2*I*a^(4/3)*x*2^(1/3)+2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d-1/2*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d-3/2*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-3*a*(a+I*a*tan(d*x+c))^(1/3)/d-9/20*(a+I*a*tan(d*x+c))^(4/3)/d+3/10*tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3)/d-6/35*(a+I*a*tan(d*x+c))^(7/3)/a/d,1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x,9,1/2*a^(4/3)*x*2^(1/3)+I*2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d-1/2*I*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d-3/2*I*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-3*I*a*(a+I*a*tan(d*x+c))^(1/3)/d-3/7*I*(a+I*a*tan(d*x+c))^(7/3)/a/d,1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x,9,1/2*I*a^(4/3)*x*2^(1/3)-2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+1/2*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d+3/2*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d+3*a*(a+I*a*tan(d*x+c))^(1/3)/d+3/4*(a+I*a*tan(d*x+c))^(4/3)/d,1],
[(a+I*a*tan(d*x+c))^(4/3),x,8,-1/2*a^(4/3)*x*2^(1/3)-I*2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+1/2*I*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d+3/2*I*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d+3*I*a*(a+I*a*tan(d*x+c))^(1/3)/d,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x,17,-1/2*I*a^(4/3)*x*2^(1/3)-sqrt(3)*a^(4/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d-1/2*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d-1/2*a^(4/3)*ln(tan(d*x+c))/d+3/2*a^(4/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d-3/2*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x,17,1/2*a^(4/3)*x*2^(1/3)-4*I*a^(4/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/d+I*2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d-1/2*I*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d-2/3*I*a^(4/3)*ln(tan(d*x+c))/d+2*I*a^(4/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d-3/2*I*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d+I*a*(a+I*a*tan(d*x+c))^(1/3)/d-cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3)/d,1],
[cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x,17,1/2*I*a^(4/3)*x*2^(1/3)+11/3*a^(4/3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/d-2^(1/3)*sqrt(3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+1/2*a^(4/3)*ln(cos(d*x+c))*2^(1/3)/d+11/18*a^(4/3)*ln(tan(d*x+c))/d-11/6*a^(4/3)*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/d+3/2*a^(4/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/d-2/3*I*a*cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3)/d-1/2*cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3)/d,1],
[(a+I*a*tan(d*x+c))^(5/3),x,9,-1/2*a^(5/3)*x*2^(2/3)+I*2^(2/3)*sqrt(3)*a^(5/3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/d+1/2*I*a^(5/3)*ln(cos(d*x+c))*2^(2/3)/d+3/2*I*a^(5/3)*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/d+3/2*I*a*(a+I*a*tan(d*x+c))^(2/3)/d,1],
[tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x,3,3/2*I*AppellF1(-1/3,-m,1,2/3,1+I*tan(d*x+c),1/2+1/2*I*tan(d*x+c))*tan(d*x+c)^m/d/((-I*tan(d*x+c))^m)/(a+I*a*tan(d*x+c))^(1/3),1],
[sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/3),x,4,3/2*I*AppellF1(-1/3,-1/2,1,2/3,1+I*tan(d*x+c),1/2+1/2*I*tan(d*x+c))*sqrt(tan(d*x+c))/d/sqrt(-I*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/3),1],
[tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x,3,3/8*I*AppellF1(-4/3,-m,1,-1/3,1+I*tan(d*x+c),1/2+1/2*I*tan(d*x+c))*tan(d*x+c)^m/d/((-I*tan(d*x+c))^m)/(a+I*a*tan(d*x+c))^(4/3),1],
[sqrt(tan(d*x+c))/(a+I*a*tan(d*x+c))^(4/3),x,4,3/8*I*AppellF1(-4/3,-1/2,1,-1/3,1+I*tan(d*x+c),1/2+1/2*I*tan(d*x+c))*sqrt(tan(d*x+c))/d/sqrt(-I*tan(d*x+c))/(a+I*a*tan(d*x+c))^(4/3),1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/3),x,12,-1/8*x*2^(2/3)/a^(1/3)+1/4*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d+1/8*I*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d+3/8*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d-15/8*I*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(1/3)+3/8*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^(1/3)+45/8*I*(a+I*a*tan(d*x+c))^(2/3)/a/d-39/20*I*(a+I*a*tan(d*x+c))^(5/3)/a^2/d,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/3),x,11,-1/8*I*x*2^(2/3)/a^(1/3)-1/4*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d-1/8*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d-3/8*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d+21/10/d/(a+I*a*tan(d*x+c))^(1/3)+3/5*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(1/3)+3/10*(a+I*a*tan(d*x+c))^(2/3)/a/d,1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x,10,1/8*x*2^(2/3)/a^(1/3)-1/4*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d-1/8*I*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d-3/8*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d-3/2*I/d/(a+I*a*tan(d*x+c))^(1/3)-3/2*I*(a+I*a*tan(d*x+c))^(2/3)/a/d,1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x,9,1/8*I*x*2^(2/3)/a^(1/3)+1/4*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d+1/8*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d+3/8*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d-3/2/d/(a+I*a*tan(d*x+c))^(1/3),1],
[1/(a+I*a*tan(d*x+c))^(1/3),x,9,-1/8*x*2^(2/3)/a^(1/3)+1/4*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d+1/8*I*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d+3/8*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d+3/2*I/d/(a+I*a*tan(d*x+c))^(1/3),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x,19,-1/8*I*x*2^(2/3)/a^(1/3)+sqrt(3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/a^(1/3)/d-1/4*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d-1/8*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d-1/2*ln(tan(d*x+c))/a^(1/3)/d+3/2*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/a^(1/3)/d-3/8*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d+3/2/d/(a+I*a*tan(d*x+c))^(1/3),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x,19,1/8*x*2^(2/3)/a^(1/3)-I*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/a^(1/3)/d-1/4*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(1/3)/d-1/8*I*ln(cos(d*x+c))*2^(2/3)/a^(1/3)/d+1/6*I*ln(tan(d*x+c))/a^(1/3)/d-1/2*I*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/a^(1/3)/d-3/8*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(1/3)/d-5/2*I/d/(a+I*a*tan(d*x+c))^(1/3)-cot(d*x+c)/d/(a+I*a*tan(d*x+c))^(1/3),1],
[1/(a+I*a*tan(d*x+c))^(2/3),x,8,-1/8*x*2^(1/3)/a^(2/3)-1/4*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/a^(2/3)/d+1/8*I*ln(cos(d*x+c))*2^(1/3)/a^(2/3)/d+3/8*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/a^(2/3)/d+3/4*I/d/(a+I*a*tan(d*x+c))^(2/3),1],
[tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(4/3),x,12,-1/16*x*2^(2/3)/a^(4/3)+1/8*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d+1/16*I*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d+3/16*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d-39/40*I*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(4/3)+3/5*tan(d*x+c)^3/d/(a+I*a*tan(d*x+c))^(4/3)-51/10*I/a/d/(a+I*a*tan(d*x+c))^(1/3)-87/40*I*(a+I*a*tan(d*x+c))^(2/3)/a^2/d,1],
[tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(4/3),x,11,-1/16*I*x*2^(2/3)/a^(4/3)-1/8*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d-1/16*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d-3/16*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d+15/8/d/(a+I*a*tan(d*x+c))^(4/3)+3/2*tan(d*x+c)^2/d/(a+I*a*tan(d*x+c))^(4/3)-27/4/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x,10,1/16*x*2^(2/3)/a^(4/3)-1/8*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d-1/16*I*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d-3/16*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d-3/8*I/d/(a+I*a*tan(d*x+c))^(4/3)+9/4*I/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[tan(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x,10,1/16*I*x*2^(2/3)/a^(4/3)+1/8*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d+1/16*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d+3/16*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d-3/8/d/(a+I*a*tan(d*x+c))^(4/3)+3/4/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[1/(a+I*a*tan(d*x+c))^(4/3),x,10,-1/16*x*2^(2/3)/a^(4/3)+1/8*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d+1/16*I*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d+3/16*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d+3/8*I/d/(a+I*a*tan(d*x+c))^(4/3)+3/4*I/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x,21,-1/16*I*x*2^(2/3)/a^(4/3)+sqrt(3)*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/a^(4/3)/d-1/8*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d-1/16*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d-1/2*ln(tan(d*x+c))/a^(4/3)/d+3/2*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/a^(4/3)/d-3/16*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d+3/8/d/(a+I*a*tan(d*x+c))^(4/3)+9/4/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x,20,1/16*x*2^(2/3)/a^(4/3)-4*I*arctan((a^(1/3)+2*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/a^(4/3)/d-1/8*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(2/3)/a^(4/3)/d-1/16*I*ln(cos(d*x+c))*2^(2/3)/a^(4/3)/d+2/3*I*ln(tan(d*x+c))/a^(4/3)/d-2*I*ln(a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))/a^(4/3)/d-3/16*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(2/3)/a^(4/3)/d-11/8*I/d/(a+I*a*tan(d*x+c))^(4/3)-cot(d*x+c)/d/(a+I*a*tan(d*x+c))^(4/3)-19/4*I/a/d/(a+I*a*tan(d*x+c))^(1/3),1],
[1/(a+I*a*tan(d*x+c))^(5/3),x,9,-1/16*x*2^(1/3)/a^(5/3)-1/8*I*sqrt(3)*arctan((a^(1/3)+2^(2/3)*(a+I*a*tan(d*x+c))^(1/3))/sqrt(3)/a^(1/3))*2^(1/3)/a^(5/3)/d+1/16*I*ln(cos(d*x+c))*2^(1/3)/a^(5/3)/d+3/16*I*ln(2^(1/3)*a^(1/3)-(a+I*a*tan(d*x+c))^(1/3))*2^(1/3)/a^(5/3)/d+3/10*I/d/(a+I*a*tan(d*x+c))^(5/3)+3/8*I/a/d/(a+I*a*tan(d*x+c))^(2/3),1],
[(e*tan(d*x+c))^m*(a+I*a*tan(d*x+c)),x,2,a*hypergeom([1, 1+m],[2+m],I*tan(d*x+c))*(e*tan(d*x+c))^(1+m)/d/e/(1+m),1],
[(e*tan(d*x+c))^m*(a-I*a*tan(d*x+c)),x,2,a*hypergeom([1, 1+m],[2+m],-I*tan(d*x+c))*(e*tan(d*x+c))^(1+m)/d/e/(1+m),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^4,x,6,-2*a^4*(2*n^2+11*n+16)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)/(2+n)/(3+n)+8*a^4*hypergeom([1, 1+n],[2+n],I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)/d/f/(1+n)-(d*tan(f*x+e))^(1+n)*(a^2+I*a^2*tan(f*x+e))^2/d/f/(3+n)-2*(4+n)*(d*tan(f*x+e))^(1+n)*(a^4+I*a^4*tan(f*x+e))/d/f/(2+n)/(3+n),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x,5,-a^3*(5+2*n)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)/(2+n)+4*a^3*hypergeom([1, 1+n],[2+n],I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)/d/f/(1+n)-(d*tan(f*x+e))^(1+n)*(a^3+I*a^3*tan(f*x+e))/d/f/(2+n),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x,4,-a^2*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+2*a^2*hypergeom([1, 1+n],[2+n],I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)/d/f/(1+n),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e)),x,2,a*hypergeom([1, 1+n],[2+n],I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)/d/f/(1+n),1],
[(d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x,6,1/2*(1-n)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/a/d/f/(1+n)+1/2*I*n*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/a/d^2/f/(2+n)+1/2*(d*tan(f*x+e))^(1+n)/d/f/(a+I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x,7,1/4*(1-n)^2*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/a^2/d/f/(1+n)+1/4*(2-n)*(d*tan(f*x+e))^(1+n)/a^2/d/f/(1+I*tan(f*x+e))+1/4*I*(2-n)*n*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/a^2/d^2/f/(2+n)+1/4*(d*tan(f*x+e))^(1+n)/d/f/(a+I*a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x,8,1/24*(1-2*n)*(1-n)*(3-n)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/a^3/d/f/(1+n)+1/24*I*(5-2*n)*(2-n)*n*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/a^3/d^2/f/(2+n)+1/6*(d*tan(f*x+e))^(1+n)/d/f/(a+I*a*tan(f*x+e))^3+1/24*(7-2*n)*(d*tan(f*x+e))^(1+n)/a/d/f/(a+I*a*tan(f*x+e))^2+1/24*(5-2*n)*(2-n)*(d*tan(f*x+e))^(1+n)/d/f/(a^3+I*a^3*tan(f*x+e)),1],
[(d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x,9,1/48*(1-n)*(3-n)*(n^2-4*n+1)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/a^4/d/f/(1+n)+1/48*(n^2-7*n+13)*(d*tan(f*x+e))^(1+n)/a^4/d/f/(1+I*tan(f*x+e))^2+1/48*(2-n)^2*(4-n)*(d*tan(f*x+e))^(1+n)/a^4/d/f/(1+I*tan(f*x+e))+1/48*I*(2-n)^2*(4-n)*n*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/a^4/d^2/f/(2+n)+1/8*(d*tan(f*x+e))^(1+n)/d/f/(a+I*a*tan(f*x+e))^4+1/24*(5-n)*(d*tan(f*x+e))^(1+n)/a/d/f/(a+I*a*tan(f*x+e))^3,1],
[(d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x,2,a*hypergeom([1, 1+n],[2+n],-I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)/d/f/(1+n),1],
[(d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x,6,1/2*(1-n)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/a/d/f/(1+n)-1/2*I*n*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/a/d^2/f/(2+n)+1/2*(d*tan(f*x+e))^(1+n)/d/f/(a-I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2),x,3,-1/3*I*AppellF1(3/2,-n,1,5/2,1+I*tan(f*x+e),1/2+1/2*I*tan(f*x+e))*(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2)/f/((-I*tan(f*x+e))^n),1],
[(d*tan(f*x+e))^n*sqrt(a+I*a*tan(f*x+e)),x,3,-I*AppellF1(1/2,-n,1,3/2,1+I*tan(f*x+e),1/2+1/2*I*tan(f*x+e))*(d*tan(f*x+e))^n*sqrt(a+I*a*tan(f*x+e))/f/((-I*tan(f*x+e))^n),1],
[(d*tan(f*x+e))^n/sqrt(a+I*a*tan(f*x+e)),x,3,I*AppellF1(-1/2,-n,1,1/2,1+I*tan(f*x+e),1/2+1/2*I*tan(f*x+e))*(d*tan(f*x+e))^n/f/((-I*tan(f*x+e))^n)/sqrt(a+I*a*tan(f*x+e)),1],
[(d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x,3,1/3*I*AppellF1(-3/2,-n,1,-1/2,1+I*tan(f*x+e),1/2+1/2*I*tan(f*x+e))*(d*tan(f*x+e))^n/f/((-I*tan(f*x+e))^n)/(a+I*a*tan(f*x+e))^(3/2),1],
[(d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x,3,AppellF1(1+n,1-m,1,2+n,-I*tan(f*x+e),I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)*(a+I*a*tan(f*x+e))^m/d/f/(1+n)/((1+I*tan(f*x+e))^m),1],
[tan(d*x+c)^4*(a+I*a*tan(d*x+c))^m,x,6,2*I*(a+I*a*tan(d*x+c))^m/d/(m^2+5*m+6)-1/2*I*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m-I*m*tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m/d/(m^2+5*m+6)+tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m/d/(3+m)+I*(m^2+3*m+6)*(a+I*a*tan(d*x+c))^(1+m)/a/d/(1+m)/(2+m)/(3+m),1],
[tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m,x,5,-2*(a+I*a*tan(d*x+c))^m/d/m/(2+m)+1/2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m+tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m/d/(2+m)-m*(a+I*a*tan(d*x+c))^(1+m)/a/d/(m^2+3*m+2),1],
[tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x,3,1/2*I*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m-I*(a+I*a*tan(d*x+c))^(1+m)/a/d/(1+m),1],
[tan(d*x+c)*(a+I*a*tan(d*x+c))^m,x,3,(a+I*a*tan(d*x+c))^m/d/m-1/2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m,1],
[(a+I*a*tan(d*x+c))^m,x,2,-1/2*I*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m,1],
[cot(d*x+c)*(a+I*a*tan(d*x+c))^m,x,5,1/2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m-hypergeom([1, m],[1+m],1+I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m,1],
[cot(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x,6,-cot(d*x+c)*(a+I*a*tan(d*x+c))^m/d+1/2*I*hypergeom([1, m],[1+m],1/2+1/2*I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/m-I*hypergeom([1, m],[1+m],1+I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d,1],
[tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m,x,3,2/5*AppellF1(5/2,1-m,1,7/2,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^m/d/((1+I*tan(d*x+c))^m),1],
[sqrt(tan(d*x+c))*(a+I*a*tan(d*x+c))^m,x,3,2/3*AppellF1(3/2,1-m,1,5/2,-I*tan(d*x+c),I*tan(d*x+c))*tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m/d/((1+I*tan(d*x+c))^m),1],
[(a+I*a*tan(d*x+c))^m/sqrt(tan(d*x+c)),x,3,2*AppellF1(1/2,1-m,1,3/2,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/((1+I*tan(d*x+c))^m),1],
[(a+I*a*tan(d*x+c))^m/tan(d*x+c)^(3/2),x,3,-2*AppellF1(-1/2,1-m,1,1/2,-I*tan(d*x+c),I*tan(d*x+c))*(a+I*a*tan(d*x+c))^m/d/((1+I*tan(d*x+c))^m)/sqrt(tan(d*x+c)),1],
[(d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e)),x,5,sqrt(2)*a*d^(5/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f-2*a*d^2*sqrt(d*tan(f*x+e))/f+2/3*a*d*(d*tan(f*x+e))^(3/2)/f+2/5*a*(d*tan(f*x+e))^(5/2)/f,1],
[(d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e)),x,4,sqrt(2)*a*d^(3/2)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f+2*a*d*sqrt(d*tan(f*x+e))/f+2/3*a*(d*tan(f*x+e))^(3/2)/f,1],
[sqrt(d*tan(f*x+e))*(a+a*tan(f*x+e)),x,3,-sqrt(2)*a*sqrt(d)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f+2*a*sqrt(d*tan(f*x+e))/f,1],
[(a+a*tan(f*x+e))/sqrt(d*tan(f*x+e)),x,2,-sqrt(2)*a*arctan(sqrt(d)*(1-tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(d)/f,1],
[(a+a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x,3,sqrt(2)*a*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(3/2)/f-2*a/d/f/sqrt(d*tan(f*x+e)),1],
[(a+a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x,4,sqrt(2)*a*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(5/2)/f-2/3*a/d/f/(d*tan(f*x+e))^(3/2)-2*a/d^2/f/sqrt(d*tan(f*x+e)),1],
[(a+a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x,5,-sqrt(2)*a*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(7/2)/f-2/5*a/d/f/(d*tan(f*x+e))^(5/2)-2/3*a/d^2/f/(d*tan(f*x+e))^(3/2)+2*a/d^3/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^2,x,15,-sqrt(2)*a^2*d^(5/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f+sqrt(2)*a^2*d^(5/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f+sqrt(2)*a^2*d^(5/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/f-4*a^2*d^2*sqrt(d*tan(f*x+e))/f+4/5*a^2*(d*tan(f*x+e))^(5/2)/f+2/7*a^2*(d*tan(f*x+e))^(7/2)/d/f,1],
[(d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^2,x,14,sqrt(2)*a^2*d^(3/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f-sqrt(2)*a^2*d^(3/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f+sqrt(2)*a^2*d^(3/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/f+4/3*a^2*(d*tan(f*x+e))^(3/2)/f+2/5*a^2*(d*tan(f*x+e))^(5/2)/d/f,1],
[sqrt(d*tan(f*x+e))*(a+a*tan(f*x+e))^2,x,14,sqrt(2)*a^2*sqrt(d)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f-sqrt(2)*a^2*sqrt(d)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/f-sqrt(2)*a^2*sqrt(d)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/f+4*a^2*sqrt(d*tan(f*x+e))/f+2/3*a^2*(d*tan(f*x+e))^(3/2)/d/f,1],
[(a+a*tan(f*x+e))^2/sqrt(d*tan(f*x+e)),x,13,-sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f+sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(d)/f-sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(d)/f+2*a^2*sqrt(d*tan(f*x+e))/d/f,1],
[(a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x,12,-sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f+sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(3/2)/f+sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/d^(3/2)/f-2*a^2/d/f/sqrt(d*tan(f*x+e)),1],
[(a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x,13,sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f-sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/d^(5/2)/f+sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/d^(5/2)/f-2/3*a^2/d/f/(d*tan(f*x+e))^(3/2)-4*a^2/d^2/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(7/2)*(a+a*tan(f*x+e))^3,x,8,-2*sqrt(2)*a^3*d^(7/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f+4*a^3*d^3*sqrt(d*tan(f*x+e))/f-4/3*a^3*d^2*(d*tan(f*x+e))^(3/2)/f-4/5*a^3*d*(d*tan(f*x+e))^(5/2)/f+4/7*a^3*(d*tan(f*x+e))^(7/2)/f+16/33*a^3*(d*tan(f*x+e))^(9/2)/d/f+2/11*(d*tan(f*x+e))^(9/2)*(a^3+a^3*tan(f*x+e))/d/f,1],
[(d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^3,x,7,-2*sqrt(2)*a^3*d^(5/2)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f-4*a^3*d^2*sqrt(d*tan(f*x+e))/f-4/3*a^3*d*(d*tan(f*x+e))^(3/2)/f+4/5*a^3*(d*tan(f*x+e))^(5/2)/f+40/63*a^3*(d*tan(f*x+e))^(7/2)/d/f+2/9*(d*tan(f*x+e))^(7/2)*(a^3+a^3*tan(f*x+e))/d/f,1],
[(d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^3,x,6,2*sqrt(2)*a^3*d^(3/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f-4*a^3*d*sqrt(d*tan(f*x+e))/f+4/3*a^3*(d*tan(f*x+e))^(3/2)/f+32/35*a^3*(d*tan(f*x+e))^(5/2)/d/f+2/7*(d*tan(f*x+e))^(5/2)*(a^3+a^3*tan(f*x+e))/d/f,1],
[sqrt(d*tan(f*x+e))*(a+a*tan(f*x+e))^3,x,5,2*sqrt(2)*a^3*sqrt(d)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/f+4*a^3*sqrt(d*tan(f*x+e))/f+8/5*a^3*(d*tan(f*x+e))^(3/2)/d/f+2/5*(d*tan(f*x+e))^(3/2)*(a^3+a^3*tan(f*x+e))/d/f,1],
[(a+a*tan(f*x+e))^3/sqrt(d*tan(f*x+e)),x,4,-2*sqrt(2)*a^3*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(d)/f+16/3*a^3*sqrt(d*tan(f*x+e))/d/f+2/3*sqrt(d*tan(f*x+e))*(a^3+a^3*tan(f*x+e))/d/f,1],
[(a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x,4,-2*sqrt(2)*a^3*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(3/2)/f+4*a^3*sqrt(d*tan(f*x+e))/d^2/f-2*(a^3+a^3*tan(f*x+e))/d/f/sqrt(d*tan(f*x+e)),1],
[(a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x,4,2*sqrt(2)*a^3*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(5/2)/f-16/3*a^3/d^2/f/sqrt(d*tan(f*x+e))-2/3*(a^3+a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(3/2),1],
[(a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x,5,2*sqrt(2)*a^3*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(7/2)/f-8/5*a^3/d^2/f/(d*tan(f*x+e))^(3/2)-4*a^3/d^3/f/sqrt(d*tan(f*x+e))-2/5*(a^3+a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(5/2),1],
[(a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x,6,-2*sqrt(2)*a^3*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/d^(9/2)/f-32/35*a^3/d^2/f/(d*tan(f*x+e))^(5/2)-4/3*a^3/d^3/f/(d*tan(f*x+e))^(3/2)+4*a^3/d^4/f/sqrt(d*tan(f*x+e))-2/7*(a^3+a^3*tan(f*x+e))/d/f/(d*tan(f*x+e))^(7/2),1],
[(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x,7,-d^(5/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/f+d^(5/2)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/f+2*d^2*sqrt(d*tan(f*x+e))/a/f,1],
[(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x,6,d^(3/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/f-d^(3/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/f,1],
[sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e)),x,6,-sqrt(d)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/f-sqrt(d)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/f,1],
[1/sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e)),x,6,arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/sqrt(d)/f+arctanh(sqrt(d)*(1+tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/sqrt(d)/f,1],
[1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x,7,-arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/d^(3/2)/f+arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/d^(3/2)/f-2/a/d/f/sqrt(d*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x,10,arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a/d^(5/2)/f-arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a/d^(5/2)/f-2/3/a/d/f/(d*tan(f*x+e))^(3/2)+2/a/d^2/f/sqrt(d*tan(f*x+e)),1],
[(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x,16,3/2*d^(5/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/f+1/2*d^(5/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-1/2*d^(5/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-1/2*d^(5/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f-1/2*d^2*sqrt(d*tan(f*x+e))/f/(a^2+a^2*tan(f*x+e)),1],
[(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x,17,-1/2*d^(3/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/f-1/2*d^(3/2)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+1/2*d^(3/2)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f-1/2*d^(3/2)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f+1/2*d*sqrt(d*tan(f*x+e))/f/(a^2+a^2*tan(f*x+e)),1],
[sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e))^2,x,16,-1/2*sqrt(d)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/f-1/2*sqrt(d)*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+1/2*sqrt(d)*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/f+1/2*sqrt(d)*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/f-1/2*sqrt(d*tan(f*x+e))/f/(a^2+a^2*tan(f*x+e)),1],
[1/sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e))^2,x,17,3/2*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/sqrt(d)/f+1/2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/sqrt(d)/f-1/2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/sqrt(d)/f+1/2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/sqrt(d)/f+1/2*sqrt(d*tan(f*x+e))/d/f/(a^2+a^2*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x,17,-5/2*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/d^(3/2)/f+1/2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(3/2)/f-1/2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(3/2)/f-1/2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/d^(3/2)/f-5/2/a^2/d/f/sqrt(d*tan(f*x+e))+1/2/d/f/sqrt(d*tan(f*x+e))/(a^2+a^2*tan(f*x+e)),1],
[1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x,19,7/2*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^2/d^(5/2)/f-1/2*arctan(1-sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(5/2)/f+1/2*arctan(1+sqrt(2)*sqrt(d*tan(f*x+e))/sqrt(d))/sqrt(2)/a^2/d^(5/2)/f-1/2*arctanh(sqrt(2)*sqrt(d*tan(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/a^2/d^(5/2)/f-7/6/a^2/d/f/(d*tan(f*x+e))^(3/2)+9/2/a^2/d^2/f/sqrt(d*tan(f*x+e))+1/2/d/f/(d*tan(f*x+e))^(3/2)/(a^2+a^2*tan(f*x+e)),1],
[(d*tan(f*x+e))^(9/2)/(a+a*tan(f*x+e))^3,x,9,-31/8*d^(9/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f+1/2*d^(9/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/f+27/8*d^4*sqrt(d*tan(f*x+e))/a^3/f-9/8*d^3*(d*tan(f*x+e))^(3/2)/a^3/f/(1+tan(f*x+e))-1/4*d^2*(d*tan(f*x+e))^(5/2)/a/f/(a+a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(7/2)/(a+a*tan(f*x+e))^3,x,8,11/8*d^(7/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f+1/2*d^(7/2)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/f-7/8*d^3*sqrt(d*tan(f*x+e))/a^3/f/(1+tan(f*x+e))-1/4*d^2*(d*tan(f*x+e))^(3/2)/a/f/(a+a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x,8,1/8*d^(5/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f-1/2*d^(5/2)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/f+5/8*d^2*sqrt(d*tan(f*x+e))/a^3/f/(1+tan(f*x+e))-1/4*d^2*sqrt(d*tan(f*x+e))/a/f/(a+a*tan(f*x+e))^2,1],
[(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x,8,-5/8*d^(3/2)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f-1/2*d^(3/2)*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/f+1/4*d*sqrt(d*tan(f*x+e))/a/f/(a+a*tan(f*x+e))^2-1/8*d*sqrt(d*tan(f*x+e))/f/(a^3+a^3*tan(f*x+e)),1],
[sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e))^3,x,8,1/8*sqrt(d)*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/f+1/2*sqrt(d)*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/f-1/4*sqrt(d*tan(f*x+e))/a/f/(a+a*tan(f*x+e))^2-3/8*sqrt(d*tan(f*x+e))/f/(a^3+a^3*tan(f*x+e)),1],
[1/sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e))^3,x,8,11/8*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/sqrt(d)/f+1/2*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/sqrt(d)/f+7/8*sqrt(d*tan(f*x+e))/a^3/d/f/(1+tan(f*x+e))+1/4*sqrt(d*tan(f*x+e))/a/d/f/(a+a*tan(f*x+e))^2,1],
[1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x,9,-31/8*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/d^(3/2)/f-1/2*arctanh((sqrt(d)+sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/d^(3/2)/f-27/8/a^3/d/f/sqrt(d*tan(f*x+e))+9/8/a^3/d/f/sqrt(d*tan(f*x+e))/(1+tan(f*x+e))+1/4/a/d/f/sqrt(d*tan(f*x+e))/(a+a*tan(f*x+e))^2,1],
[1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x,10,59/8*arctan(sqrt(d*tan(f*x+e))/sqrt(d))/a^3/d^(5/2)/f-1/2*arctan((sqrt(d)-sqrt(d)*tan(f*x+e))/sqrt(2)/sqrt(d*tan(f*x+e)))/sqrt(2)/a^3/d^(5/2)/f-55/24/a^3/d/f/(d*tan(f*x+e))^(3/2)+63/8/a^3/d^2/f/sqrt(d*tan(f*x+e))+11/8/a^3/d/f/(d*tan(f*x+e))^(3/2)/(1+tan(f*x+e))+1/4/a/d/f/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,1],
[tan(f*x+e)^5*sqrt(1+tan(f*x+e)),x,11,-sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f+2*sqrt(1+tan(f*x+e))/f+52/315*(1+tan(f*x+e))^(3/2)/f-26/105*tan(f*x+e)*(1+tan(f*x+e))^(3/2)/f-4/21*tan(f*x+e)^2*(1+tan(f*x+e))^(3/2)/f+2/9*tan(f*x+e)^3*(1+tan(f*x+e))^(3/2)/f,1],
[tan(f*x+e)^3*sqrt(1+tan(f*x+e)),x,9,sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f+sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-2*sqrt(1+tan(f*x+e))/f-4/15*(1+tan(f*x+e))^(3/2)/f+2/5*tan(f*x+e)*(1+tan(f*x+e))^(3/2)/f,1],
[tan(f*x+e)*sqrt(1+tan(f*x+e)),x,6,-sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f+2*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)*sqrt(1+tan(f*x+e)),x,9,sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-2*arctanh(sqrt(1+tan(f*x+e)))/f+sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f,1],
[cot(f*x+e)^3*sqrt(1+tan(f*x+e)),x,11,-sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f+9/4*arctanh(sqrt(1+tan(f*x+e)))/f-sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-1/4*cot(f*x+e)*sqrt(1+tan(f*x+e))/f-1/2*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^5*sqrt(1+tan(f*x+e)),x,13,sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*tan(f*x+e))/sqrt(-7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f-139/64*arctanh(sqrt(1+tan(f*x+e)))/f+sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*tan(f*x+e))/sqrt(7+5*sqrt(2))/sqrt(1+tan(f*x+e)))/f+11/64*cot(f*x+e)*sqrt(1+tan(f*x+e))/f+53/96*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f-1/24*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f-1/4*cot(f*x+e)^4*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^4*sqrt(1+tan(f*x+e)),x,13,-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(2+2*sqrt(2))/f-18/35*(1+tan(f*x+e))^(3/2)/f-8/35*tan(f*x+e)*(1+tan(f*x+e))^(3/2)/f+2/7*tan(f*x+e)^2*(1+tan(f*x+e))^(3/2)/f,1],
[tan(f*x+e)^2*sqrt(1+tan(f*x+e)),x,11,sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(2+2*sqrt(2))/f+2/3*(1+tan(f*x+e))^(3/2)/f,1],
[sqrt(1+tan(f*x+e)),x,10,-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(2+2*sqrt(2))/f,1],
[cot(f*x+e)^2*sqrt(1+tan(f*x+e)),x,15,sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-arctanh(sqrt(1+tan(f*x+e)))/f+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(2+2*sqrt(2))/f-cot(f*x+e)*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^4*sqrt(1+tan(f*x+e)),x,18,-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+7/8*arctanh(sqrt(1+tan(f*x+e)))/f-sqrt(-1/2+1/2*sqrt(2))*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/f+9/8*cot(f*x+e)*sqrt(1+tan(f*x+e))/f-1/12*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f-1/3*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^5*(1+tan(f*x+e))^(3/2),x,18,sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f+2*sqrt(1+tan(f*x+e))/f+2/3*(1+tan(f*x+e))^(3/2)/f+20/231*(1+tan(f*x+e))^(5/2)/f-50/231*tan(f*x+e)*(1+tan(f*x+e))^(5/2)/f-4/33*tan(f*x+e)^2*(1+tan(f*x+e))^(5/2)/f+2/11*tan(f*x+e)^3*(1+tan(f*x+e))^(5/2)/f,1],
[tan(f*x+e)^3*(1+tan(f*x+e))^(3/2),x,16,-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f-2*sqrt(1+tan(f*x+e))/f-2/3*(1+tan(f*x+e))^(3/2)/f-4/35*(1+tan(f*x+e))^(5/2)/f+2/7*tan(f*x+e)*(1+tan(f*x+e))^(5/2)/f,1],
[tan(f*x+e)*(1+tan(f*x+e))^(3/2),x,13,sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f+2*sqrt(1+tan(f*x+e))/f+2/3*(1+tan(f*x+e))^(3/2)/f,1],
[cot(f*x+e)*(1+tan(f*x+e))^(3/2),x,15,-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-2*arctanh(sqrt(1+tan(f*x+e)))/f+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f,1],
[cot(f*x+e)^3*(1+tan(f*x+e))^(3/2),x,17,sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+5/4*arctanh(sqrt(1+tan(f*x+e)))/f-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f-5/4*cot(f*x+e)*sqrt(1+tan(f*x+e))/f-1/2*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^5*(1+tan(f*x+e))^(3/2),x,19,-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-83/64*arctanh(sqrt(1+tan(f*x+e)))/f+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f+83/64*cot(f*x+e)*sqrt(1+tan(f*x+e))/f+15/32*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f-3/8*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f-1/4*cot(f*x+e)^4*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^4*(1+tan(f*x+e))^(3/2),x,10,-sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+2*sqrt(1+tan(f*x+e))/f-22/63*(1+tan(f*x+e))^(5/2)/f-8/63*tan(f*x+e)*(1+tan(f*x+e))^(5/2)/f+2/9*tan(f*x+e)^2*(1+tan(f*x+e))^(5/2)/f,1],
[tan(f*x+e)^2*(1+tan(f*x+e))^(3/2),x,8,sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-2*sqrt(1+tan(f*x+e))/f+2/5*(1+tan(f*x+e))^(5/2)/f,1],
[(1+tan(f*x+e))^(3/2),x,7,-sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+2*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^2*(1+tan(f*x+e))^(3/2),x,11,sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-3*arctanh(sqrt(1+tan(f*x+e)))/f+sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-cot(f*x+e)*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^4*(1+tan(f*x+e))^(3/2),x,13,-sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+25/8*arctanh(sqrt(1+tan(f*x+e)))/f-sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+7/8*cot(f*x+e)*sqrt(1+tan(f*x+e))/f-7/12*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f-1/3*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^5/sqrt(1+tan(f*x+e)),x,10,-1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+44/105*sqrt(1+tan(f*x+e))/f-22/105*tan(f*x+e)*sqrt(1+tan(f*x+e))/f-12/35*tan(f*x+e)^2*sqrt(1+tan(f*x+e))/f+2/7*tan(f*x+e)^3*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^3/sqrt(1+tan(f*x+e)),x,8,1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-4/3*sqrt(1+tan(f*x+e))/f+2/3*tan(f*x+e)*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)/sqrt(1+tan(f*x+e)),x,5,-1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f,1],
[cot(f*x+e)/sqrt(1+tan(f*x+e)),x,9,1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-2*arctanh(sqrt(1+tan(f*x+e)))/f+1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f,1],
[cot(f*x+e)^3/sqrt(1+tan(f*x+e)),x,12,-1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+5/4*arctanh(sqrt(1+tan(f*x+e)))/f-1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f+3/4*cot(f*x+e)*sqrt(1+tan(f*x+e))/f-1/2*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^5/sqrt(1+tan(f*x+e)),x,14,1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*tan(f*x+e))/sqrt(-14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-115/64*arctanh(sqrt(1+tan(f*x+e)))/f+1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*tan(f*x+e))/sqrt(14+10*sqrt(2))/sqrt(1+tan(f*x+e)))/f-13/64*cot(f*x+e)*sqrt(1+tan(f*x+e))/f+13/96*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f+7/24*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f-1/4*cot(f*x+e)^4*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^4/sqrt(1+tan(f*x+e)),x,13,-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f-14/15*sqrt(1+tan(f*x+e))/f-8/15*tan(f*x+e)*sqrt(1+tan(f*x+e))/f+2/5*tan(f*x+e)^2*sqrt(1+tan(f*x+e))/f,1],
[tan(f*x+e)^2/sqrt(1+tan(f*x+e)),x,11,1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f+2*sqrt(1+tan(f*x+e))/f,1],
[1/sqrt(1+tan(f*x+e)),x,10,-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f,1],
[cot(f*x+e)^2/sqrt(1+tan(f*x+e)),x,18,1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+arctanh(sqrt(1+tan(f*x+e)))/f-1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f-cot(f*x+e)*sqrt(1+tan(f*x+e))/f,1],
[cot(f*x+e)^4/sqrt(1+tan(f*x+e)),x,18,-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f+1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+tan(f*x+e)))/sqrt(-2+2*sqrt(2)))/f-3/8*arctanh(sqrt(1+tan(f*x+e)))/f+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+tan(f*x+e))/(1+sqrt(2)+tan(f*x+e)))/sqrt(1+sqrt(2))/f+3/8*cot(f*x+e)*sqrt(1+tan(f*x+e))/f+5/12*cot(f*x+e)^2*sqrt(1+tan(f*x+e))/f-1/3*cot(f*x+e)^3*sqrt(1+tan(f*x+e))/f,1],
[(d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x,7,1/2*AppellF1(1+n,-m,1,2+n,-tan(f*x+e),-I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)*(a+a*tan(f*x+e))^m/d/f/(1+n)/((1+tan(f*x+e))^m)+1/2*AppellF1(1+n,-m,1,2+n,-tan(f*x+e),I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)*(a+a*tan(f*x+e))^m/d/f/(1+n)/((1+tan(f*x+e))^m),1],
[tan(d*x+c)^5*(a+b*tan(d*x+c)),x,6,-b*x-a*ln(cos(d*x+c))/d+b*tan(d*x+c)/d-1/2*a*tan(d*x+c)^2/d-1/3*b*tan(d*x+c)^3/d+1/4*a*tan(d*x+c)^4/d+1/5*b*tan(d*x+c)^5/d,1],
[tan(d*x+c)^4*(a+b*tan(d*x+c)),x,5,a*x-b*ln(cos(d*x+c))/d-a*tan(d*x+c)/d-1/2*b*tan(d*x+c)^2/d+1/3*a*tan(d*x+c)^3/d+1/4*b*tan(d*x+c)^4/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c)),x,4,b*x+a*ln(cos(d*x+c))/d-b*tan(d*x+c)/d+1/2*a*tan(d*x+c)^2/d+1/3*b*tan(d*x+c)^3/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c)),x,3,-a*x+b*ln(cos(d*x+c))/d+a*tan(d*x+c)/d+1/2*b*tan(d*x+c)^2/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c)),x,2,-b*x-a*ln(cos(d*x+c))/d+b*tan(d*x+c)/d,1],
[a+b*tan(d*x+c),x,2,a*x-b*ln(cos(d*x+c))/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c)),x,2,b*x+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c)),x,3,-a*x-a*cot(d*x+c)/d+b*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c)),x,4,-b*x-b*cot(d*x+c)/d-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^4*(a+b*tan(d*x+c)),x,5,a*x+a*cot(d*x+c)/d-1/2*b*cot(d*x+c)^2/d-1/3*a*cot(d*x+c)^3/d-b*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*(a+b*tan(d*x+c)),x,6,b*x+b*cot(d*x+c)/d+1/2*a*cot(d*x+c)^2/d-1/3*b*cot(d*x+c)^3/d-1/4*a*cot(d*x+c)^4/d+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^6*(a+b*tan(d*x+c)),x,7,-a*x-a*cot(d*x+c)/d+1/2*b*cot(d*x+c)^2/d+1/3*a*cot(d*x+c)^3/d-1/4*b*cot(d*x+c)^4/d-1/5*a*cot(d*x+c)^5/d+b*ln(sin(d*x+c))/d,1],
[tan(d*x+c)^4*(a+b*tan(d*x+c))^2,x,6,(a^2-b^2)*x-2*a*b*ln(cos(d*x+c))/d-(a^2-b^2)*tan(d*x+c)/d-a*b*tan(d*x+c)^2/d+1/3*(a^2-b^2)*tan(d*x+c)^3/d+1/2*a*b*tan(d*x+c)^4/d+1/5*b^2*tan(d*x+c)^5/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^2,x,5,2*a*b*x+(a^2-b^2)*ln(cos(d*x+c))/d-2*a*b*tan(d*x+c)/d+1/2*(a^2-b^2)*tan(d*x+c)^2/d+2/3*a*b*tan(d*x+c)^3/d+1/4*b^2*tan(d*x+c)^4/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^2,x,3,-(a^2-b^2)*x+2*a*b*ln(cos(d*x+c))/d-b^2*tan(d*x+c)/d+1/3*(a+b*tan(d*x+c))^3/b/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c))^2,x,3,-2*a*b*x-(a^2-b^2)*ln(cos(d*x+c))/d+a*b*tan(d*x+c)/d+1/2*(a+b*tan(d*x+c))^2/d,1],
[(a+b*tan(d*x+c))^2,x,2,(a^2-b^2)*x-2*a*b*ln(cos(d*x+c))/d+b^2*tan(d*x+c)/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c))^2,x,3,2*a*b*x-b^2*ln(cos(d*x+c))/d+a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^2,x,3,-(a^2-b^2)*x-a^2*cot(d*x+c)/d+2*a*b*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^2,x,4,-2*a*b*x-2*a*b*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)^2/d-(a^2-b^2)*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^4*(a+b*tan(d*x+c))^2,x,5,(a^2-b^2)*x+(a^2-b^2)*cot(d*x+c)/d-a*b*cot(d*x+c)^2/d-1/3*a^2*cot(d*x+c)^3/d-2*a*b*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*(a+b*tan(d*x+c))^2,x,6,2*a*b*x+2*a*b*cot(d*x+c)/d+1/2*(a^2-b^2)*cot(d*x+c)^2/d-2/3*a*b*cot(d*x+c)^3/d-1/4*a^2*cot(d*x+c)^4/d+(a^2-b^2)*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^6*(a+b*tan(d*x+c))^2,x,7,-(a^2-b^2)*x-(a^2-b^2)*cot(d*x+c)/d+a*b*cot(d*x+c)^2/d+1/3*(a^2-b^2)*cot(d*x+c)^3/d-1/2*a*b*cot(d*x+c)^4/d-1/5*a^2*cot(d*x+c)^5/d+2*a*b*ln(sin(d*x+c))/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^3,x,7,b*(3*a^2-b^2)*x+a*(a^2-3*b^2)*ln(cos(d*x+c))/d-b*(a^2-b^2)*tan(d*x+c)/d-1/2*a*(a+b*tan(d*x+c))^2/d-1/3*(a+b*tan(d*x+c))^3/d-1/20*a*(a+b*tan(d*x+c))^4/b^2/d+1/5*tan(d*x+c)*(a+b*tan(d*x+c))^4/b/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^3,x,4,-a*(a^2-3*b^2)*x+b*(3*a^2-b^2)*ln(cos(d*x+c))/d-2*a*b^2*tan(d*x+c)/d-1/2*b*(a+b*tan(d*x+c))^2/d+1/4*(a+b*tan(d*x+c))^4/b/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c))^3,x,4,-b*(3*a^2-b^2)*x-a*(a^2-3*b^2)*ln(cos(d*x+c))/d+b*(a^2-b^2)*tan(d*x+c)/d+1/2*a*(a+b*tan(d*x+c))^2/d+1/3*(a+b*tan(d*x+c))^3/d,1],
[(a+b*tan(d*x+c))^3,x,3,a*(a^2-3*b^2)*x-b*(3*a^2-b^2)*ln(cos(d*x+c))/d+2*a*b^2*tan(d*x+c)/d+1/2*b*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c))^3,x,4,b*(3*a^2-b^2)*x-3*a*b^2*ln(cos(d*x+c))/d+a^3*ln(sin(d*x+c))/d+b^2*(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^3,x,4,-a*(a^2-3*b^2)*x-b^3*ln(cos(d*x+c))/d+3*a^2*b*ln(sin(d*x+c))/d-a^2*cot(d*x+c)*(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^3,x,4,-b*(3*a^2-b^2)*x-5/2*a^2*b*cot(d*x+c)/d-a*(a^2-3*b^2)*ln(sin(d*x+c))/d-1/2*a^2*cot(d*x+c)^2*(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^4*(a+b*tan(d*x+c))^3,x,5,a*(a^2-3*b^2)*x+a*(a^2-3*b^2)*cot(d*x+c)/d-7/6*a^2*b*cot(d*x+c)^2/d-b*(3*a^2-b^2)*ln(sin(d*x+c))/d-1/3*a^2*cot(d*x+c)^3*(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^5*(a+b*tan(d*x+c))^3,x,6,b*(3*a^2-b^2)*x+b*(3*a^2-b^2)*cot(d*x+c)/d+1/2*a*(a^2-3*b^2)*cot(d*x+c)^2/d-3/4*a^2*b*cot(d*x+c)^3/d+a*(a^2-3*b^2)*ln(sin(d*x+c))/d-1/4*a^2*cot(d*x+c)^4*(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^6*(a+b*tan(d*x+c))^3,x,7,-a*(a^2-3*b^2)*x-a*(a^2-3*b^2)*cot(d*x+c)/d+1/2*b*(3*a^2-b^2)*cot(d*x+c)^2/d+1/3*a*(a^2-3*b^2)*cot(d*x+c)^3/d-11/20*a^2*b*cot(d*x+c)^4/d+b*(3*a^2-b^2)*ln(sin(d*x+c))/d-1/5*a^2*cot(d*x+c)^5*(a+b*tan(d*x+c))/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^4,x,8,4*a*b*(a^2-b^2)*x+(a^4-6*a^2*b^2+b^4)*ln(cos(d*x+c))/d-a*b*(a^2-3*b^2)*tan(d*x+c)/d-1/2*(a^2-b^2)*(a+b*tan(d*x+c))^2/d-1/3*a*(a+b*tan(d*x+c))^3/d-1/4*(a+b*tan(d*x+c))^4/d-1/30*a*(a+b*tan(d*x+c))^5/b^2/d+1/6*tan(d*x+c)*(a+b*tan(d*x+c))^5/b/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^4,x,5,-(a^4-6*a^2*b^2+b^4)*x+4*a*b*(a^2-b^2)*ln(cos(d*x+c))/d-b^2*(3*a^2-b^2)*tan(d*x+c)/d-a*b*(a+b*tan(d*x+c))^2/d-1/3*b*(a+b*tan(d*x+c))^3/d+1/5*(a+b*tan(d*x+c))^5/b/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c))^4,x,5,-4*a*b*(a^2-b^2)*x-(a^4-6*a^2*b^2+b^4)*ln(cos(d*x+c))/d+a*b*(a^2-3*b^2)*tan(d*x+c)/d+1/2*(a^2-b^2)*(a+b*tan(d*x+c))^2/d+1/3*a*(a+b*tan(d*x+c))^3/d+1/4*(a+b*tan(d*x+c))^4/d,1],
[(a+b*tan(d*x+c))^4,x,4,(a^4-6*a^2*b^2+b^4)*x-4*a*b*(a^2-b^2)*ln(cos(d*x+c))/d+b^2*(3*a^2-b^2)*tan(d*x+c)/d+a*b*(a+b*tan(d*x+c))^2/d+1/3*b*(a+b*tan(d*x+c))^3/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c))^4,x,5,4*a*b*(a^2-b^2)*x-b^2*(6*a^2-b^2)*ln(cos(d*x+c))/d+a^4*ln(sin(d*x+c))/d+3*a*b^3*tan(d*x+c)/d+1/2*b^2*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^4,x,5,-(a^4-6*a^2*b^2+b^4)*x-4*a*b^3*ln(cos(d*x+c))/d+4*a^3*b*ln(sin(d*x+c))/d+b^2*(a^2+b^2)*tan(d*x+c)/d-a^2*cot(d*x+c)*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^4,x,5,-4*a*b*(a^2-b^2)*x-3*a^3*b*cot(d*x+c)/d-b^4*ln(cos(d*x+c))/d-a^2*(a^2-6*b^2)*ln(sin(d*x+c))/d-1/2*a^2*cot(d*x+c)^2*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^4*(a+b*tan(d*x+c))^4,x,5,(a^4-6*a^2*b^2+b^4)*x+1/3*a^2*(3*a^2-17*b^2)*cot(d*x+c)/d-4/3*a^3*b*cot(d*x+c)^2/d-4*a*b*(a^2-b^2)*ln(sin(d*x+c))/d-1/3*a^2*cot(d*x+c)^3*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^5*(a+b*tan(d*x+c))^4,x,6,4*a*b*(a^2-b^2)*x+4*a*b*(a^2-b^2)*cot(d*x+c)/d+1/4*a^2*(2*a^2-11*b^2)*cot(d*x+c)^2/d-5/6*a^3*b*cot(d*x+c)^3/d+(a^4-6*a^2*b^2+b^4)*ln(sin(d*x+c))/d-1/4*a^2*cot(d*x+c)^4*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^6*(a+b*tan(d*x+c))^4,x,7,-(a^4-6*a^2*b^2+b^4)*x-(a^4-6*a^2*b^2+b^4)*cot(d*x+c)/d+2*a*b*(a^2-b^2)*cot(d*x+c)^2/d+1/15*a^2*(5*a^2-27*b^2)*cot(d*x+c)^3/d-3/5*a^3*b*cot(d*x+c)^4/d+4*a*b*(a^2-b^2)*ln(sin(d*x+c))/d-1/5*a^2*cot(d*x+c)^5*(a+b*tan(d*x+c))^2/d,1],
[cot(d*x+c)^7*(a+b*tan(d*x+c))^4,x,8,-4*a*b*(a^2-b^2)*x-4*a*b*(a^2-b^2)*cot(d*x+c)/d-1/2*(a^4-6*a^2*b^2+b^4)*cot(d*x+c)^2/d+4/3*a*b*(a^2-b^2)*cot(d*x+c)^3/d+1/12*a^2*(3*a^2-16*b^2)*cot(d*x+c)^4/d-7/15*a^3*b*cot(d*x+c)^5/d-(a^4-6*a^2*b^2+b^4)*ln(sin(d*x+c))/d-1/6*a^2*cot(d*x+c)^6*(a+b*tan(d*x+c))^2/d,1],
[tan(d*x+c)^6/(a+b*tan(d*x+c)),x,8,-a*x/(a^2+b^2)-b*ln(cos(d*x+c))/(a^2+b^2)/d+a^6*ln(a+b*tan(d*x+c))/b^5/(a^2+b^2)/d-a*(a^2-b^2)*tan(d*x+c)/b^4/d+1/2*(a^2-b^2)*tan(d*x+c)^2/b^3/d-1/3*a*tan(d*x+c)^3/b^2/d+1/4*tan(d*x+c)^4/b/d,1],
[tan(d*x+c)^5/(a+b*tan(d*x+c)),x,7,b*x/(a^2+b^2)-a*ln(cos(d*x+c))/(a^2+b^2)/d-a^5*ln(a+b*tan(d*x+c))/b^4/(a^2+b^2)/d+(a^2-b^2)*tan(d*x+c)/b^3/d-1/2*a*tan(d*x+c)^2/b^2/d+1/3*tan(d*x+c)^3/b/d,1],
[tan(d*x+c)^4/(a+b*tan(d*x+c)),x,6,a*x/(a^2+b^2)+b*ln(cos(d*x+c))/(a^2+b^2)/d+a^4*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d-a*tan(d*x+c)/b^2/d+1/2*tan(d*x+c)^2/b/d,1],
[tan(d*x+c)^3/(a+b*tan(d*x+c)),x,5,-b*x/(a^2+b^2)+a*ln(cos(d*x+c))/(a^2+b^2)/d-a^3*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d+tan(d*x+c)/b/d,1],
[tan(d*x+c)^2/(a+b*tan(d*x+c)),x,4,-a*x/(a^2+b^2)-ln(cos(d*x+c))/b/d+a^2*ln(a*cos(d*x+c)+b*sin(d*x+c))/b/(a^2+b^2)/d,1],
[tan(d*x+c)/(a+b*tan(d*x+c)),x,2,b*x/(a^2+b^2)-a*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)/d,1],
[1/(a+b*tan(d*x+c)),x,2,a*x/(a^2+b^2)+b*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)/d,1],
[cot(d*x+c)/(a+b*tan(d*x+c)),x,3,-b*x/(a^2+b^2)+ln(sin(d*x+c))/a/d-b^2*ln(a*cos(d*x+c)+b*sin(d*x+c))/a/(a^2+b^2)/d,1],
[cot(d*x+c)^2/(a+b*tan(d*x+c)),x,4,-a*x/(a^2+b^2)-cot(d*x+c)/a/d-b*ln(sin(d*x+c))/a^2/d+b^3*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^2/(a^2+b^2)/d,1],
[cot(d*x+c)^3/(a+b*tan(d*x+c)),x,5,b*x/(a^2+b^2)+b*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)^2/a/d-(a^2-b^2)*ln(sin(d*x+c))/a^3/d-b^4*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^3/(a^2+b^2)/d,1],
[cot(d*x+c)^4/(a+b*tan(d*x+c)),x,6,a*x/(a^2+b^2)+(a^2-b^2)*cot(d*x+c)/a^3/d+1/2*b*cot(d*x+c)^2/a^2/d-1/3*cot(d*x+c)^3/a/d+b*(a^2-b^2)*ln(sin(d*x+c))/a^4/d+b^5*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^4/(a^2+b^2)/d,1],
[tan(d*x+c)^6/(a+b*tan(d*x+c))^2,x,8,-(a^2-b^2)*x/(a^2+b^2)^2-2*a*b*ln(cos(d*x+c))/(a^2+b^2)^2/d-2*a^5*(2*a^2+3*b^2)*ln(a+b*tan(d*x+c))/b^5/(a^2+b^2)^2/d+(4*a^4+2*a^2*b^2-b^4)*tan(d*x+c)/b^4/(a^2+b^2)/d-a*(2*a^2+b^2)*tan(d*x+c)^2/b^3/(a^2+b^2)/d+1/3*(4*a^2+b^2)*tan(d*x+c)^3/b^2/(a^2+b^2)/d-a^2*tan(d*x+c)^4/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+b*tan(d*x+c))^2,x,7,2*a*b*x/(a^2+b^2)^2-(a^2-b^2)*ln(cos(d*x+c))/(a^2+b^2)^2/d+a^4*(3*a^2+5*b^2)*ln(a+b*tan(d*x+c))/b^4/(a^2+b^2)^2/d-a*(3*a^2+2*b^2)*tan(d*x+c)/b^3/(a^2+b^2)/d+1/2*(3*a^2+b^2)*tan(d*x+c)^2/b^2/(a^2+b^2)/d-a^2*tan(d*x+c)^3/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^4/(a+b*tan(d*x+c))^2,x,6,(a^2-b^2)*x/(a^2+b^2)^2+2*a*b*ln(cos(d*x+c))/(a^2+b^2)^2/d-2*a^3*(a^2+2*b^2)*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)^2/d+(2*a^2+b^2)*tan(d*x+c)/b^2/(a^2+b^2)/d-a^2*tan(d*x+c)^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^3/(a+b*tan(d*x+c))^2,x,5,-2*a*b*x/(a^2+b^2)^2+(a^2-b^2)*ln(cos(d*x+c))/(a^2+b^2)^2/d+a^2*(a^2+3*b^2)*ln(a+b*tan(d*x+c))/b^2/(a^2+b^2)^2/d+a^3/b^2/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+b*tan(d*x+c))^2,x,3,-(a^2-b^2)*x/(a^2+b^2)^2-2*a*b*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^2/d-a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)/(a+b*tan(d*x+c))^2,x,3,2*a*b*x/(a^2+b^2)^2-(a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^2/d+a/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^2,x,3,(a^2-b^2)*x/(a^2+b^2)^2+2*a*b*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^2/d-b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)/(a+b*tan(d*x+c))^2,x,4,-2*a*b*x/(a^2+b^2)^2+ln(sin(d*x+c))/a^2/d-b^2*(3*a^2+b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^2/(a^2+b^2)^2/d+b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+b*tan(d*x+c))^2,x,5,-(a^2-b^2)*x/(a^2+b^2)^2-2*b*ln(sin(d*x+c))/a^3/d+2*b^3*(2*a^2+b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^3/(a^2+b^2)^2/d-b*(a^2+2*b^2)/a^2/(a^2+b^2)/d/(a+b*tan(d*x+c))-cot(d*x+c)/a/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)^3/(a+b*tan(d*x+c))^2,x,6,2*a*b*x/(a^2+b^2)^2-(a^2-3*b^2)*ln(sin(d*x+c))/a^4/d-b^4*(5*a^2+3*b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^4/(a^2+b^2)^2/d+b^2*(2*a^2+3*b^2)/a^3/(a^2+b^2)/d/(a+b*tan(d*x+c))+3/2*b*cot(d*x+c)/a^2/d/(a+b*tan(d*x+c))-1/2*cot(d*x+c)^2/a/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^6/(a+b*tan(d*x+c))^3,x,8,-a*(a^2-3*b^2)*x/(a^2+b^2)^3-b*(3*a^2-b^2)*ln(cos(d*x+c))/(a^2+b^2)^3/d+a^4*(6*a^4+17*a^2*b^2+15*b^4)*ln(a+b*tan(d*x+c))/b^5/(a^2+b^2)^3/d-a*(6*a^4+11*a^2*b^2+3*b^4)*tan(d*x+c)/b^4/(a^2+b^2)^2/d+1/2*(6*a^4+11*a^2*b^2+b^4)*tan(d*x+c)^2/b^3/(a^2+b^2)^2/d-1/2*a^2*tan(d*x+c)^4/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-2*a^2*(a^2+2*b^2)*tan(d*x+c)^3/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+b*tan(d*x+c))^3,x,7,b*(3*a^2-b^2)*x/(a^2+b^2)^3-a*(a^2-3*b^2)*ln(cos(d*x+c))/(a^2+b^2)^3/d-a^3*(3*a^4+9*a^2*b^2+10*b^4)*ln(a+b*tan(d*x+c))/b^4/(a^2+b^2)^3/d+(3*a^4+6*a^2*b^2+b^4)*tan(d*x+c)/b^3/(a^2+b^2)^2/d-1/2*a^2*tan(d*x+c)^3/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/2*a^2*(3*a^2+7*b^2)*tan(d*x+c)^2/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^4/(a+b*tan(d*x+c))^3,x,6,a*(a^2-3*b^2)*x/(a^2+b^2)^3+b*(3*a^2-b^2)*ln(cos(d*x+c))/(a^2+b^2)^3/d+a^2*(a^4+3*a^2*b^2+6*b^4)*ln(a+b*tan(d*x+c))/b^3/(a^2+b^2)^3/d-1/2*a^2*tan(d*x+c)^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+a^3*(a^2+3*b^2)/b^3/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^3/(a+b*tan(d*x+c))^3,x,4,-b*(3*a^2-b^2)*x/(a^2+b^2)^3+a*(a^2-3*b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d-1/2*a^2*tan(d*x+c)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/2*a^2*(a^2+5*b^2)/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+b*tan(d*x+c))^3,x,4,-a*(a^2-3*b^2)*x/(a^2+b^2)^3-b*(3*a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d-1/2*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+2*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)/(a+b*tan(d*x+c))^3,x,4,b*(3*a^2-b^2)*x/(a^2+b^2)^3-a*(a^2-3*b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d+1/2*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+(a^2-b^2)/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^3,x,4,a*(a^2-3*b^2)*x/(a^2+b^2)^3+b*(3*a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d-1/2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-2*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)/(a+b*tan(d*x+c))^3,x,5,-b*(3*a^2-b^2)*x/(a^2+b^2)^3+ln(sin(d*x+c))/a^3/d-b^2*(6*a^4+3*a^2*b^2+b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^3/(a^2+b^2)^3/d+1/2*b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+b^2*(3*a^2+b^2)/a^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+b*tan(d*x+c))^3,x,6,-a*(a^2-3*b^2)*x/(a^2+b^2)^3-3*b*ln(sin(d*x+c))/a^4/d+b^3*(10*a^4+9*a^2*b^2+3*b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^4/(a^2+b^2)^3/d-1/2*b*(2*a^2+3*b^2)/a^2/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-cot(d*x+c)/a/d/(a+b*tan(d*x+c))^2-b*(a^4+6*a^2*b^2+3*b^4)/a^3/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^6/(a+b*tan(d*x+c))^4,x,8,-(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^4-4*a*b*(a^2-b^2)*ln(cos(d*x+c))/(a^2+b^2)^4/d-4*a^3*(a^6+4*a^4*b^2+6*a^2*b^4+5*b^6)*ln(a+b*tan(d*x+c))/b^5/(a^2+b^2)^4/d+(4*a^6+12*a^4*b^2+13*a^2*b^4+b^6)*tan(d*x+c)/b^4/(a^2+b^2)^3/d-1/3*a^2*tan(d*x+c)^4/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-1/3*a^2*(2*a^2+5*b^2)*tan(d*x+c)^3/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-2*a^2*(a^4+3*a^2*b^2+4*b^4)*tan(d*x+c)^2/b^3/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+b*tan(d*x+c))^4,x,7,4*a*b*(a^2-b^2)*x/(a^2+b^2)^4-(a^4-6*a^2*b^2+b^4)*ln(cos(d*x+c))/(a^2+b^2)^4/d+a^2*(a^6+4*a^4*b^2+5*a^2*b^4+10*b^6)*ln(a+b*tan(d*x+c))/b^4/(a^2+b^2)^4/d-1/3*a^2*tan(d*x+c)^3/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-1/2*a^2*(a^2+3*b^2)*tan(d*x+c)^2/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+a^3*(a^4+3*a^2*b^2+6*b^4)/b^4/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^4/(a+b*tan(d*x+c))^4,x,5,(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^4+4*a*b*(a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-1/3*a^2*tan(d*x+c)^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+1/3*a^3*(a^2+4*b^2)/b^3/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-1/3*a^2*(2*a^4+7*a^2*b^2+17*b^4)/b^3/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^3/(a+b*tan(d*x+c))^4,x,5,-4*a*b*(a^2-b^2)*x/(a^2+b^2)^4+(a^4-6*a^2*b^2+b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-1/3*a^2*tan(d*x+c)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-1/6*a^2*(a^2+7*b^2)/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-a*(a^2-3*b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+b*tan(d*x+c))^4,x,5,-(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^4-4*a*b*(a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-1/3*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+b*(3*a^2-b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)/(a+b*tan(d*x+c))^4,x,5,4*a*b*(a^2-b^2)*x/(a^2+b^2)^4-(a^4-6*a^2*b^2+b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d+1/3*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+1/2*(a^2-b^2)/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+a*(a^2-3*b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^4,x,5,(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^4+4*a*b*(a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-1/3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-b*(3*a^2-b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)/(a+b*tan(d*x+c))^4,x,6,-4*a*b*(a^2-b^2)*x/(a^2+b^2)^4+ln(sin(d*x+c))/a^4/d-b^2*(10*a^6+5*a^4*b^2+4*a^2*b^4+b^6)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^4/(a^2+b^2)^4/d+1/3*b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^3+1/2*b^2*(3*a^2+b^2)/a^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+b^2*(6*a^4+3*a^2*b^2+b^4)/a^3/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+b*tan(d*x+c))^4,x,7,-(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^4-4*b*ln(sin(d*x+c))/a^5/d+4*b^3*(5*a^6+6*a^4*b^2+4*a^2*b^4+b^6)*ln(a*cos(d*x+c)+b*sin(d*x+c))/a^5/(a^2+b^2)^4/d-1/3*b*(3*a^2+4*b^2)/a^2/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-cot(d*x+c)/a/d/(a+b*tan(d*x+c))^3-b*(a^4+4*a^2*b^2+2*b^4)/a^3/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-b*(a^6+13*a^4*b^2+12*a^2*b^4+4*b^6)/a^4/(a^2+b^2)^3/d/(a+b*tan(d*x+c)),1],
[1/(3+5*tan(d*x+c)),x,2,3/34*x+5/34*ln(3*cos(d*x+c)+5*sin(d*x+c))/d,1],
[1/(3+5*tan(d*x+c))^2,x,3,-4/289*x+15/578*ln(3*cos(d*x+c)+5*sin(d*x+c))/d-5/34/d/(3+5*tan(d*x+c)),1],
[1/(3+5*tan(d*x+c))^3,x,4,-99/19652*x+5/19652*ln(3*cos(d*x+c)+5*sin(d*x+c))/d-5/68/d/(3+5*tan(d*x+c))^2-15/578/d/(3+5*tan(d*x+c)),1],
[1/(3+5*tan(d*x+c))^4,x,5,-161/334084*x-60/83521*ln(3*cos(d*x+c)+5*sin(d*x+c))/d-5/102/d/(3+5*tan(d*x+c))^3-15/1156/d/(3+5*tan(d*x+c))^2-5/19652/d/(3+5*tan(d*x+c)),1],
[1/(5+3*tan(d*x+c)),x,2,5/34*x+3/34*ln(5*cos(d*x+c)+3*sin(d*x+c))/d,1],
[1/(5+3*tan(d*x+c))^2,x,3,4/289*x+15/578*ln(5*cos(d*x+c)+3*sin(d*x+c))/d-3/34/d/(5+3*tan(d*x+c)),1],
[1/(5+3*tan(d*x+c))^3,x,4,-5/19652*x+99/19652*ln(5*cos(d*x+c)+3*sin(d*x+c))/d-3/68/d/(5+3*tan(d*x+c))^2-15/578/d/(5+3*tan(d*x+c)),1],
[1/(5+3*tan(d*x+c))^4,x,5,-161/334084*x+60/83521*ln(5*cos(d*x+c)+3*sin(d*x+c))/d-1/34/d/(5+3*tan(d*x+c))^3-15/1156/d/(5+3*tan(d*x+c))^2-99/19652/d/(5+3*tan(d*x+c)),1],
[tan(d*x+c)^4*sqrt(a+b*tan(d*x+c)),x,13,-b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d+2/105*(8*a^2-35*b^2)*(a+b*tan(d*x+c))^(3/2)/b^3/d-8/35*a*tan(d*x+c)*(a+b*tan(d*x+c))^(3/2)/b^2/d+2/7*tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)/b/d,1],
[tan(d*x+c)^3*sqrt(a+b*tan(d*x+c)),x,11,sqrt(a-I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+sqrt(a+I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-2*sqrt(a+b*tan(d*x+c))/d-4/15*a*(a+b*tan(d*x+c))^(3/2)/b^2/d+2/5*tan(d*x+c)*(a+b*tan(d*x+c))^(3/2)/b/d,1],
[tan(d*x+c)^2*sqrt(a+b*tan(d*x+c)),x,11,b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d+2/3*(a+b*tan(d*x+c))^(3/2)/b/d,1],
[tan(d*x+c)*sqrt(a+b*tan(d*x+c)),x,8,-sqrt(a-I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-sqrt(a+I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(a+b*tan(d*x+c)),x,10,-b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d,1],
[cot(d*x+c)*sqrt(a+b*tan(d*x+c)),x,11,-2*sqrt(a)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d+sqrt(a-I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+sqrt(a+I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d,1],
[cot(d*x+c)^2*sqrt(a+b*tan(d*x+c)),x,15,-b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/sqrt(a)/d+b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^3*sqrt(a+b*tan(d*x+c)),x,13,1/4*(8*a^2+b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(3/2)/d-sqrt(a-I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-sqrt(a+I*b)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-1/4*b*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/a/d-1/2*cot(d*x+c)^2*sqrt(a+b*tan(d*x+c))/d,1],
[tan(d*x+c)^4*(a+b*tan(d*x+c))^(3/2),x,11,-I*(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+I*(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*b*sqrt(a+b*tan(d*x+c))/d+2/315*(8*a^2-63*b^2)*(a+b*tan(d*x+c))^(5/2)/b^3/d-8/63*a*tan(d*x+c)*(a+b*tan(d*x+c))^(5/2)/b^2/d+2/9*tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)/b/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x,12,(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-2*a*sqrt(a+b*tan(d*x+c))/d-2/3*(a+b*tan(d*x+c))^(3/2)/d-4/35*a*(a+b*tan(d*x+c))^(5/2)/b^2/d+2/7*tan(d*x+c)*(a+b*tan(d*x+c))^(5/2)/b/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x,9,I*(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-I*(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-2*b*sqrt(a+b*tan(d*x+c))/d+2/5*(a+b*tan(d*x+c))^(5/2)/b/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c))^(3/2),x,9,-(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*a*sqrt(a+b*tan(d*x+c))/d+2/3*(a+b*tan(d*x+c))^(3/2)/d,1],
[(a+b*tan(d*x+c))^(3/2),x,8,-I*(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+I*(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*b*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c))^(3/2),x,11,-2*a^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d+(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x,12,-3*sqrt(a)*b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d+I*(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-I*(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-a*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x,13,1/4*(8*a^2-3*b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/sqrt(a)/d-(a-I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(3/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-5/4*b*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d-1/2*a*cot(d*x+c)^2*sqrt(a+b*tan(d*x+c))/d,1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x,13,(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-2*(a^2-b^2)*sqrt(a+b*tan(d*x+c))/d-2/3*a*(a+b*tan(d*x+c))^(3/2)/d-2/5*(a+b*tan(d*x+c))^(5/2)/d-4/63*a*(a+b*tan(d*x+c))^(7/2)/b^2/d+2/9*tan(d*x+c)*(a+b*tan(d*x+c))^(7/2)/b/d,1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x,10,I*(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-I*(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-4*a*b*sqrt(a+b*tan(d*x+c))/d-2/3*b*(a+b*tan(d*x+c))^(3/2)/d+2/7*(a+b*tan(d*x+c))^(7/2)/b/d,1],
[tan(d*x+c)*(a+b*tan(d*x+c))^(5/2),x,10,-(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*(a^2-b^2)*sqrt(a+b*tan(d*x+c))/d+2/3*a*(a+b*tan(d*x+c))^(3/2)/d+2/5*(a+b*tan(d*x+c))^(5/2)/d,1],
[(a+b*tan(d*x+c))^(5/2),x,9,-I*(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+I*(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+4*a*b*sqrt(a+b*tan(d*x+c))/d+2/3*b*(a+b*tan(d*x+c))^(3/2)/d,1],
[cot(d*x+c)*(a+b*tan(d*x+c))^(5/2),x,12,-2*a^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d+(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*b^2*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x,12,-5*a^(3/2)*b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d+I*(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-I*(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-a^2*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x,13,1/4*sqrt(a)*(8*a^2-15*b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/d-(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d-9/4*a*b*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d-1/2*a^2*cot(d*x+c)^2*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2),x,14,5/8*b*(8*a^2-b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/sqrt(a)/d-I*(a-I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+I*(a+I*b)^(5/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+1/8*(8*a^2-11*b^2)*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/d-13/12*a*b*cot(d*x+c)^2*sqrt(a+b*tan(d*x+c))/d-1/3*a^2*cot(d*x+c)^3*sqrt(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^(7/2),x,10,-I*(a-I*b)^(7/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/d+I*(a+I*b)^(7/2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/d+2*b*(3*a^2-b^2)*sqrt(a+b*tan(d*x+c))/d+4/3*a*b*(a+b*tan(d*x+c))^(3/2)/d+2/5*b*(a+b*tan(d*x+c))^(5/2)/d,1],
[tan(d*x+c)^5/sqrt(a+b*tan(d*x+c)),x,12,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d-4/105*a*(24*a^2-35*b^2)*sqrt(a+b*tan(d*x+c))/b^4/d+2/105*(24*a^2-35*b^2)*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b^3/d-12/35*a*tan(d*x+c)^2*sqrt(a+b*tan(d*x+c))/b^2/d+2/7*tan(d*x+c)^3*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)^4/sqrt(a+b*tan(d*x+c)),x,13,b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a+sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d+2/15*(8*a^2-15*b^2)*sqrt(a+b*tan(d*x+c))/b^3/d-8/15*a*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b^2/d+2/5*tan(d*x+c)^2*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)^3/sqrt(a+b*tan(d*x+c)),x,10,arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d-4/3*a*sqrt(a+b*tan(d*x+c))/b^2/d+2/3*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)^2/sqrt(a+b*tan(d*x+c)),x,11,-b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a+sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d+2*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)/sqrt(a+b*tan(d*x+c)),x,7,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d,1],
[1/sqrt(a+b*tan(d*x+c)),x,10,b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a+sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d,1],
[cot(d*x+c)/sqrt(a+b*tan(d*x+c)),x,11,-2*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/sqrt(a)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d,1],
[cot(d*x+c)^2/sqrt(a+b*tan(d*x+c)),x,16,b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(3/2)/d-b*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*tan(d*x+c))/(a+sqrt(a^2+b^2)+b*tan(d*x+c)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a+sqrt(a^2+b^2))/d-b*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d+b*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*tan(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a^2+b^2)/sqrt(a-sqrt(a^2+b^2))/d-cot(d*x+c)*sqrt(a+b*tan(d*x+c))/a/d,1],
[cot(d*x+c)^3/sqrt(a+b*tan(d*x+c)),x,14,1/4*(8*a^2-3*b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(5/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d+3/4*b*cot(d*x+c)*sqrt(a+b*tan(d*x+c))/a^2/d-1/2*cot(d*x+c)^2*sqrt(a+b*tan(d*x+c))/a/d,1],
[tan(d*x+c)^5/(a+b*tan(d*x+c))^(3/2),x,11,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-2*a^2*tan(d*x+c)^3/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))+2/5*(16*a^4+6*a^2*b^2-5*b^4)*sqrt(a+b*tan(d*x+c))/b^4/(a^2+b^2)/d-2/5*a*(8*a^2+3*b^2)*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d+2/5*(6*a^2+b^2)*tan(d*x+c)^2*sqrt(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d,1],
[tan(d*x+c)^4/(a+b*tan(d*x+c))^(3/2),x,10,-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-2*a^2*tan(d*x+c)^2/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))-2/3*a*(8*a^2+5*b^2)*sqrt(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d+2/3*(4*a^2+b^2)*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d,1],
[tan(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x,9,arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-2*a^2*tan(d*x+c)/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))+2*(2*a^2+b^2)*sqrt(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d,1],
[tan(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x,8,I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-2*a^2/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)/(a+b*tan(d*x+c))^(3/2),x,8,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d+2*a/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^(3/2),x,8,-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-2*b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)/(a+b*tan(d*x+c))^(3/2),x,12,-2*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(3/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d+2*b^2/a/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x,13,3*b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(5/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-b*(a^2+3*b^2)/a^2/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))-cot(d*x+c)/a/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x,14,1/4*(8*a^2-15*b^2)*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(7/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d+1/4*b^2*(7*a^2+15*b^2)/a^3/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))+5/4*b*cot(d*x+c)/a^2/d/sqrt(a+b*tan(d*x+c))-1/2*cot(d*x+c)^2/a/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^5/(a+b*tan(d*x+c))^(5/2),x,11,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-2/3*a^2*tan(d*x+c)^3/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-4*a^2*(a^2+2*b^2)*tan(d*x+c)^2/b^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c))-4/3*a*(8*a^4+15*a^2*b^2+4*b^4)*sqrt(a+b*tan(d*x+c))/b^4/(a^2+b^2)^2/d+2/3*(8*a^4+15*a^2*b^2+b^4)*tan(d*x+c)*sqrt(a+b*tan(d*x+c))/b^3/(a^2+b^2)^2/d,1],
[tan(d*x+c)^4/(a+b*tan(d*x+c))^(5/2),x,10,-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-2/3*a^2*tan(d*x+c)^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+4/3*a^3*(2*a^2+5*b^2)/b^3/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c))+2/3*(4*a^2+3*b^2)*sqrt(a+b*tan(d*x+c))/b^3/(a^2+b^2)/d,1],
[tan(d*x+c)^3/(a+b*tan(d*x+c))^(5/2),x,9,arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-2/3*a^2*tan(d*x+c)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-4/3*a^2*(a^2+4*b^2)/b^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x,9,I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-2/3*a^2/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+4*a*b/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)/(a+b*tan(d*x+c))^(5/2),x,9,-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d-arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d+2/3*a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+2*(a^2-b^2)/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^(5/2),x,9,-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-2/3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-4*a*b/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)/(a+b*tan(d*x+c))^(5/2),x,13,-2*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(5/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d+arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d+2/3*b^2/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+2*b^2*(3*a^2+b^2)/a^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x,14,5*b*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a))/a^(7/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-1/3*b*(3*a^2+5*b^2)/a^2/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-cot(d*x+c)/a/d/(a+b*tan(d*x+c))^(3/2)-b*(a^4+10*a^2*b^2+5*b^4)/a^3/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/(a+b*tan(d*x+c))^(7/2),x,10,-I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a-I*b))/(a-I*b)^(7/2)/d+I*arctanh(sqrt(a+b*tan(d*x+c))/sqrt(a+I*b))/(a+I*b)^(7/2)/d-2/5*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(5/2)-4/3*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^(3/2)-2*b*(3*a^2-b^2)/(a^2+b^2)^3/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x,12,(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2*b*sqrt(tan(d*x+c))/d+2/3*a*tan(d*x+c)^(3/2)/d+2/5*b*tan(d*x+c)^(5/2)/d,1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x,11,(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*a*sqrt(tan(d*x+c))/d+2/3*b*tan(d*x+c)^(3/2)/d,1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c)),x,10,-(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*b*sqrt(tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))/sqrt(tan(d*x+c)),x,9,-(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d,1],
[(a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x,10,(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2*a/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x,11,(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2/3*a/d/tan(d*x+c)^(3/2)-2*b/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x,12,-(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2/5*a/d/tan(d*x+c)^(5/2)-2/3*b/d/tan(d*x+c)^(3/2)+2*a/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x,13,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-4*a*b*sqrt(tan(d*x+c))/d+2/3*(a^2-b^2)*tan(d*x+c)^(3/2)/d+4/5*a*b*tan(d*x+c)^(5/2)/d+2/7*b^2*tan(d*x+c)^(7/2)/d,1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x,12,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*(a^2-b^2)*sqrt(tan(d*x+c))/d+4/3*a*b*tan(d*x+c)^(3/2)/d+2/5*b^2*tan(d*x+c)^(5/2)/d,1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^2,x,11,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+4*a*b*sqrt(tan(d*x+c))/d+2/3*b^2*tan(d*x+c)^(3/2)/d,1],
[(a+b*tan(d*x+c))^2/sqrt(tan(d*x+c)),x,10,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*b^2*sqrt(tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^2/tan(d*x+c)^(3/2),x,10,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2*a^2/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^2/tan(d*x+c)^(5/2),x,11,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2/3*a^2/d/tan(d*x+c)^(3/2)-4*a*b/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^2/tan(d*x+c)^(7/2),x,12,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2/5*a^2/d/tan(d*x+c)^(5/2)-4/3*a*b/d/tan(d*x+c)^(3/2)+2*(a^2-b^2)/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x,14,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-2*b*(3*a^2-b^2)*sqrt(tan(d*x+c))/d+2/3*a*(a^2-3*b^2)*tan(d*x+c)^(3/2)/d+2/5*b*(3*a^2-b^2)*tan(d*x+c)^(5/2)/d+40/63*a*b^2*tan(d*x+c)^(7/2)/d+2/9*b^2*tan(d*x+c)^(7/2)*(a+b*tan(d*x+c))/d,1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x,13,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*a*(a^2-3*b^2)*sqrt(tan(d*x+c))/d+2/3*b*(3*a^2-b^2)*tan(d*x+c)^(3/2)/d+32/35*a*b^2*tan(d*x+c)^(5/2)/d+2/7*b^2*tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^3,x,12,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*b*(3*a^2-b^2)*sqrt(tan(d*x+c))/d+8/5*a*b^2*tan(d*x+c)^(3/2)/d+2/5*b^2*tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^3/sqrt(tan(d*x+c)),x,11,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+16/3*a*b^2*sqrt(tan(d*x+c))/d+2/3*b^2*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^3/tan(d*x+c)^(3/2),x,11,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d+2*b*(a^2+b^2)*sqrt(tan(d*x+c))/d-2*a^2*(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^3/tan(d*x+c)^(5/2),x,11,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-16/3*a^2*b/d/sqrt(tan(d*x+c))-2/3*a^2*(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2),1],
[(a+b*tan(d*x+c))^3/tan(d*x+c)^(7/2),x,12,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-8/5*a^2*b/d/tan(d*x+c)^(3/2)+2*a*(a^2-3*b^2)/d/sqrt(tan(d*x+c))-2/5*a^2*(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2),1],
[(a+b*tan(d*x+c))^3/tan(d*x+c)^(9/2),x,13,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-32/35*a^2*b/d/tan(d*x+c)^(5/2)+2/3*a*(a^2-3*b^2)/d/tan(d*x+c)^(3/2)+2*b*(3*a^2-b^2)/d/sqrt(tan(d*x+c))-2/7*a^2*(a+b*tan(d*x+c))/d/tan(d*x+c)^(7/2),1],
[(a+b*tan(d*x+c))^3/tan(d*x+c)^(11/2),x,14,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d-40/63*a^2*b/d/tan(d*x+c)^(7/2)+2/5*a*(a^2-3*b^2)/d/tan(d*x+c)^(5/2)+2/3*b*(3*a^2-b^2)/d/tan(d*x+c)^(3/2)-2*a*(a^2-3*b^2)/d/sqrt(tan(d*x+c))-2/9*a^2*(a+b*tan(d*x+c))/d/tan(d*x+c)^(9/2),1],
[(a+b*tan(d*x+c))/sqrt(tan(d*x+c)),x,9,-(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/d+(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/d,1],
[(a+b*tan(d*x+c))/sqrt(-tan(d*x+c)),x,9,(a-b)*arctan(1-sqrt(2)*sqrt(-tan(d*x+c)))/sqrt(2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(-tan(d*x+c)))/sqrt(2)/d-(a+b)*arctanh(sqrt(2)*sqrt(-tan(d*x+c))/(1-tan(d*x+c)))/sqrt(2)/d,1],
[(a+b*tan(d*x+c))/sqrt(e*tan(d*x+c)),x,9,-(a+b)*arctan(1-sqrt(2)*sqrt(e*tan(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)+(a+b)*arctan(1+sqrt(2)*sqrt(e*tan(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)+(a-b)*arctanh(sqrt(2)*sqrt(e*tan(d*x+c))/(sqrt(e)+sqrt(e)*tan(d*x+c)))/sqrt(2)/d/sqrt(e),1],
[(a+b*tan(d*x+c))/sqrt(-e*tan(d*x+c)),x,9,(a-b)*arctan(1-sqrt(2)*sqrt(-e*tan(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a-b)*arctan(1+sqrt(2)*sqrt(-e*tan(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a+b)*arctanh(sqrt(2)*sqrt(-e*tan(d*x+c))/(sqrt(e)-sqrt(e)*tan(d*x+c)))/sqrt(2)/d/sqrt(e),1],
[tan(d*x+c)^(9/2)/(a+b*tan(d*x+c)),x,16,-(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*a^(9/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(7/2)/(a^2+b^2)/d-(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*(a^2-b^2)*sqrt(tan(d*x+c))/b^3/d-2/3*a*tan(d*x+c)^(3/2)/b^2/d+2/5*tan(d*x+c)^(5/2)/b/d,1],
[tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x,15,-(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*a^(7/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(5/2)/(a^2+b^2)/d+(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*a*sqrt(tan(d*x+c))/b^2/d+2/3*tan(d*x+c)^(3/2)/b/d,1],
[tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x,14,(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*a^(5/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(3/2)/(a^2+b^2)/d+(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*sqrt(tan(d*x+c))/b/d,1],
[tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x,13,(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*a^(3/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/sqrt(b)/(a^2+b^2)/d-(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[sqrt(tan(d*x+c))/(a+b*tan(d*x+c)),x,13,-(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*sqrt(a)*sqrt(b)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/(a^2+b^2)/d-(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/sqrt(tan(d*x+c))/(a+b*tan(d*x+c)),x,13,-(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*b^(3/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/sqrt(a)/(a^2+b^2)/d+(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x,14,(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*b^(5/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(3/2)/(a^2+b^2)/d+(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2/a/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x,15,(a-b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*b^(7/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(5/2)/(a^2+b^2)/d-(a+b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2/3/a/d/tan(d*x+c)^(3/2)+2*b/a^2/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x,16,-(a+b)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*b^(9/2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(7/2)/(a^2+b^2)/d-(a-b)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2/5/a/d/tan(d*x+c)^(5/2)+2/3*b/a^2/d/tan(d*x+c)^(3/2)+2*(a^2-b^2)/a^3/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^2,x,16,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a^(7/2)*(5*a^2+9*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(7/2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a*(5*a^2+4*b^2)*sqrt(tan(d*x+c))/b^3/(a^2+b^2)/d+1/3*(5*a^2+2*b^2)*tan(d*x+c)^(3/2)/b^2/(a^2+b^2)/d-a^2*tan(d*x+c)^(5/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x,15,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a^(5/2)*(3*a^2+7*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(5/2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(3*a^2+2*b^2)*sqrt(tan(d*x+c))/b^2/(a^2+b^2)/d-a^2*tan(d*x+c)^(3/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x,14,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a^(3/2)*(a^2+5*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(3/2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a^2*sqrt(tan(d*x+c))/b/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x,14,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+sqrt(a)*(a^2-3*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/sqrt(b)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^2,x,14,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-sqrt(b)*(3*a^2-b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/sqrt(a)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-b*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^2,x,14,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b^(3/2)*(5*a^2+b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(3/2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b^2*sqrt(tan(d*x+c))/a/(a^2+b^2)/d/(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x,15,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-b^(5/2)*(7*a^2+3*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(5/2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(2*a^2+3*b^2)/a^2/(a^2+b^2)/d/sqrt(tan(d*x+c))+b^2/a/(a^2+b^2)/d/sqrt(tan(d*x+c))/(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x,16,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b^(7/2)*(9*a^2+5*b^2)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(7/2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-1/3*(2*a^2+5*b^2)/a^2/(a^2+b^2)/d/tan(d*x+c)^(3/2)+b*(4*a^2+5*b^2)/a^3/(a^2+b^2)/d/sqrt(tan(d*x+c))+b^2/a/(a^2+b^2)/d/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(11/2)/(a+b*tan(d*x+c))^3,x,17,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*a^(7/2)*(35*a^4+102*a^2*b^2+99*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(9/2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*a*(35*a^4+67*a^2*b^2+24*b^4)*sqrt(tan(d*x+c))/b^4/(a^2+b^2)^2/d+1/12*(35*a^4+67*a^2*b^2+8*b^4)*tan(d*x+c)^(3/2)/b^3/(a^2+b^2)^2/d-1/2*a^2*tan(d*x+c)^(7/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/4*a^2*(7*a^2+15*b^2)*tan(d*x+c)^(5/2)/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^3,x,16,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*a^(5/2)*(15*a^4+46*a^2*b^2+63*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(7/2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*(15*a^4+31*a^2*b^2+8*b^4)*sqrt(tan(d*x+c))/b^3/(a^2+b^2)^2/d-1/2*a^2*tan(d*x+c)^(5/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/4*a^2*(5*a^2+13*b^2)*tan(d*x+c)^(3/2)/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x,15,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*a^(3/2)*(3*a^4+6*a^2*b^2+35*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(5/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*a^2*tan(d*x+c)^(3/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/4*a^2*(3*a^2+11*b^2)*sqrt(tan(d*x+c))/b^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x,15,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*sqrt(a)*(a^4+18*a^2*b^2-15*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/b^(3/2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*a^2*sqrt(tan(d*x+c))/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+1/4*a*(a^2+9*b^2)*sqrt(tan(d*x+c))/b/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x,15,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*(3*a^4-26*a^2*b^2+3*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/sqrt(a)/sqrt(b)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*a*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+1/4*(3*a^2-5*b^2)*sqrt(tan(d*x+c))/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^3,x,15,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*sqrt(b)*(15*a^4-18*a^2*b^2-b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(3/2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*b*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c))^2-1/4*b*(7*a^2-b^2)*sqrt(tan(d*x+c))/a/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^3,x,15,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*b^(3/2)*(35*a^4+6*a^2*b^2+3*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(5/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*b^2*sqrt(tan(d*x+c))/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+1/4*b^2*(11*a^2+3*b^2)*sqrt(tan(d*x+c))/a^2/(a^2+b^2)^2/d/(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x,16,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*b^(5/2)*(63*a^4+46*a^2*b^2+15*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(7/2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*(8*a^4+31*a^2*b^2+15*b^4)/a^3/(a^2+b^2)^2/d/sqrt(tan(d*x+c))+1/2*b^2/a/(a^2+b^2)/d/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^2+1/4*b^2*(13*a^2+5*b^2)/a^2/(a^2+b^2)^2/d/sqrt(tan(d*x+c))/(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x,17,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*b^(7/2)*(99*a^4+102*a^2*b^2+35*b^4)*arctan(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a))/a^(9/2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(tan(d*x+c))/(1+tan(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/12*(8*a^4+67*a^2*b^2+35*b^4)/a^3/(a^2+b^2)^2/d/tan(d*x+c)^(3/2)+1/4*b*(24*a^4+67*a^2*b^2+35*b^4)/a^4/(a^2+b^2)^2/d/sqrt(tan(d*x+c))+1/2*b^2/a/(a^2+b^2)/d/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2+1/4*b^2*(15*a^2+7*b^2)/a^2/(a^2+b^2)^2/d/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c)),x,11,-sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/4*(a^2+8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(3/2)/d+sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/4*a*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b/d+1/2*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(3/2)/b/d,1],
[tan(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c)),x,10,I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(b)/d+I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c)),x,10,sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+2*sqrt(b)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d,1],
[sqrt(a+b*tan(d*x+c))/sqrt(tan(d*x+c)),x,7,-I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d,1],
[sqrt(a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x,8,-sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[sqrt(a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x,10,I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/3*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)-2/3*b*sqrt(a+b*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[sqrt(a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x,10,sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/5*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)-2/15*b*sqrt(a+b*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)+2/15*(15*a^2+2*b^2)*sqrt(a+b*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x,12,I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/8*a*(a^2+24*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(3/2)/d-I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/8*(a^2+8*b^2)*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b/d-1/12*a*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(3/2)/b/d+1/3*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(5/2)/b/d,1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x,11,(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+1/4*(3*a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(b)/d+(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+3/4*a*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d+1/2*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(3/2)/d,1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(3/2),x,10,-I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+3*a*sqrt(b)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+b*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^(3/2)/sqrt(tan(d*x+c)),x,11,-(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+2*b^(3/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d,1],
[(a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x,8,I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2*a*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x,9,(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/3*a*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)-8/3*b*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x,10,-I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/5*a*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)-4/5*b*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)+2/5*(5*a^2-b^2)*sqrt(a+b*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x,11,-(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/7*a*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(7/2)-16/35*b*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)+2/105*(35*a^2-3*b^2)*sqrt(a+b*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)+4/105*b*(70*a^2+3*b^2)*sqrt(a+b*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x,13,(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/64*(5*a^4+240*a^2*b^2-128*b^4)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(3/2)/d-(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-1/64*a*(5*a^2+112*b^2)*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b/d-1/96*(5*a^2+48*b^2)*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(3/2)/b/d-1/24*a*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(5/2)/b/d+1/4*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(7/2)/b/d,1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x,12,-I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+5/8*a*(a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(b)/d-I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+1/8*(11*a^2-8*b^2)*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d+13/12*a*b*tan(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d+1/3*b^2*tan(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^(5/2),x,11,-(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+1/4*sqrt(b)*(15*a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+9/4*a*b*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d+1/2*b^2*tan(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^(5/2)/sqrt(tan(d*x+c)),x,10,I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+5*a*b^(3/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+b^2*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x,10,(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+2*b^(5/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2*a^2*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x,9,-I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/3*a^2*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)-14/3*a*b*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x,10,-(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/5*a^2*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)-22/15*a*b*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)+2/15*(15*a^2-23*b^2)*sqrt(a+b*tan(d*x+c))/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x,11,I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d+I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/7*a^2*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(7/2)-6/7*a*b*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)+2/21*(7*a^2-9*b^2)*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(3/2)+2/21*b*(49*a^2-3*b^2)*sqrt(a+b*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x,12,(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/d-2/9*a^2*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(9/2)-38/63*a*b*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(7/2)+2/105*(21*a^2-25*b^2)*sqrt(a+b*tan(d*x+c))/d/tan(d*x+c)^(5/2)+2/315*b*(231*a^2-5*b^2)*sqrt(a+b*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)-2/315*(315*a^4-483*a^2*b^2-10*b^4)*sqrt(a+b*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/sqrt(a+b*tan(d*x+c)),x,13,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d+1/4*(3*a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(5/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d-3/4*a*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b^2/d+1/2*tan(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)^(5/2)/sqrt(a+b*tan(d*x+c)),x,11,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d-a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(3/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d+sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b/d,1],
[tan(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c)),x,11,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d+2*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(b)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d,1],
[sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)),x,6,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d,1],
[1/sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)),x,7,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d,1],
[1/tan(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c)),x,8,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d-2*sqrt(a+b*tan(d*x+c))/a/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/sqrt(a+b*tan(d*x+c)),x,10,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d-2/3*sqrt(a+b*tan(d*x+c))/a/d/tan(d*x+c)^(3/2)+4/3*b*sqrt(a+b*tan(d*x+c))/a^2/d/sqrt(tan(d*x+c)),1],
[1/tan(d*x+c)^(7/2)/sqrt(a+b*tan(d*x+c)),x,10,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a-b)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/sqrt(I*a+b)/d-2/5*sqrt(a+b*tan(d*x+c))/a/d/tan(d*x+c)^(5/2)+8/15*b*sqrt(a+b*tan(d*x+c))/a^2/d/tan(d*x+c)^(3/2)+2/15*(15*a^2-8*b^2)*sqrt(a+b*tan(d*x+c))/a^3/d/sqrt(tan(d*x+c)),1],
[tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x,11,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d-3*a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(5/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d-2*a^2*tan(d*x+c)^(3/2)/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c))+(3*a^2+b^2)*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d,1],
[tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x,10,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d+2*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(3/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d-2*a^2*sqrt(tan(d*x+c))/b/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x,8,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d+2*a*sqrt(tan(d*x+c))/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x,8,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d-2*b*sqrt(tan(d*x+c))/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x,8,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d+2*b^2*sqrt(tan(d*x+c))/a/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x,9,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d-2/a/d/sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c))-2*b*(a^2+2*b^2)*sqrt(tan(d*x+c))/a^2/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x,10,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(3/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(3/2)/d-2/3/a/d/tan(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c))+8/3*b/a^2/d/sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c))+2/3*b^2*(5*a^2+8*b^2)*sqrt(tan(d*x+c))/a^3/(a^2+b^2)/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^(5/2),x,12,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d-5*a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(7/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/3*a^2*tan(d*x+c)^(5/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-2/3*a^2*(5*a^2+11*b^2)*tan(d*x+c)^(3/2)/b^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c))+(5*a^4+10*a^2*b^2+b^4)*sqrt(tan(d*x+c))*sqrt(a+b*tan(d*x+c))/b^3/(a^2+b^2)^2/d,1],
[tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(5/2),x,11,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d+2*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/b^(5/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/3*a^2*tan(d*x+c)^(3/2)/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-2*a^2*(a^2+3*b^2)*sqrt(tan(d*x+c))/b^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x,9,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/3*a^2*sqrt(tan(d*x+c))/b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+2/3*a*(a^2+7*b^2)*sqrt(tan(d*x+c))/b/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x,9,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d+2/3*a*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+4/3*(a^2-2*b^2)*sqrt(tan(d*x+c))/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x,9,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/3*b*sqrt(tan(d*x+c))/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-2/3*b*(5*a^2-b^2)*sqrt(tan(d*x+c))/a/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x,9,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d+2/3*b^2*sqrt(tan(d*x+c))/a/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+4/3*b^2*(4*a^2+b^2)*sqrt(tan(d*x+c))/a^2/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x,10,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/a/d/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(3/2)-2/3*b*(3*a^2+4*b^2)*sqrt(tan(d*x+c))/a^2/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)-2/3*b*(3*a^4+17*a^2*b^2+8*b^4)*sqrt(tan(d*x+c))/a^3/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x,11,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a-b)^(5/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))/(I*a+b)^(5/2)/d-2/3/a/d/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2)+4*b/a^2/d/sqrt(tan(d*x+c))/(a+b*tan(d*x+c))^(3/2)+2/3*b^2*(7*a^2+8*b^2)*sqrt(tan(d*x+c))/a^3/(a^2+b^2)/d/(a+b*tan(d*x+c))^(3/2)+4/3*b^2*(4*a^4+15*a^2*b^2+8*b^4)*sqrt(tan(d*x+c))/a^4/(a^2+b^2)^2/d/sqrt(a+b*tan(d*x+c)),1],
[1/sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)),x,7,arctanh(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)))/sqrt(3-2*I)/d+arctanh(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[1/sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)),x,7,arctanh(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)))/sqrt(3-2*I)/d+arctanh(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[1/sqrt(2-3*tan(d*x+c))/sqrt(tan(d*x+c)),x,7,arctan(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(2-3*tan(d*x+c)))/sqrt(3-2*I)/d+arctan(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(2-3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[1/sqrt(-2-3*tan(d*x+c))/sqrt(tan(d*x+c)),x,7,arctan(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(-2-3*tan(d*x+c)))/sqrt(3-2*I)/d+arctan(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(-2-3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[1/sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)),x,7,arctanh(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)))/sqrt(2-3*I)/d+arctanh(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[1/sqrt(3-2*tan(d*x+c))/sqrt(tan(d*x+c)),x,7,arctan(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(3-2*tan(d*x+c)))/sqrt(2-3*I)/d+arctan(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(3-2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[1/sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)),x,7,arctanh(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)))/sqrt(2-3*I)/d+arctanh(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[1/sqrt(-3-2*tan(d*x+c))/sqrt(tan(d*x+c)),x,7,arctan(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(-3-2*tan(d*x+c)))/sqrt(2-3*I)/d+arctan(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(-3-2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)),x,6,I*arctanh(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)))/sqrt(3-2*I)/d-I*arctanh(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(2+3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)),x,6,-I*arctanh(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)))/sqrt(3-2*I)/d+I*arctanh(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(-2+3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(2-3*tan(d*x+c)),x,6,-I*arctan(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(2-3*tan(d*x+c)))/sqrt(3-2*I)/d+I*arctan(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(2-3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(-2-3*tan(d*x+c)),x,6,I*arctan(sqrt(3-2*I)*sqrt(tan(d*x+c))/sqrt(-2-3*tan(d*x+c)))/sqrt(3-2*I)/d-I*arctan(sqrt(3+2*I)*sqrt(tan(d*x+c))/sqrt(-2-3*tan(d*x+c)))/sqrt(3+2*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)),x,6,I*arctanh(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)))/sqrt(2-3*I)/d-I*arctanh(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(3+2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(3-2*tan(d*x+c)),x,6,-I*arctan(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(3-2*tan(d*x+c)))/sqrt(2-3*I)/d+I*arctan(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(3-2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)),x,6,-I*arctanh(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)))/sqrt(2-3*I)/d+I*arctanh(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(-3+2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[sqrt(tan(d*x+c))/sqrt(-3-2*tan(d*x+c)),x,6,I*arctan(sqrt(2-3*I)*sqrt(tan(d*x+c))/sqrt(-3-2*tan(d*x+c)))/sqrt(2-3*I)/d-I*arctan(sqrt(2+3*I)*sqrt(tan(d*x+c))/sqrt(-3-2*tan(d*x+c)))/sqrt(2+3*I)/d,1],
[tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x,35,-1/2*b*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/(a^2+b^2)/d+1/2*b*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/(a^2+b^2)/d-sqrt(3)*a^(5/3)*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c)^(1/3))/sqrt(3)/a^(1/3))/b^(2/3)/(a^2+b^2)/d+1/2*sqrt(3)*a*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/(a^2+b^2)/d+b*arctan(tan(d*x+c)^(1/3))/(a^2+b^2)/d-3/2*a^(5/3)*ln(a^(1/3)+b^(1/3)*tan(d*x+c)^(1/3))/b^(2/3)/(a^2+b^2)/d-1/2*a*ln(1+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/4*sqrt(3)*b*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d-1/4*sqrt(3)*b*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/2*a^(5/3)*ln(a+b*tan(d*x+c))/b^(2/3)/(a^2+b^2)/d+1/4*a*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/(a^2+b^2)/d,1],
[tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x,32,-1/2*b*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/(a^2+b^2)/d+1/2*b*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/(a^2+b^2)/d+sqrt(3)*a^(1/3)*b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c)^(1/3))/sqrt(3)/a^(1/3))/(a^2+b^2)/d-1/2*sqrt(3)*a*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/(a^2+b^2)/d+b*arctan(tan(d*x+c)^(1/3))/(a^2+b^2)/d-3/2*a^(1/3)*b^(2/3)*ln(a^(1/3)+b^(1/3)*tan(d*x+c)^(1/3))/(a^2+b^2)/d-1/2*a*ln(1+tan(d*x+c)^(2/3))/(a^2+b^2)/d-1/4*sqrt(3)*b*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/4*sqrt(3)*b*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/2*a^(1/3)*b^(2/3)*ln(a+b*tan(d*x+c))/(a^2+b^2)/d+1/4*a*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/(a^2+b^2)/d,1],
[1/tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x,31,1/2*b*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/(a^2+b^2)/d-1/2*b*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/(a^2+b^2)/d-sqrt(3)*b^(4/3)*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c)^(1/3))/sqrt(3)/a^(1/3))/a^(1/3)/(a^2+b^2)/d-1/2*sqrt(3)*a*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/(a^2+b^2)/d-b*arctan(tan(d*x+c)^(1/3))/(a^2+b^2)/d-3/2*b^(4/3)*ln(a^(1/3)+b^(1/3)*tan(d*x+c)^(1/3))/a^(1/3)/(a^2+b^2)/d+1/2*a*ln(1+tan(d*x+c)^(2/3))/(a^2+b^2)/d-1/4*sqrt(3)*b*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/4*sqrt(3)*b*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/2*b^(4/3)*ln(a+b*tan(d*x+c))/a^(1/3)/(a^2+b^2)/d-1/4*a*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/(a^2+b^2)/d,1],
[1/tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x,32,1/2*b*arctan(sqrt(3)-2*tan(d*x+c)^(1/3))/(a^2+b^2)/d-1/2*b*arctan(sqrt(3)+2*tan(d*x+c)^(1/3))/(a^2+b^2)/d+sqrt(3)*b^(8/3)*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c)^(1/3))/sqrt(3)/a^(1/3))/a^(5/3)/(a^2+b^2)/d+1/2*sqrt(3)*a*arctan((1-2*tan(d*x+c)^(2/3))/sqrt(3))/(a^2+b^2)/d-b*arctan(tan(d*x+c)^(1/3))/(a^2+b^2)/d-3/2*b^(8/3)*ln(a^(1/3)+b^(1/3)*tan(d*x+c)^(1/3))/a^(5/3)/(a^2+b^2)/d+1/2*a*ln(1+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/4*sqrt(3)*b*ln(1-sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d-1/4*sqrt(3)*b*ln(1+sqrt(3)*tan(d*x+c)^(1/3)+tan(d*x+c)^(2/3))/(a^2+b^2)/d+1/2*b^(8/3)*ln(a+b*tan(d*x+c))/a^(5/3)/(a^2+b^2)/d-1/4*a*ln(1-tan(d*x+c)^(2/3)+tan(d*x+c)^(4/3))/(a^2+b^2)/d-3/2*a/(a^2+b^2)/d/tan(d*x+c)^(2/3)-3/2*b^2/a/(a^2+b^2)/d/tan(d*x+c)^(2/3),1],
[tan(d*x+c)^(4/3)/sqrt(a+b*tan(d*x+c)),x,7,3/14*AppellF1(7/3,1/2,1,10/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(7/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c))+3/14*AppellF1(7/3,1/2,1,10/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(7/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(2/3)/sqrt(a+b*tan(d*x+c)),x,7,3/10*AppellF1(5/3,1/2,1,8/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(5/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c))+3/10*AppellF1(5/3,1/2,1,8/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(5/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c)),1],
[tan(d*x+c)^(1/3)/sqrt(a+b*tan(d*x+c)),x,7,3/8*AppellF1(4/3,1/2,1,7/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(4/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c))+3/8*AppellF1(4/3,1/2,1,7/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(4/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(1/3)/sqrt(a+b*tan(d*x+c)),x,7,3/4*AppellF1(2/3,1/2,1,5/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(2/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c))+3/4*AppellF1(2/3,1/2,1,5/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(2/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(2/3)/sqrt(a+b*tan(d*x+c)),x,7,3/2*AppellF1(1/3,1/2,1,4/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(1/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c))+3/2*AppellF1(1/3,1/2,1,4/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(1/3)*sqrt((a+b*tan(d*x+c))/a)/d/sqrt(a+b*tan(d*x+c)),1],
[1/tan(d*x+c)^(4/3)/sqrt(a+b*tan(d*x+c)),x,7,-3/2*AppellF1(-1/3,1/2,1,2/3,-b*tan(d*x+c)/a,-I*tan(d*x+c))*sqrt((a+b*tan(d*x+c))/a)/d/tan(d*x+c)^(1/3)/sqrt(a+b*tan(d*x+c))-3/2*AppellF1(-1/3,1/2,1,2/3,-b*tan(d*x+c)/a,I*tan(d*x+c))*sqrt((a+b*tan(d*x+c))/a)/d/tan(d*x+c)^(1/3)/sqrt(a+b*tan(d*x+c)),1],
[tan(f*x+e)^4*(c+d*tan(f*x+e))^(1/3),x,20,-1/4*(c-sqrt(-d^2))^(1/3)*x-1/4*(c+sqrt(-d^2))^(1/3)*x-1/2*sqrt(3)*sqrt(-d^2)*(c-sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-sqrt(-d^2))^(1/3))/sqrt(3))/d/f+1/2*sqrt(3)*sqrt(-d^2)*(c+sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+sqrt(-d^2))^(1/3))/sqrt(3))/d/f+1/4*sqrt(-d^2)*(c-sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/d/f-1/4*sqrt(-d^2)*(c+sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/d/f+3/4*sqrt(-d^2)*(c-sqrt(-d^2))^(1/3)*ln((c-sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/d/f-3/4*sqrt(-d^2)*(c+sqrt(-d^2))^(1/3)*ln((c+sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/d/f+3/140*(9*c^2-35*d^2)*(c+d*tan(f*x+e))^(4/3)/d^3/f-9/35*c*tan(f*x+e)*(c+d*tan(f*x+e))^(4/3)/d^2/f+3/10*tan(f*x+e)^2*(c+d*tan(f*x+e))^(4/3)/d/f,1],
[tan(f*x+e)^3*(c+d*tan(f*x+e))^(1/3),x,19,-1/4*I*(c-I*d)^(1/3)*x+1/4*I*(c+I*d)^(1/3)*x+1/2*sqrt(3)*(c-I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-I*d)^(1/3))/sqrt(3))/f+1/2*sqrt(3)*(c+I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+I*d)^(1/3))/sqrt(3))/f-1/4*(c-I*d)^(1/3)*ln(cos(f*x+e))/f-1/4*(c+I*d)^(1/3)*ln(cos(f*x+e))/f-3/4*(c-I*d)^(1/3)*ln((c-I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f-3/4*(c+I*d)^(1/3)*ln((c+I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f-3*(c+d*tan(f*x+e))^(1/3)/f-9/28*c*(c+d*tan(f*x+e))^(4/3)/d^2/f+3/7*tan(f*x+e)*(c+d*tan(f*x+e))^(4/3)/d/f,1],
[tan(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x,18,1/4*(c-sqrt(-d^2))^(1/3)*x+1/4*(c+sqrt(-d^2))^(1/3)*x-1/2*sqrt(3)*d*(c-sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f+1/2*sqrt(3)*d*(c+sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f+1/4*d*(c-sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f-1/4*d*(c+sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f+3/4*d*(c-sqrt(-d^2))^(1/3)*ln((c-sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f-3/4*d*(c+sqrt(-d^2))^(1/3)*ln((c+sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f+3/4*(c+d*tan(f*x+e))^(4/3)/d/f,1],
[tan(f*x+e)*(c+d*tan(f*x+e))^(1/3),x,16,1/4*I*(c-I*d)^(1/3)*x-1/4*I*(c+I*d)^(1/3)*x-1/2*sqrt(3)*(c-I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-I*d)^(1/3))/sqrt(3))/f-1/2*sqrt(3)*(c+I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+I*d)^(1/3))/sqrt(3))/f+1/4*(c-I*d)^(1/3)*ln(cos(f*x+e))/f+1/4*(c+I*d)^(1/3)*ln(cos(f*x+e))/f+3/4*(c-I*d)^(1/3)*ln((c-I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f+3/4*(c+I*d)^(1/3)*ln((c+I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f+3*(c+d*tan(f*x+e))^(1/3)/f,1],
[(c+d*tan(f*x+e))^(1/3),x,17,-1/4*(c-sqrt(-d^2))^(1/3)*x-1/4*(c+sqrt(-d^2))^(1/3)*x+1/2*sqrt(3)*d*(c-sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f-1/2*sqrt(3)*d*(c+sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f-1/4*d*(c-sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f+1/4*d*(c+sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f-3/4*d*(c-sqrt(-d^2))^(1/3)*ln((c-sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f+3/4*d*(c+sqrt(-d^2))^(1/3)*ln((c+sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f,1],
[cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x,25,-1/4*I*(c-I*d)^(1/3)*x+1/4*I*(c+I*d)^(1/3)*x-sqrt(3)*c^(1/3)*arctan((c^(1/3)+2*(c+d*tan(f*x+e))^(1/3))/sqrt(3)/c^(1/3))/f+1/2*sqrt(3)*(c-I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-I*d)^(1/3))/sqrt(3))/f+1/2*sqrt(3)*(c+I*d)^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+I*d)^(1/3))/sqrt(3))/f-1/4*(c-I*d)^(1/3)*ln(cos(f*x+e))/f-1/4*(c+I*d)^(1/3)*ln(cos(f*x+e))/f-1/2*c^(1/3)*ln(tan(f*x+e))/f+3/2*c^(1/3)*ln(c^(1/3)-(c+d*tan(f*x+e))^(1/3))/f-3/4*(c-I*d)^(1/3)*ln((c-I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f-3/4*(c+I*d)^(1/3)*ln((c+I*d)^(1/3)-(c+d*tan(f*x+e))^(1/3))/f,1],
[cot(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x,26,1/4*(c-sqrt(-d^2))^(1/3)*x+1/4*(c+sqrt(-d^2))^(1/3)*x-d*arctan((c^(1/3)+2*(c+d*tan(f*x+e))^(1/3))/sqrt(3)/c^(1/3))/sqrt(3)/c^(2/3)/f-1/2*sqrt(3)*d*(c-sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c-sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f+1/2*sqrt(3)*d*(c+sqrt(-d^2))^(1/3)*arctan((1+2*(c+d*tan(f*x+e))^(1/3)/(c+sqrt(-d^2))^(1/3))/sqrt(3))/sqrt(-d^2)/f+1/4*d*(c-sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f-1/4*d*(c+sqrt(-d^2))^(1/3)*ln(cos(f*x+e))/sqrt(-d^2)/f-1/6*d*ln(tan(f*x+e))/c^(2/3)/f+1/2*d*ln(c^(1/3)-(c+d*tan(f*x+e))^(1/3))/c^(2/3)/f+3/4*d*(c-sqrt(-d^2))^(1/3)*ln((c-sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f-3/4*d*(c+sqrt(-d^2))^(1/3)*ln((c+sqrt(-d^2))^(1/3)-(c+d*tan(f*x+e))^(1/3))/sqrt(-d^2)/f-cot(f*x+e)*(c+d*tan(f*x+e))^(1/3)/f,1],
[(a+b*tan(d*x+c))^(5/3),x,18,-1/4*(a-I*b)^(5/3)*x-1/4*(a+I*b)^(5/3)*x+1/2*I*sqrt(3)*(a-I*b)^(5/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-I*b)^(1/3))/sqrt(3))/d-1/2*I*sqrt(3)*(a+I*b)^(5/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+I*b)^(1/3))/sqrt(3))/d+1/4*I*(a-I*b)^(5/3)*ln(cos(d*x+c))/d-1/4*I*(a+I*b)^(5/3)*ln(cos(d*x+c))/d+3/4*I*(a-I*b)^(5/3)*ln((a-I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/d-3/4*I*(a+I*b)^(5/3)*ln((a+I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/d+3/2*b*(a+b*tan(d*x+c))^(2/3)/d,1],
[(a+b*tan(d*x+c))^(4/3),x,16,-1/4*(a-I*b)^(4/3)*x-1/4*(a+I*b)^(4/3)*x-1/2*I*sqrt(3)*(a-I*b)^(4/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-I*b)^(1/3))/sqrt(3))/d+1/2*I*sqrt(3)*(a+I*b)^(4/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+I*b)^(1/3))/sqrt(3))/d+1/4*I*(a-I*b)^(4/3)*ln(cos(d*x+c))/d-1/4*I*(a+I*b)^(4/3)*ln(cos(d*x+c))/d+3/4*I*(a-I*b)^(4/3)*ln((a-I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/d-3/4*I*(a+I*b)^(4/3)*ln((a+I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/d+3*b*(a+b*tan(d*x+c))^(1/3)/d,1],
[(a+b*tan(d*x+c))^(2/3),x,19,-1/4*(a-sqrt(-b^2))^(2/3)*x-1/4*(a+sqrt(-b^2))^(2/3)*x-1/2*sqrt(3)*b*(a-sqrt(-b^2))^(2/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/d+1/2*sqrt(3)*b*(a+sqrt(-b^2))^(2/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/d-1/4*b*(a-sqrt(-b^2))^(2/3)*ln(cos(d*x+c))/sqrt(-b^2)/d+1/4*b*(a+sqrt(-b^2))^(2/3)*ln(cos(d*x+c))/sqrt(-b^2)/d-3/4*b*(a-sqrt(-b^2))^(2/3)*ln((a-sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/d+3/4*b*(a+sqrt(-b^2))^(2/3)*ln((a+sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/d,1],
[(a+b*tan(d*x+c))^(1/3),x,17,-1/4*(a-sqrt(-b^2))^(1/3)*x-1/4*(a+sqrt(-b^2))^(1/3)*x+1/2*sqrt(3)*b*(a-sqrt(-b^2))^(1/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/d-1/2*sqrt(3)*b*(a+sqrt(-b^2))^(1/3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/d-1/4*b*(a-sqrt(-b^2))^(1/3)*ln(cos(d*x+c))/sqrt(-b^2)/d+1/4*b*(a+sqrt(-b^2))^(1/3)*ln(cos(d*x+c))/sqrt(-b^2)/d-3/4*b*(a-sqrt(-b^2))^(1/3)*ln((a-sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/d+3/4*b*(a+sqrt(-b^2))^(1/3)*ln((a+sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/d,1],
[1/(a+b*tan(d*x+c))^(1/3),x,17,-1/4*x/(a-sqrt(-b^2))^(1/3)-1/4*x/(a+sqrt(-b^2))^(1/3)-1/2*sqrt(3)*b*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/(a-sqrt(-b^2))^(1/3)/d+1/2*sqrt(3)*b*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/(a+sqrt(-b^2))^(1/3)/d-1/4*b*ln(cos(d*x+c))/sqrt(-b^2)/(a-sqrt(-b^2))^(1/3)/d+1/4*b*ln(cos(d*x+c))/sqrt(-b^2)/(a+sqrt(-b^2))^(1/3)/d-3/4*b*ln((a-sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/(a-sqrt(-b^2))^(1/3)/d+3/4*b*ln((a+sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/(a+sqrt(-b^2))^(1/3)/d,1],
[1/(a+b*tan(d*x+c))^(2/3),x,15,-1/4*x/(a-sqrt(-b^2))^(2/3)-1/4*x/(a+sqrt(-b^2))^(2/3)+1/2*sqrt(3)*b*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/(a-sqrt(-b^2))^(2/3)/d-1/2*sqrt(3)*b*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+sqrt(-b^2))^(1/3))/sqrt(3))/sqrt(-b^2)/(a+sqrt(-b^2))^(2/3)/d-1/4*b*ln(cos(d*x+c))/sqrt(-b^2)/(a-sqrt(-b^2))^(2/3)/d+1/4*b*ln(cos(d*x+c))/sqrt(-b^2)/(a+sqrt(-b^2))^(2/3)/d-3/4*b*ln((a-sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/(a-sqrt(-b^2))^(2/3)/d+3/4*b*ln((a+sqrt(-b^2))^(1/3)-(a+b*tan(d*x+c))^(1/3))/sqrt(-b^2)/(a+sqrt(-b^2))^(2/3)/d,1],
[1/(a+b*tan(d*x+c))^(4/3),x,18,-1/4*x/(a-I*b)^(4/3)-1/4*x/(a+I*b)^(4/3)+1/2*I*sqrt(3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-I*b)^(1/3))/sqrt(3))/(a-I*b)^(4/3)/d-1/2*I*sqrt(3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+I*b)^(1/3))/sqrt(3))/(a+I*b)^(4/3)/d+1/4*I*ln(cos(d*x+c))/(a-I*b)^(4/3)/d-1/4*I*ln(cos(d*x+c))/(a+I*b)^(4/3)/d+3/4*I*ln((a-I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/(a-I*b)^(4/3)/d-3/4*I*ln((a+I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/(a+I*b)^(4/3)/d-3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(1/3),1],
[1/(a+b*tan(d*x+c))^(5/3),x,16,-1/4*x/(a-I*b)^(5/3)-1/4*x/(a+I*b)^(5/3)-1/2*I*sqrt(3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a-I*b)^(1/3))/sqrt(3))/(a-I*b)^(5/3)/d+1/2*I*sqrt(3)*arctan((1+2*(a+b*tan(d*x+c))^(1/3)/(a+I*b)^(1/3))/sqrt(3))/(a+I*b)^(5/3)/d+1/4*I*ln(cos(d*x+c))/(a-I*b)^(5/3)/d-1/4*I*ln(cos(d*x+c))/(a+I*b)^(5/3)/d+3/4*I*ln((a-I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/(a-I*b)^(5/3)/d-3/4*I*ln((a+I*b)^(1/3)-(a+b*tan(d*x+c))^(1/3))/(a+I*b)^(5/3)/d-3/2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^(2/3),1],
[(d*tan(f*x+e))^n*(a+b*tan(f*x+e))^4,x,8,-b^2*(b^2*(3+n)-a^2*(17+5*n))*(d*tan(f*x+e))^(1+n)/d/f/(1+n)/(3+n)+(a^4-6*a^2*b^2+b^4)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+2*a*b^3*(4+n)*tan(f*x+e)*(d*tan(f*x+e))^(1+n)/d/f/(2+n)/(3+n)+4*a*b*(a^2-b^2)*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/d^2/f/(2+n)+b^2*(d*tan(f*x+e))^(1+n)*(a+b*tan(f*x+e))^2/d/f/(3+n),1],
[(d*tan(f*x+e))^n*(a+b*tan(f*x+e))^3,x,7,a*b^2*(5+2*n)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)/(2+n)+a*(a^2-3*b^2)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+b*(3*a^2-b^2)*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/d^2/f/(2+n)+b^2*(d*tan(f*x+e))^(1+n)*(a+b*tan(f*x+e))/d/f/(2+n),1],
[(d*tan(f*x+e))^n*(a+b*tan(f*x+e))^2,x,6,b^2*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+(a^2-b^2)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+2*a*b*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/d^2/f/(2+n),1],
[(d*tan(f*x+e))^n*(a+b*tan(f*x+e)),x,5,a*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/d/f/(1+n)+b*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/d^2/f/(2+n),1],
[(d*tan(f*x+e))^n/(a+b*tan(f*x+e)),x,8,a*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/(a^2+b^2)/d/f/(1+n)+b^2*hypergeom([1, 1+n],[2+n],-b*tan(f*x+e)/a)*(d*tan(f*x+e))^(1+n)/a/(a^2+b^2)/d/f/(1+n)-b*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/(a^2+b^2)/d^2/f/(2+n),1],
[(d*tan(f*x+e))^n/(a+b*tan(f*x+e))^2,x,9,(a^2-b^2)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(1+n)/(a^2+b^2)^2/d/f/(1+n)+b^2*(a^2*(2-n)-b^2*n)*hypergeom([1, 1+n],[2+n],-b*tan(f*x+e)/a)*(d*tan(f*x+e))^(1+n)/a^2/(a^2+b^2)^2/d/f/(1+n)-2*a*b*hypergeom([1, 1+1/2*n],[2+1/2*n],-tan(f*x+e)^2)*(d*tan(f*x+e))^(2+n)/(a^2+b^2)^2/d^2/f/(2+n)+b^2*(d*tan(f*x+e))^(1+n)/a/(a^2+b^2)/d/f/(a+b*tan(f*x+e)),1],
[tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2),x,7,1/5*AppellF1(5/2,-m,1,7/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a-I*b))*tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)/(I*a+b)/d/((-b*tan(d*x+c)/a)^m)-1/5*AppellF1(5/2,-m,1,7/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a+I*b))*tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)/(I*a-b)/d/((-b*tan(d*x+c)/a)^m),1],
[tan(d*x+c)^m*sqrt(a+b*tan(d*x+c)),x,7,1/3*AppellF1(3/2,-m,1,5/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a-I*b))*tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)/(I*a+b)/d/((-b*tan(d*x+c)/a)^m)-1/3*AppellF1(3/2,-m,1,5/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a+I*b))*tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)/(I*a-b)/d/((-b*tan(d*x+c)/a)^m),1],
[tan(d*x+c)^m/sqrt(a+b*tan(d*x+c)),x,7,AppellF1(1/2,-m,1,3/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a-I*b))*tan(d*x+c)^m*sqrt(a+b*tan(d*x+c))/(I*a+b)/d/((-b*tan(d*x+c)/a)^m)-AppellF1(1/2,-m,1,3/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a+I*b))*tan(d*x+c)^m*sqrt(a+b*tan(d*x+c))/(I*a-b)/d/((-b*tan(d*x+c)/a)^m),1],
[tan(d*x+c)^m/(a+b*tan(d*x+c))^(3/2),x,7,-AppellF1(-1/2,-m,1,1/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a-I*b))*tan(d*x+c)^m/(I*a+b)/d/((-b*tan(d*x+c)/a)^m)/sqrt(a+b*tan(d*x+c))+AppellF1(-1/2,-m,1,1/2,(a+b*tan(d*x+c))/a,(a+b*tan(d*x+c))/(a+I*b))*tan(d*x+c)^m/(I*a-b)/d/((-b*tan(d*x+c)/a)^m)/sqrt(a+b*tan(d*x+c)),1],
[(d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x,7,1/2*AppellF1(1+n,-m,1,2+n,-b*tan(f*x+e)/a,-I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)*(a+b*tan(f*x+e))^m/d/f/(1+n)/(((a+b*tan(f*x+e))/a)^m)+1/2*AppellF1(1+n,-m,1,2+n,-b*tan(f*x+e)/a,I*tan(f*x+e))*(d*tan(f*x+e))^(1+n)*(a+b*tan(f*x+e))^m/d/f/(1+n)/(((a+b*tan(f*x+e))/a)^m),1],
[tan(d*x+c)^4*(a+b*tan(d*x+c))^n,x,8,(2*a^2-b^2*(2+n)*(3+n))*(a+b*tan(d*x+c))^(1+n)/b^3/d/(1+n)/(2+n)/(3+n)-1/2*sqrt(-b^2)*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a-sqrt(-b^2))/d/(1+n)+1/2*sqrt(-b^2)*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a+sqrt(-b^2))/d/(1+n)-2*a*tan(d*x+c)*(a+b*tan(d*x+c))^(1+n)/b^2/d/(2+n)/(3+n)+tan(d*x+c)^2*(a+b*tan(d*x+c))^(1+n)/b/d/(3+n),1],
[tan(d*x+c)^3*(a+b*tan(d*x+c))^n,x,8,-a*(a+b*tan(d*x+c))^(1+n)/b^2/d/(1+n)/(2+n)+1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-I*b))*(a+b*tan(d*x+c))^(1+n)/(a-I*b)/d/(1+n)+1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+I*b))*(a+b*tan(d*x+c))^(1+n)/(a+I*b)/d/(1+n)+tan(d*x+c)*(a+b*tan(d*x+c))^(1+n)/b/d/(2+n),1],
[tan(d*x+c)^2*(a+b*tan(d*x+c))^n,x,6,(a+b*tan(d*x+c))^(1+n)/b/d/(1+n)-1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a-sqrt(-b^2))/d/(1+n)+1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a+sqrt(-b^2))/d/(1+n),1],
[tan(d*x+c)*(a+b*tan(d*x+c))^n,x,5,-1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-I*b))*(a+b*tan(d*x+c))^(1+n)/(a-I*b)/d/(1+n)-1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+I*b))*(a+b*tan(d*x+c))^(1+n)/(a+I*b)/d/(1+n),1],
[(a+b*tan(d*x+c))^n,x,5,1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a-sqrt(-b^2))/d/(1+n)-1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a+sqrt(-b^2))/d/(1+n),1],
[cot(d*x+c)*(a+b*tan(d*x+c))^n,x,8,-hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/a)*(a+b*tan(d*x+c))^(1+n)/a/d/(1+n)+1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-I*b))*(a+b*tan(d*x+c))^(1+n)/(a-I*b)/d/(1+n)+1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+I*b))*(a+b*tan(d*x+c))^(1+n)/(a+I*b)/d/(1+n),1],
[cot(d*x+c)^2*(a+b*tan(d*x+c))^n,x,10,-cot(d*x+c)*(a+b*tan(d*x+c))^(1+n)/a/d-b*n*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/a)*(a+b*tan(d*x+c))^(1+n)/a^2/d/(1+n)-1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a-sqrt(-b^2))/d/(1+n)+1/2*b*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/sqrt(-b^2)/(a+sqrt(-b^2))/d/(1+n),1],
[cot(d*x+c)^3*(a+b*tan(d*x+c))^n,x,11,1/2*b*(1-n)*cot(d*x+c)*(a+b*tan(d*x+c))^(1+n)/a^2/d-1/2*cot(d*x+c)^2*(a+b*tan(d*x+c))^(1+n)/a/d+1/2*(2*a^2+b^2*(1-n)*n)*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/a)*(a+b*tan(d*x+c))^(1+n)/a^3/d/(1+n)-1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-I*b))*(a+b*tan(d*x+c))^(1+n)/(a-I*b)/d/(1+n)-1/2*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+I*b))*(a+b*tan(d*x+c))^(1+n)/(a+I*b)/d/(1+n),1],
[tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x,7,1/5*AppellF1(5/2,-n,1,7/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n)+1/5*AppellF1(5/2,-n,1,7/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n),1],
[sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^n,x,7,1/3*AppellF1(3/2,-n,1,5/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n)+1/3*AppellF1(3/2,-n,1,5/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n),1],
[(a+b*tan(d*x+c))^n/sqrt(tan(d*x+c)),x,7,AppellF1(1/2,-n,1,3/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n)+AppellF1(1/2,-n,1,3/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*sqrt(tan(d*x+c))*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n),1],
[(a+b*tan(d*x+c))^n/tan(d*x+c)^(3/2),x,7,-AppellF1(-1/2,-n,1,1/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/sqrt(tan(d*x+c))/(((a+b*tan(d*x+c))/a)^n)-AppellF1(-1/2,-n,1,1/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/sqrt(tan(d*x+c))/(((a+b*tan(d*x+c))/a)^n),1],
[cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c)),x,5,-2*(-1)^(3/4)*a*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2*I*a*sqrt(cot(d*x+c))/d-2/3*a*cot(d*x+c)^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c)),x,4,-2*(-1)^(1/4)*a*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2*a*sqrt(cot(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c)),x,3,2*(-1)^(3/4)*a*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d,1],
[(a+I*a*tan(d*x+c))/sqrt(cot(d*x+c)),x,4,2*(-1)^(1/4)*a*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d+2*I*a/d/sqrt(cot(d*x+c)),1],
[(a+I*a*tan(d*x+c))/cot(d*x+c)^(3/2),x,5,-2*(-1)^(3/4)*a*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d+2/3*I*a/d/cot(d*x+c)^(3/2)+2*a/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2,x,6,4*(-1)^(1/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d+4*a^2*sqrt(cot(d*x+c))/d-4/3*I*a^2*cot(d*x+c)^(3/2)/d-2/5*a^2*cot(d*x+c)^(5/2)/d,1],
[cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2,x,5,-4*(-1)^(3/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-4*I*a^2*sqrt(cot(d*x+c))/d-2/3*a^2*cot(d*x+c)^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2,x,4,-4*(-1)^(1/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2*a^2*sqrt(cot(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^2,x,4,4*(-1)^(3/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2*a^2/d/sqrt(cot(d*x+c)),1],
[(a+I*a*tan(d*x+c))^2/sqrt(cot(d*x+c)),x,5,4*(-1)^(1/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2/3*a^2/d/cot(d*x+c)^(3/2)+4*I*a^2/d/sqrt(cot(d*x+c)),1],
[(a+I*a*tan(d*x+c))^2/cot(d*x+c)^(3/2),x,6,-4*(-1)^(3/4)*a^2*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2/5*a^2/d/cot(d*x+c)^(5/2)+4/3*I*a^2/d/cot(d*x+c)^(3/2)+4*a^2/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3,x,6,8*(-1)^(1/4)*a^3*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d+8*a^3*sqrt(cot(d*x+c))/d-8/5*I*a^3*cot(d*x+c)^(3/2)/d-2/5*cot(d*x+c)^(3/2)*(I*a^3+a^3*cot(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3,x,5,-8*(-1)^(3/4)*a^3*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-16/3*I*a^3*sqrt(cot(d*x+c))/d-2/3*sqrt(cot(d*x+c))*(I*a^3+a^3*cot(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3,x,5,-8*(-1)^(1/4)*a^3*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-2*(I*a^3+a^3*cot(d*x+c))/d/sqrt(cot(d*x+c)),1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^3,x,5,8*(-1)^(3/4)*a^3*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-16/3*a^3/d/sqrt(cot(d*x+c))-2/3*(I*a^3+a^3*cot(d*x+c))/d/cot(d*x+c)^(3/2),1],
[(a+I*a*tan(d*x+c))^3/sqrt(cot(d*x+c)),x,6,8*(-1)^(1/4)*a^3*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/d-8/5*a^3/d/cot(d*x+c)^(3/2)+8*I*a^3/d/sqrt(cot(d*x+c))-2/5*(I*a^3+a^3*cot(d*x+c))/d/cot(d*x+c)^(5/2),1],
[cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x,12,(-5/4-3/4*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(5/4+3/4*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(5/4-3/4*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a/d-5/2*sqrt(cot(d*x+c))/a/d+1/2*cot(d*x+c)^(3/2)/d/(I*a+a*cot(d*x+c)),1],
[sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c)),x,11,(3/4-1/4*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(-3/4+1/4*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(3/4+1/4*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a/d+1/2*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c)),x,4,1/2*(-1)^(1/4)*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/a/d+1/2*I*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x,11,(1/4-3/4*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(-1/4+3/4*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(1/4+3/4*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a/d-1/2*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x,12,(3/4+5/4*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d-(3/4+5/4*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a/d+(-3/4+5/4*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a/d-5/2*I/a/d/sqrt(cot(d*x+c))-1/2/d/sqrt(cot(d*x+c))/(I*a+a*cot(d*x+c)),1],
[cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x,13,(-25/16-21/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(25/16+21/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(25/16-21/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d-25/8*sqrt(cot(d*x+c))/a^2/d+7/8*cot(d*x+c)^(3/2)/a^2/d/(I+cot(d*x+c))+1/4*cot(d*x+c)^(5/2)/d/(I*a+a*cot(d*x+c))^2,1],
[sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^2,x,12,(9/16-5/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(-9/16+5/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(9/16+5/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d+5/8*sqrt(cot(d*x+c))/a^2/d/(I+cot(d*x+c))+1/4*cot(d*x+c)^(3/2)/d/(I*a+a*cot(d*x+c))^2,1],
[1/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^2,x,12,(1/16-3/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(-1/16+3/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d-(1/16+3/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d+3/8*I*sqrt(cot(d*x+c))/a^2/d/(I+cot(d*x+c))+1/4*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^2,1],
[1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x,12,(-1/16-3/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(1/16+3/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(-1/16+3/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d+1/8*sqrt(cot(d*x+c))/a^2/d/(I+cot(d*x+c))+1/4*I*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^2,1],
[1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x,12,(-9/16-5/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(9/16+5/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(9/16-5/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d+5/8*I*sqrt(cot(d*x+c))/a^2/d/(I+cot(d*x+c))-1/4*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^2,1],
[1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^2,x,13,(25/16-21/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(-25/16+21/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^2/d+(25/16+21/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^2/d-25/8/a^2/d/sqrt(cot(d*x+c))+7/8*I/a^2/d/sqrt(cot(d*x+c))/(I+cot(d*x+c))-1/4/d/sqrt(cot(d*x+c))/(I*a+a*cot(d*x+c))^2,1],
[sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^3,x,13,(7/16-5/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+(-7/16+5/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+(7/16+5/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^3/d+1/6*cot(d*x+c)^(5/2)/d/(I*a+a*cot(d*x+c))^3+1/3*cot(d*x+c)^(3/2)/a/d/(I*a+a*cot(d*x+c))^2+5/8*sqrt(cot(d*x+c))/d/(I*a^3+a^3*cot(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^3,x,15,-1/8*I*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+1/8*I*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d-1/8*I*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^3/d+1/6*cot(d*x+c)^(3/2)/d/(I*a+a*cot(d*x+c))^3+1/4*sqrt(cot(d*x+c))/a/d/(I*a+a*cot(d*x+c))^2+1/4*I*sqrt(cot(d*x+c))/d/(I*a^3+a^3*cot(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x,7,-1/8*(-1)^(3/4)*arctanh((-1)^(3/4)*sqrt(cot(d*x+c)))/a^3/d+1/6*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^3+1/6*I*sqrt(cot(d*x+c))/a/d/(I*a+a*cot(d*x+c))^2+1/8*sqrt(cot(d*x+c))/d/(I*a^3+a^3*cot(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x,14,-1/8*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+1/8*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+1/8*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^3/d+1/6*I*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^3+1/12*sqrt(cot(d*x+c))/a/d/(I*a+a*cot(d*x+c))^2,1],
[1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x,13,(-5/16+7/16*I)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d+(5/16-7/16*I)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/a^3/d-(5/16+7/16*I)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/a^3/d-1/6*sqrt(cot(d*x+c))/d/(I*a+a*cot(d*x+c))^3+1/3*I*sqrt(cot(d*x+c))/a/d/(I*a+a*cot(d*x+c))^2+5/8*sqrt(cot(d*x+c))/d/(I*a^3+a^3*cot(d*x+c)),1],
[cot(d*x+c)^(7/2)*sqrt(a+I*a*tan(d*x+c)),x,7,(-1-I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+26/15*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-2/15*I*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d-2/5*cot(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c)),x,6,(-1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2/3*I*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-2/3*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c)),x,4,(1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c)),x,3,(1-I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[sqrt(a+I*a*tan(d*x+c))/sqrt(cot(d*x+c)),x,7,-2*(-1)^(3/4)*sqrt(a)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[sqrt(a+I*a*tan(d*x+c))/cot(d*x+c)^(3/2),x,9,-(-1)^(1/4)*sqrt(a)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(-1+I)*sqrt(a)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+sqrt(a+I*a*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2),x,8,(-2-2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2/5*I*a^2*cot(d*x+c)^(3/2)/d/sqrt(a+I*a*tan(d*x+c))-2/5*a^2*cot(d*x+c)^(5/2)/d/sqrt(a+I*a*tan(d*x+c))+12/5*a*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-4/5*I*a*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x,5,(-2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*I*a*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-2/3*cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x,4,(2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*a*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^(3/2),x,7,2*(-1)^(1/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(2-2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[(a+I*a*tan(d*x+c))^(3/2)/sqrt(cot(d*x+c)),x,9,-3*(-1)^(3/4)*a^(3/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(2+2*I)*a^(3/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-a^2/d/cot(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))+I*a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2),x,8,(4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+104/21*I*a^2*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d+32/21*a^2*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/d-6/7*I*a^2*cot(d*x+c)^(5/2)*sqrt(a+I*a*tan(d*x+c))/d-2/7*a^2*cot(d*x+c)^(7/2)*sqrt(a+I*a*tan(d*x+c))/d,1],
[cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2),x,6,(-4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+4*a^2*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-2/3*I*a*cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)/d-2/5*cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2)/d,1],
[cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x,5,(-4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-4*I*a^2*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d-2/3*a*cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x,8,2*(-1)^(3/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*a^2*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^(5/2),x,8,5*(-1)^(1/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(4-4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[(a+I*a*tan(d*x+c))^(5/2)/sqrt(cot(d*x+c)),x,9,-23/4*(-1)^(3/4)*a^(5/2)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(4+4*I)*a^(5/2)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-1/2*a^2*sqrt(a+I*a*tan(d*x+c))/d/cot(d*x+c)^(3/2)+9/4*I*a^2*sqrt(a+I*a*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c)),x,7,(-1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+cot(d*x+c)^(3/2)/d/sqrt(a+I*a*tan(d*x+c))+7/3*I*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a/d-5/3*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[cot(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c)),x,6,(1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+sqrt(cot(d*x+c))/d/sqrt(a+I*a*tan(d*x+c))-3*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a/d,1],
[sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),x,5,(1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+1/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),x,4,(-1/2-1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+I/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c)),x,8,-2*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+(-1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d-1/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/sqrt(a+I*a*tan(d*x+c)),x,9,-(-1)^(3/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d+(1/2+1/2*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(a)/d-1/d/cot(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-2*I*sqrt(a+I*a*tan(d*x+c))/a/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x,8,(-1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+1/3*cot(d*x+c)^(3/2)/d/(a+I*a*tan(d*x+c))^(3/2)+5/2*cot(d*x+c)^(3/2)/a/d/sqrt(a+I*a*tan(d*x+c))+13/2*I*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^2/d-7/2*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x,7,(1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+1/3*sqrt(cot(d*x+c))/d/(a+I*a*tan(d*x+c))^(3/2)+11/6*sqrt(cot(d*x+c))/a/d/sqrt(a+I*a*tan(d*x+c))-25/6*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^2/d,1],
[sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x,6,(1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+1/3/d/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(3/2)+7/6/a/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x,5,(-1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+1/3/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+1/2*I/a/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x,5,(-1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+1/3*I/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+1/2/a/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x,9,2*(-1)^(3/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+(1/4+1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d-1/3/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+3/2*I/a/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x,10,-3*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d+(1/4-1/4*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(3/2)/d-1/3/d/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2)+13/6*I/a/d/cot(d*x+c)^(3/2)/sqrt(a+I*a*tan(d*x+c))-7/2*sqrt(a+I*a*tan(d*x+c))/a^2/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x,9,(-1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5*cot(d*x+c)^(3/2)/d/(a+I*a*tan(d*x+c))^(5/2)+7/10*cot(d*x+c)^(3/2)/a/d/(a+I*a*tan(d*x+c))^(3/2)+89/20*cot(d*x+c)^(3/2)/a^2/d/sqrt(a+I*a*tan(d*x+c))+707/60*I*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^3/d-361/60*cot(d*x+c)^(3/2)*sqrt(a+I*a*tan(d*x+c))/a^3/d,1],
[cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x,8,(1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5*sqrt(cot(d*x+c))/d/(a+I*a*tan(d*x+c))^(5/2)+17/30*sqrt(cot(d*x+c))/a/d/(a+I*a*tan(d*x+c))^(3/2)+151/60*sqrt(cot(d*x+c))/a^2/d/sqrt(a+I*a*tan(d*x+c))-317/60*sqrt(cot(d*x+c))*sqrt(a+I*a*tan(d*x+c))/a^3/d,1],
[sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x,7,(1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5/d/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(5/2)+13/30/a/d/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(3/2)+67/60/a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x,7,(-1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5*I/d/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(5/2)+1/10*I/a/d/sqrt(cot(d*x+c))/(a+I*a*tan(d*x+c))^(3/2)-1/20*I/a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x,6,(-1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5/d/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2)+1/6*I/a/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+1/4/a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x,6,(1/8+1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+1/5*I/d/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2)+1/6/a/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)-1/4*I/a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x,10,2*(-1)^(1/4)*arctan((-1)^(3/4)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d+(1/8-1/8*I)*arctanh((1+I)*sqrt(a)*sqrt(tan(d*x+c))/sqrt(a+I*a*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/a^(5/2)/d-1/5/d/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2)+1/2*I/a/d/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2)+7/4/a^2/d/sqrt(cot(d*x+c))/sqrt(a+I*a*tan(d*x+c)),1],
[(d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x,6,I*a^3*d^2*(1-2*n)*(d*cot(f*x+e))^(-2+n)/f/(1-n)/(2-n)+d^2*(d*cot(f*x+e))^(-2+n)*(I*a^3+a^3*cot(f*x+e))/f/(1-n)-4*I*a^3*d^2*(d*cot(f*x+e))^(-2+n)*hypergeom([1, -2+n],[-1+n],-I*cot(f*x+e))/f/(2-n),1],
[(d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x,5,a^2*d*(d*cot(f*x+e))^(-1+n)/f/(1-n)-2*a^2*d*(d*cot(f*x+e))^(-1+n)*hypergeom([1, -1+n],[n],-I*cot(f*x+e))/f/(1-n),1],
[(d*cot(f*x+e))^n*(a+I*a*tan(f*x+e)),x,3,-I*a*(d*cot(f*x+e))^n*hypergeom([1, n],[1+n],-I*cot(f*x+e))/f/n,1],
[(d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x,7,-1/2*(d*cot(f*x+e))^(2+n)/d^2/f/(I*a+a*cot(f*x+e))-1/2*I*n*(d*cot(f*x+e))^(2+n)*hypergeom([1, 1+1/2*n],[2+1/2*n],-cot(f*x+e)^2)/a/d^2/f/(2+n)+1/2*(1+n)*(d*cot(f*x+e))^(3+n)*hypergeom([1, 3/2+1/2*n],[5/2+1/2*n],-cot(f*x+e)^2)/a/d^3/f/(3+n),1],
[(d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x,8,-1/4*I*n*(d*cot(f*x+e))^(3+n)/a^2/d^3/f/(I+cot(f*x+e))-1/4*(d*cot(f*x+e))^(3+n)/d^3/f/(I*a+a*cot(f*x+e))^2+1/4*(1+n)^2*(d*cot(f*x+e))^(3+n)*hypergeom([1, 3/2+1/2*n],[5/2+1/2*n],-cot(f*x+e)^2)/a^2/d^3/f/(3+n)+1/4*I*n*(2+n)*(d*cot(f*x+e))^(4+n)*hypergeom([1, 2+1/2*n],[3+1/2*n],-cot(f*x+e)^2)/a^2/d^4/f/(4+n),1],
[(d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x,4,AppellF1(1-n,1-m,1,2-n,-I*tan(f*x+e),I*tan(f*x+e))*(d*cot(f*x+e))^n*tan(f*x+e)*(a+I*a*tan(f*x+e))^m/f/(1-n)/((1+I*tan(f*x+e))^m),1],
[cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n,x,4,-2*AppellF1(-1/2,1-n,1,1/2,-I*tan(d*x+c),I*tan(d*x+c))*sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^n/d/((1+I*tan(d*x+c))^n),1],
[sqrt(cot(d*x+c))*(a+I*a*tan(d*x+c))^n,x,4,2*AppellF1(1/2,1-n,1,3/2,-I*tan(d*x+c),I*tan(d*x+c))*(a+I*a*tan(d*x+c))^n/d/sqrt(cot(d*x+c))/((1+I*tan(d*x+c))^n),1],
[(a+I*a*tan(d*x+c))^n/sqrt(cot(d*x+c)),x,4,2/3*AppellF1(3/2,1-n,1,5/2,-I*tan(d*x+c),I*tan(d*x+c))*(a+I*a*tan(d*x+c))^n/d/cot(d*x+c)^(3/2)/((1+I*tan(d*x+c))^n),1],
[(a+I*a*tan(d*x+c))^n/cot(d*x+c)^(3/2),x,4,2/5*AppellF1(5/2,1-n,1,7/2,-I*tan(d*x+c),I*tan(d*x+c))*(a+I*a*tan(d*x+c))^n/d/cot(d*x+c)^(5/2)/((1+I*tan(d*x+c))^n),1],
[cot(d*x+c)^(7/2)*(a+b*tan(d*x+c)),x,13,(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*a*sqrt(cot(d*x+c))/d-2/3*b*cot(d*x+c)^(3/2)/d-2/5*a*cot(d*x+c)^(5/2)/d,1],
[cot(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x,12,-(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-2*b*sqrt(cot(d*x+c))/d-2/3*a*cot(d*x+c)^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x,11,-(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-2*a*sqrt(cot(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c)),x,10,(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d,1],
[(a+b*tan(d*x+c))/sqrt(cot(d*x+c)),x,11,(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*b/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x,12,-(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2/3*b/d/cot(d*x+c)^(3/2)+2*a/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))/cot(d*x+c)^(5/2),x,13,-(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2/5*b/d/cot(d*x+c)^(5/2)+2/3*a/d/cot(d*x+c)^(3/2)-2*b/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^2,x,14,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+4*a*b*sqrt(cot(d*x+c))/d+2/3*(a^2-b^2)*cot(d*x+c)^(3/2)/d-4/5*a*b*cot(d*x+c)^(5/2)/d-2/7*a^2*cot(d*x+c)^(7/2)/d,1],
[cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2,x,13,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*(a^2-b^2)*sqrt(cot(d*x+c))/d-4/3*a*b*cot(d*x+c)^(3/2)/d-2/5*a^2*cot(d*x+c)^(5/2)/d,1],
[cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x,12,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-4*a*b*sqrt(cot(d*x+c))/d-2/3*a^2*cot(d*x+c)^(3/2)/d,1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x,11,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-2*a^2*sqrt(cot(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^2,x,11,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*b^2/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^2/sqrt(cot(d*x+c)),x,12,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2/3*b^2/d/cot(d*x+c)^(3/2)+4*a*b/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^2/cot(d*x+c)^(3/2),x,13,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2/5*b^2/d/cot(d*x+c)^(5/2)+4/3*a*b/d/cot(d*x+c)^(3/2)+2*(a^2-b^2)/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^2/cot(d*x+c)^(5/2),x,14,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2/7*b^2/d/cot(d*x+c)^(7/2)+4/5*a*b/d/cot(d*x+c)^(5/2)+2/3*(a^2-b^2)/d/cot(d*x+c)^(3/2)-4*a*b/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3,x,14,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*b*(3*a^2-b^2)*sqrt(cot(d*x+c))/d+2/3*a*(a^2-3*b^2)*cot(d*x+c)^(3/2)/d-32/35*a^2*b*cot(d*x+c)^(5/2)/d-2/7*a^2*cot(d*x+c)^(5/2)*(b+a*cot(d*x+c))/d,1],
[cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3,x,13,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+2*a*(a^2-3*b^2)*sqrt(cot(d*x+c))/d-8/5*a^2*b*cot(d*x+c)^(3/2)/d-2/5*a^2*cot(d*x+c)^(3/2)*(b+a*cot(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x,12,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-16/3*a^2*b*sqrt(cot(d*x+c))/d-2/3*a^2*sqrt(cot(d*x+c))*(b+a*cot(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x,12,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d-2*a*(a^2+b^2)*sqrt(cot(d*x+c))/d+2*b^2*(b+a*cot(d*x+c))/d/sqrt(cot(d*x+c)),1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^3,x,12,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+16/3*a*b^2/d/sqrt(cot(d*x+c))+2/3*b^2*(b+a*cot(d*x+c))/d/cot(d*x+c)^(3/2),1],
[(a+b*tan(d*x+c))^3/sqrt(cot(d*x+c)),x,13,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+8/5*a*b^2/d/cot(d*x+c)^(3/2)+2*b*(3*a^2-b^2)/d/sqrt(cot(d*x+c))+2/5*b^2*(b+a*cot(d*x+c))/d/cot(d*x+c)^(5/2),1],
[(a+b*tan(d*x+c))^3/cot(d*x+c)^(3/2),x,14,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/d+32/35*a*b^2/d/cot(d*x+c)^(5/2)+2/3*b*(3*a^2-b^2)/d/cot(d*x+c)^(3/2)+2*a*(a^2-3*b^2)/d/sqrt(cot(d*x+c))+2/7*b^2*(b+a*cot(d*x+c))/d/cot(d*x+c)^(7/2),1],
[cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x,16,-(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*b^(7/2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(5/2)/(a^2+b^2)/d-(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*b*sqrt(cot(d*x+c))/a^2/d-2/3*cot(d*x+c)^(3/2)/a/d,1],
[cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x,15,-(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*b^(5/2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(3/2)/(a^2+b^2)/d+(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*sqrt(cot(d*x+c))/a/d,1],
[sqrt(cot(d*x+c))/(a+b*tan(d*x+c)),x,14,(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*b^(3/2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/sqrt(a)/(a^2+b^2)/d+(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/sqrt(cot(d*x+c))/(a+b*tan(d*x+c)),x,14,(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*sqrt(a)*sqrt(b)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/(a^2+b^2)/d-(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x,14,-(a-b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a-b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*a^(3/2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/sqrt(b)/(a^2+b^2)/d-(a+b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x,15,-(a+b)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+(a+b)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2*a^(5/2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/b^(3/2)/(a^2+b^2)/d+(a-b)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d+2/b/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x,17,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-b^(7/2)*(9*a^2+5*b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(7/2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b*(4*a^2+5*b^2)*sqrt(cot(d*x+c))/a^3/(a^2+b^2)/d-1/3*(2*a^2+5*b^2)*cot(d*x+c)^(3/2)/a^2/(a^2+b^2)/d+b^2*cot(d*x+c)^(5/2)/a/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x,16,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b^(5/2)*(7*a^2+3*b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(5/2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(2*a^2+3*b^2)*sqrt(cot(d*x+c))/a^2/(a^2+b^2)/d+b^2*cot(d*x+c)^(3/2)/a/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^2,x,15,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-b^(3/2)*(5*a^2+b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(3/2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b^2*sqrt(cot(d*x+c))/a/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^2,x,15,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+sqrt(b)*(3*a^2-b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/sqrt(a)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-b*sqrt(cot(d*x+c))/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x,15,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-sqrt(a)*(a^2-3*b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/sqrt(b)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a*sqrt(cot(d*x+c))/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x,15,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a^(3/2)*(a^2+5*b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/b^(3/2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a^2*sqrt(cot(d*x+c))/b/(a^2+b^2)/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x,16,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a^(5/2)*(3*a^2+7*b^2)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/b^(5/2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+(3*a^2+2*b^2)/b^2/(a^2+b^2)/d/sqrt(cot(d*x+c))-a^2/b/(a^2+b^2)/d/sqrt(cot(d*x+c))/(b+a*cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x,18,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*b^(7/2)*(99*a^4+102*a^2*b^2+35*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(9/2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*b*(24*a^4+67*a^2*b^2+35*b^4)*sqrt(cot(d*x+c))/a^4/(a^2+b^2)^2/d-1/12*(8*a^4+67*a^2*b^2+35*b^4)*cot(d*x+c)^(3/2)/a^3/(a^2+b^2)^2/d+1/2*b^2*cot(d*x+c)^(7/2)/a/(a^2+b^2)/d/(b+a*cot(d*x+c))^2+1/4*b^2*(15*a^2+7*b^2)*cot(d*x+c)^(5/2)/a^2/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x,17,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*b^(5/2)*(63*a^4+46*a^2*b^2+15*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(7/2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*(8*a^4+31*a^2*b^2+15*b^4)*sqrt(cot(d*x+c))/a^3/(a^2+b^2)^2/d+1/2*b^2*cot(d*x+c)^(5/2)/a/(a^2+b^2)/d/(b+a*cot(d*x+c))^2+1/4*b^2*(13*a^2+5*b^2)*cot(d*x+c)^(3/2)/a^2/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^3,x,16,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*b^(3/2)*(35*a^4+6*a^2*b^2+3*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(5/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*b^2*cot(d*x+c)^(3/2)/a/(a^2+b^2)/d/(b+a*cot(d*x+c))^2+1/4*b^2*(11*a^2+3*b^2)*sqrt(cot(d*x+c))/a^2/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^3,x,16,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/4*sqrt(b)*(15*a^4-18*a^2*b^2-b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/a^(3/2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*b^2*sqrt(cot(d*x+c))/a/(a^2+b^2)/d/(b+a*cot(d*x+c))^2-1/4*b*(9*a^2+b^2)*sqrt(cot(d*x+c))/a/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x,16,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*(3*a^4-26*a^2*b^2+3*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/sqrt(a)/sqrt(b)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*b*sqrt(cot(d*x+c))/(a^2+b^2)/d/(b+a*cot(d*x+c))^2+1/4*(5*a^2-3*b^2)*sqrt(cot(d*x+c))/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x,16,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*sqrt(a)*(a^4+18*a^2*b^2-15*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/b^(3/2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*a*sqrt(cot(d*x+c))/(a^2+b^2)/d/(b+a*cot(d*x+c))^2-1/4*a*(a^2-7*b^2)*sqrt(cot(d*x+c))/b/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x,16,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*a^(3/2)*(3*a^4+6*a^2*b^2+35*b^4)*arctan(sqrt(a)*sqrt(cot(d*x+c))/sqrt(b))/b^(5/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(cot(d*x+c))/(1+cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*a^2*sqrt(cot(d*x+c))/b/(a^2+b^2)/d/(b+a*cot(d*x+c))^2-1/4*a^2*(3*a^2+11*b^2)*sqrt(cot(d*x+c))/b^2/(a^2+b^2)^2/d/(b+a*cot(d*x+c)),1],
[cot(d*x+c)^(7/2)*sqrt(a+b*tan(d*x+c)),x,11,sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2/15*(15*a^2+2*b^2)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a^2/d-2/15*b*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/a/d-2/5*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c)),x,11,I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2/3*b*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a/d-2/3*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c)),x,9,-sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c)),x,8,-I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[sqrt(a+b*tan(d*x+c))/sqrt(cot(d*x+c)),x,11,sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2*sqrt(b)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[sqrt(a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x,11,I*sqrt(I*a-b)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(b)/d+I*sqrt(I*a+b)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2),x,12,-(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+4/105*b*(70*a^2+3*b^2)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a^2/d+2/105*(35*a^2-3*b^2)*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/a/d-16/35*b*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d-2/7*a*cot(d*x+c)^(7/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2),x,11,-I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2/5*(5*a^2-b^2)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a/d-4/5*b*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d-2/5*a*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x,10,(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-8/3*b*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d-2/3*a*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x,9,I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*a*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^(3/2),x,12,-(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2*b^(3/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d,1],
[(a+b*tan(d*x+c))^(3/2)/sqrt(cot(d*x+c)),x,11,-I*(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+3*a*sqrt(b)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+I*(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+b*sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(3/2),x,12,(I*a-b)^(3/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+1/4*(3*a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(b)/d+(I*a+b)^(3/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+3/4*a*sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c))+1/2*(a+b*tan(d*x+c))^(3/2)/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2),x,13,(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2/315*(315*a^4-483*a^2*b^2-10*b^4)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a^2/d+2/315*b*(231*a^2-5*b^2)*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/a/d+2/105*(21*a^2-25*b^2)*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d-38/63*a*b*cot(d*x+c)^(7/2)*sqrt(a+b*tan(d*x+c))/d-2/9*a^2*cot(d*x+c)^(9/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2),x,12,I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2/21*b*(49*a^2-3*b^2)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a/d+2/21*(7*a^2-9*b^2)*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d-6/7*a*b*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d-2/7*a^2*cot(d*x+c)^(7/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2),x,11,-(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2/15*(15*a^2-23*b^2)*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d-22/15*a*b*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d-2/5*a^2*cot(d*x+c)^(5/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x,10,-I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-14/3*a*b*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d-2/3*a^2*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/d,1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x,11,(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+2*b^(5/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d-2*a^2*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/d,1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^(5/2),x,11,I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+5*a*b^(3/2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+b^2*sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/sqrt(cot(d*x+c)),x,12,-(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+1/4*sqrt(b)*(15*a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+1/2*b^2*sqrt(a+b*tan(d*x+c))/d/cot(d*x+c)^(3/2)+9/4*a*b*sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[(a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(3/2),x,13,-I*(I*a-b)^(5/2)*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+5/8*a*(a^2-8*b^2)*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(b)/d-I*(I*a+b)^(5/2)*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/d+1/3*b^2*sqrt(a+b*tan(d*x+c))/d/cot(d*x+c)^(5/2)+13/12*a*b*sqrt(a+b*tan(d*x+c))/d/cot(d*x+c)^(3/2)+1/8*(11*a^2-8*b^2)*sqrt(a+b*tan(d*x+c))/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/sqrt(a+b*tan(d*x+c)),x,11,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d+4/3*b*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a^2/d-2/3*cot(d*x+c)^(3/2)*sqrt(a+b*tan(d*x+c))/a/d,1],
[cot(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c)),x,9,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d-2*sqrt(cot(d*x+c))*sqrt(a+b*tan(d*x+c))/a/d,1],
[sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),x,8,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d,1],
[1/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),x,7,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d,1],
[1/cot(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c)),x,12,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d+2*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(b)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d,1],
[1/cot(d*x+c)^(5/2)/sqrt(a+b*tan(d*x+c)),x,12,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a-b)/d-a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/b^(3/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/sqrt(I*a+b)/d+sqrt(a+b*tan(d*x+c))/b/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x,11,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d+2/3*b^2*(5*a^2+8*b^2)/a^3/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c))+8/3*b*sqrt(cot(d*x+c))/a^2/d/sqrt(a+b*tan(d*x+c))-2/3*cot(d*x+c)^(3/2)/a/d/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x,10,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d-2*b*(a^2+2*b^2)/a^2/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c))-2*sqrt(cot(d*x+c))/a/d/sqrt(a+b*tan(d*x+c)),1],
[sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2),x,9,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d+2*b^2/a/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2),x,9,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d-2*b/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x,9,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d+2*a/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x,11,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d+2*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/b^(3/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d-2*a^2/b/(a^2+b^2)/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x,12,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(3/2)/d-3*a*arctanh(sqrt(b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/b^(5/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(3/2)/d-2*a^2/b/(a^2+b^2)/d/cot(d*x+c)^(3/2)/sqrt(a+b*tan(d*x+c))+(3*a^2+b^2)*sqrt(a+b*tan(d*x+c))/b^2/(a^2+b^2)/d/sqrt(cot(d*x+c)),1],
[cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x,12,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d+2/3*b^2*(7*a^2+8*b^2)/a^3/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)+4*b*sqrt(cot(d*x+c))/a^2/d/(a+b*tan(d*x+c))^(3/2)-2/3*cot(d*x+c)^(3/2)/a/d/(a+b*tan(d*x+c))^(3/2)+4/3*b^2*(4*a^4+15*a^2*b^2+8*b^4)/a^4/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x,11,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d-2/3*b*(3*a^2+4*b^2)/a^2/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)-2*sqrt(cot(d*x+c))/a/d/(a+b*tan(d*x+c))^(3/2)-2/3*b*(3*a^4+17*a^2*b^2+8*b^4)/a^3/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(5/2),x,10,-arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d-arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d+2/3*b^2/a/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)+4/3*b^2*(4*a^2+b^2)/a^2/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(5/2),x,10,-I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d+I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d-2/3*b/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)-2/3*b*(5*a^2-b^2)/a/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x,10,arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d+arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d+2/3*a/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)+4/3*(a^2-2*b^2)/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x,10,I*arctan(sqrt(I*a-b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a-b)^(5/2)/d-I*arctanh(sqrt(I*a+b)*sqrt(tan(d*x+c))/sqrt(a+b*tan(d*x+c)))*sqrt(cot(d*x+c))*sqrt(tan(d*x+c))/(I*a+b)^(5/2)/d-2/3*a^2/b/(a^2+b^2)/d/sqrt(cot(d*x+c))/(a+b*tan(d*x+c))^(3/2)+2/3*a*(a^2+7*b^2)/b/(a^2+b^2)^2/d/sqrt(cot(d*x+c))/sqrt(a+b*tan(d*x+c)),1],
[(d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x,8,a^2*b*d^2*(1-2*n)*(d*cot(f*x+e))^(-2+n)/f/(1-n)/(2-n)+a^2*d^2*(d*cot(f*x+e))^(-2+n)*(b+a*cot(f*x+e))/f/(1-n)-b*(3*a^2-b^2)*d^2*(d*cot(f*x+e))^(-2+n)*hypergeom([1, -1+1/2*n],[1/2*n],-cot(f*x+e)^2)/f/(2-n)-a*(a^2-3*b^2)*d*(d*cot(f*x+e))^(-1+n)*hypergeom([1, -1/2+1/2*n],[1/2+1/2*n],-cot(f*x+e)^2)/f/(1-n),1],
[(d*cot(f*x+e))^n*(a+b*tan(f*x+e))^2,x,7,a^2*d*(d*cot(f*x+e))^(-1+n)/f/(1-n)-(a^2-b^2)*d*(d*cot(f*x+e))^(-1+n)*hypergeom([1, -1/2+1/2*n],[1/2+1/2*n],-cot(f*x+e)^2)/f/(1-n)-2*a*b*(d*cot(f*x+e))^n*hypergeom([1, 1/2*n],[1+1/2*n],-cot(f*x+e)^2)/f/n,1],
[(d*cot(f*x+e))^n*(a+b*tan(f*x+e)),x,6,-b*(d*cot(f*x+e))^n*hypergeom([1, 1/2*n],[1+1/2*n],-cot(f*x+e)^2)/f/n-a*(d*cot(f*x+e))^(1+n)*hypergeom([1, 1/2+1/2*n],[3/2+1/2*n],-cot(f*x+e)^2)/d/f/(1+n),1],
[(d*cot(f*x+e))^n/(a+b*tan(f*x+e)),x,9,-b*(d*cot(f*x+e))^(2+n)*hypergeom([1, 1+1/2*n],[2+1/2*n],-cot(f*x+e)^2)/(a^2+b^2)/d^2/f/(2+n)-a^2*(d*cot(f*x+e))^(2+n)*hypergeom([1, 2+n],[3+n],-a*cot(f*x+e)/b)/b/(a^2+b^2)/d^2/f/(2+n)+a*(d*cot(f*x+e))^(3+n)*hypergeom([1, 3/2+1/2*n],[5/2+1/2*n],-cot(f*x+e)^2)/(a^2+b^2)/d^3/f/(3+n),1],
[(d*cot(f*x+e))^n/(a+b*tan(f*x+e))^2,x,10,-a^2*(d*cot(f*x+e))^(3+n)/b/(a^2+b^2)/d^3/f/(b+a*cot(f*x+e))+(a^2-b^2)*(d*cot(f*x+e))^(3+n)*hypergeom([1, 3/2+1/2*n],[5/2+1/2*n],-cot(f*x+e)^2)/(a^2+b^2)^2/d^3/f/(3+n)+a^2*(b^2*n+a^2*(2+n))*(d*cot(f*x+e))^(3+n)*hypergeom([1, 3+n],[4+n],-a*cot(f*x+e)/b)/b^2/(a^2+b^2)^2/d^3/f/(3+n)+2*a*b*(d*cot(f*x+e))^(4+n)*hypergeom([1, 2+1/2*n],[3+1/2*n],-cot(f*x+e)^2)/(a^2+b^2)^2/d^4/f/(4+n),1],
[(d*cot(f*x+e))^n*(a+b*tan(f*x+e))^m,x,8,1/2*AppellF1(1-n,-m,1,2-n,-b*tan(f*x+e)/a,-I*tan(f*x+e))*(d*cot(f*x+e))^n*tan(f*x+e)*(a+b*tan(f*x+e))^m/f/(1-n)/(((a+b*tan(f*x+e))/a)^m)+1/2*AppellF1(1-n,-m,1,2-n,-b*tan(f*x+e)/a,I*tan(f*x+e))*(d*cot(f*x+e))^n*tan(f*x+e)*(a+b*tan(f*x+e))^m/f/(1-n)/(((a+b*tan(f*x+e))/a)^m),1],
[cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x,8,-AppellF1(-1/2,-n,1,1/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n)-AppellF1(-1/2,-n,1,1/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^n/d/(((a+b*tan(d*x+c))/a)^n),1],
[sqrt(cot(d*x+c))*(a+b*tan(d*x+c))^n,x,8,AppellF1(1/2,-n,1,3/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/sqrt(cot(d*x+c))/(((a+b*tan(d*x+c))/a)^n)+AppellF1(1/2,-n,1,3/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/sqrt(cot(d*x+c))/(((a+b*tan(d*x+c))/a)^n),1],
[(a+b*tan(d*x+c))^n/sqrt(cot(d*x+c)),x,8,1/3*AppellF1(3/2,-n,1,5/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/cot(d*x+c)^(3/2)/(((a+b*tan(d*x+c))/a)^n)+1/3*AppellF1(3/2,-n,1,5/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/cot(d*x+c)^(3/2)/(((a+b*tan(d*x+c))/a)^n),1],
[(a+b*tan(d*x+c))^n/cot(d*x+c)^(3/2),x,8,1/5*AppellF1(5/2,-n,1,7/2,-b*tan(d*x+c)/a,-I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/cot(d*x+c)^(5/2)/(((a+b*tan(d*x+c))/a)^n)+1/5*AppellF1(5/2,-n,1,7/2,-b*tan(d*x+c)/a,I*tan(d*x+c))*(a+b*tan(d*x+c))^n/d/cot(d*x+c)^(5/2)/(((a+b*tan(d*x+c))/a)^n),1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e)),x,3,-1/3*I*c*(a+I*a*tan(f*x+e))^3/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e)),x,4,-1/2*I*c*(a+I*a*tan(f*x+e))^2/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x,3,a*c*tan(f*x+e)/f,1],
[(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,3,I*c/f/(a+I*a*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,3,1/2*I*c/f/(a+I*a*tan(f*x+e))^2,1],
[(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,3,1/3*I*c/f/(a+I*a*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^2,x,4,-1/2*I*c^2*(a+I*a*tan(f*x+e))^4/f+1/5*I*c^2*(a+I*a*tan(f*x+e))^5/a/f,1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^2,x,4,1/4*I*a^3*c^2*sec(f*x+e)^4/f+a^3*c^2*tan(f*x+e)/f+1/3*a^3*c^2*tan(f*x+e)^3/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^2,x,3,a^2*c^2*tan(f*x+e)/f+1/3*a^2*c^2*tan(f*x+e)^3/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x,4,1/2*I*a*(c-I*c*tan(f*x+e))^2/f,1],
[(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x,4,-c^2*x/a-I*c^2*ln(cos(f*x+e))/a/f+2*I*c^2/a/f/(1+I*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x,3,c^2*tan(f*x+e)/f/(a+I*a*tan(f*x+e))^2,1],
[(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x,4,2/3*I*c^2/f/(a+I*a*tan(f*x+e))^3-1/2*I*c^2/a/f/(a+I*a*tan(f*x+e))^2,1],
[(c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^4,x,4,1/2*I*c^2/f/(a+I*a*tan(f*x+e))^4-1/3*I*a^2*c^2/f/(a^2+I*a^2*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^3,x,4,-4/5*I*c^3*(a+I*a*tan(f*x+e))^5/f+2/3*I*c^3*(a+I*a*tan(f*x+e))^6/a/f-1/7*I*c^3*(a+I*a*tan(f*x+e))^7/a^2/f,1],
[(a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^3,x,4,1/6*I*a^4*c^3*sec(f*x+e)^6/f+a^4*c^3*tan(f*x+e)/f+2/3*a^4*c^3*tan(f*x+e)^3/f+1/5*a^4*c^3*tan(f*x+e)^5/f,1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^3,x,3,a^3*c^3*tan(f*x+e)/f+2/3*a^3*c^3*tan(f*x+e)^3/f+1/5*a^3*c^3*tan(f*x+e)^5/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^3,x,4,-1/4*I*a^2*c^3*sec(f*x+e)^4/f+a^2*c^3*tan(f*x+e)/f+1/3*a^2*c^3*tan(f*x+e)^3/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x,3,1/3*I*a*(c-I*c*tan(f*x+e))^3/f,1],
[(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x,4,-4*c^3*x/a-4*I*c^3*ln(cos(f*x+e))/a/f+c^3*tan(f*x+e)/a/f+4*I*c^3/f/(a+I*a*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x,4,c^3*x/a^2+I*c^3*ln(cos(f*x+e))/a^2/f+2*I*c^3/a^2/f/(1+I*tan(f*x+e))^2-4*I*c^3/a^2/f/(1+I*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x,3,1/6*I*c^3*(a^2-I*a^2*tan(f*x+e))^3/f/(a^3+I*a^3*tan(f*x+e))^3,1],
[(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^4,x,4,I*c^3/f/(a+I*a*tan(f*x+e))^4-4/3*I*c^3/a/f/(a+I*a*tan(f*x+e))^3+1/2*I*c^3/f/(a^2+I*a^2*tan(f*x+e))^2,1],
[(c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^5,x,4,4/5*I*c^3/f/(a+I*a*tan(f*x+e))^5+1/3*I*c^3/a^2/f/(a+I*a*tan(f*x+e))^3-I*a^3*c^3/f/(a^2+I*a^2*tan(f*x+e))^4,1],
[(a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^4,x,4,1/8*I*a^5*c^4*sec(f*x+e)^8/f+a^5*c^4*tan(f*x+e)/f+a^5*c^4*tan(f*x+e)^3/f+3/5*a^5*c^4*tan(f*x+e)^5/f+1/7*a^5*c^4*tan(f*x+e)^7/f,1],
[(a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^4,x,3,a^4*c^4*tan(f*x+e)/f+a^4*c^4*tan(f*x+e)^3/f+3/5*a^4*c^4*tan(f*x+e)^5/f+1/7*a^4*c^4*tan(f*x+e)^7/f,1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^4,x,4,-1/6*I*a^3*c^4*sec(f*x+e)^6/f+a^3*c^4*tan(f*x+e)/f+2/3*a^3*c^4*tan(f*x+e)^3/f+1/5*a^3*c^4*tan(f*x+e)^5/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^4,x,4,1/2*I*a^2*(c-I*c*tan(f*x+e))^4/f-1/5*I*a^2*(c-I*c*tan(f*x+e))^5/c/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x,3,1/4*I*a*(c-I*c*tan(f*x+e))^4/f,1],
[(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x,4,-12*c^4*x/a-12*I*c^4*ln(cos(f*x+e))/a/f+5*c^4*tan(f*x+e)/a/f-1/2*I*c^4*tan(f*x+e)^2/a/f+8*I*c^4/f/(a+I*a*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x,4,6*c^4*x/a^2+6*I*c^4*ln(cos(f*x+e))/a^2/f-c^4*tan(f*x+e)/a^2/f+4*I*c^4/f/(a+I*a*tan(f*x+e))^2-12*I*c^4/f/(a^2+I*a^2*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x,4,-c^4*x/a^3-I*c^4*ln(cos(f*x+e))/a^3/f+8/3*I*c^4/a^3/f/(1+I*tan(f*x+e))^3-6*I*c^4/a^3/f/(1+I*tan(f*x+e))^2+6*I*c^4/a^3/f/(1+I*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^4,x,3,1/8*I*c^4*(a^2-I*a^2*tan(f*x+e))^4/f/(a^3+I*a^3*tan(f*x+e))^4,1],
[(c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^5,x,4,1/10*I*c^4*(1-I*tan(f*x+e))^4/f/(a+I*a*tan(f*x+e))^5+1/80*I*c^4*(a-I*a*tan(f*x+e))^4/a^5/f/(a+I*a*tan(f*x+e))^4,1],
[(a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e)),x,4,-12*a^4*x/c+12*I*a^4*ln(cos(f*x+e))/c/f+5*a^4*tan(f*x+e)/c/f+1/2*I*a^4*tan(f*x+e)^2/c/f-8*I*a^4/f/(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x,4,-4*a^3*x/c+4*I*a^3*ln(cos(f*x+e))/c/f+a^3*tan(f*x+e)/c/f-4*I*a^3/f/(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x,4,-a^2*x/c+I*a^2*ln(cos(f*x+e))/c/f-2*I*a^2/c/f/(1-I*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x,3,-I*a/f/(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x,3,1/2*x/a/c+1/2*cos(f*x+e)*sin(f*x+e)/a/c/f,1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x,5,3/8*x/a^2/c+1/4*I*cos(f*x+e)^4/a^2/c/f+3/8*cos(f*x+e)*sin(f*x+e)/a^2/c/f+1/4*cos(f*x+e)^3*sin(f*x+e)/a^2/c/f,1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x,5,1/4*x/a^3/c-1/16*I/a^3/f/(c-I*c*tan(f*x+e))+1/12*I*c^2/a^3/f/(c+I*c*tan(f*x+e))^3+1/8*I*c/a^3/f/(c+I*c*tan(f*x+e))^2+3/16*I/a^3/f/(c+I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^2,x,4,6*a^4*x/c^2-6*I*a^4*ln(cos(f*x+e))/c^2/f-a^4*tan(f*x+e)/c^2/f-4*I*a^4/f/(c-I*c*tan(f*x+e))^2+12*I*a^4/f/(c^2-I*c^2*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x,4,a^3*x/c^2-I*a^3*ln(cos(f*x+e))/c^2/f-2*I*a^3/c^2/f/(1-I*tan(f*x+e))^2+4*I*a^3/c^2/f/(1-I*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x,3,a^2*tan(f*x+e)/f/(c-I*c*tan(f*x+e))^2,1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x,3,-1/2*I*a/f/(c-I*c*tan(f*x+e))^2,1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x,5,3/8*x/a/c^2-1/8*I/a/f/(c-I*c*tan(f*x+e))^2-1/4*I/a/f/(c^2-I*c^2*tan(f*x+e))+1/8*I/a/f/(c^2+I*c^2*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x,4,3/8*x/a^2/c^2+3/8*cos(f*x+e)*sin(f*x+e)/a^2/c^2/f+1/4*cos(f*x+e)^3*sin(f*x+e)/a^2/c^2/f,1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x,6,5/16*x/a^3/c^2+1/6*I*cos(f*x+e)^6/a^3/c^2/f+5/16*cos(f*x+e)*sin(f*x+e)/a^3/c^2/f+5/24*cos(f*x+e)^3*sin(f*x+e)/a^3/c^2/f+1/6*cos(f*x+e)^5*sin(f*x+e)/a^3/c^2/f,1],
[(a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^3,x,4,-40*a^6*x/c^3+40*I*a^6*ln(cos(f*x+e))/c^3/f+9*a^6*tan(f*x+e)/c^3/f+1/2*I*a^6*tan(f*x+e)^2/c^3/f-32/3*I*a^6/f/(c-I*c*tan(f*x+e))^3+40*I*a^6/c/f/(c-I*c*tan(f*x+e))^2-80*I*a^6/f/(c^3-I*c^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^3,x,4,-8*a^5*x/c^3+8*I*a^5*ln(cos(f*x+e))/c^3/f+a^5*tan(f*x+e)/c^3/f-16/3*I*a^5/f/(c-I*c*tan(f*x+e))^3-24*I*a^5/f/(c^3-I*c^3*tan(f*x+e))+16*I*a^5*c^5/f/(c^4-I*c^4*tan(f*x+e))^2,1],
[(a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^3,x,4,-a^4*x/c^3+I*a^4*ln(cos(f*x+e))/c^3/f-8/3*I*a^4/c^3/f/(1-I*tan(f*x+e))^3+6*I*a^4/c^3/f/(1-I*tan(f*x+e))^2-6*I*a^4/c^3/f/(1-I*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x,3,-1/6*I*a^3*(c^2+I*c^2*tan(f*x+e))^3/f/(c^3-I*c^3*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x,4,-2/3*I*a^2/f/(c-I*c*tan(f*x+e))^3+1/2*I*a^2/c/f/(c-I*c*tan(f*x+e))^2,1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x,3,-1/3*I*a/f/(c-I*c*tan(f*x+e))^3,1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x,5,1/4*x/a/c^3-1/12*I/a/f/(c-I*c*tan(f*x+e))^3-1/8*I/a/c/f/(c-I*c*tan(f*x+e))^2-3/16*I/a/f/(c^3-I*c^3*tan(f*x+e))+1/16*I/a/f/(c^3+I*c^3*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x,5,5/16*x/a^2/c^3-1/24*I/a^2/f/(c-I*c*tan(f*x+e))^3-3/32*I*c^3/a^2/f/(c^3-I*c^3*tan(f*x+e))^2-3/16*I/a^2/f/(c^3-I*c^3*tan(f*x+e))+1/32*I*c^3/a^2/f/(c^3+I*c^3*tan(f*x+e))^2+1/8*I/a^2/f/(c^3+I*c^3*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x,5,5/16*x/a^3/c^3+5/16*cos(f*x+e)*sin(f*x+e)/a^3/c^3/f+5/24*cos(f*x+e)^3*sin(f*x+e)/a^3/c^3/f+1/6*cos(f*x+e)^5*sin(f*x+e)/a^3/c^3/f,1],
[(a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^4,x,4,10*a^6*x/c^4-10*I*a^6*ln(cos(f*x+e))/c^4/f-a^6*tan(f*x+e)/c^4/f-8*I*a^6/f/(c-I*c*tan(f*x+e))^4+80/3*I*a^6/c/f/(c-I*c*tan(f*x+e))^3-40*I*a^6/f/(c^2-I*c^2*tan(f*x+e))^2+40*I*a^6/f/(c^4-I*c^4*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^4,x,4,a^5*x/c^4-I*a^5*ln(cos(f*x+e))/c^4/f-4*I*a^5/c^4/f/(1-I*tan(f*x+e))^4+32/3*I*a^5/c^4/f/(1-I*tan(f*x+e))^3-12*I*a^5/c^4/f/(1-I*tan(f*x+e))^2+8*I*a^5/c^4/f/(1-I*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^4,x,3,-1/8*I*a^4*(c^2+I*c^2*tan(f*x+e))^4/f/(c^3-I*c^3*tan(f*x+e))^4,1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x,4,-I*a^3/f/(c-I*c*tan(f*x+e))^4+4/3*I*a^3/c/f/(c-I*c*tan(f*x+e))^3-1/2*I*a^3/f/(c^2-I*c^2*tan(f*x+e))^2,1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x,4,-1/2*I*a^2/f/(c-I*c*tan(f*x+e))^4+1/3*I*a^2*c^2/f/(c^2-I*c^2*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x,3,-1/4*I*a/f/(c-I*c*tan(f*x+e))^4,1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x,5,5/32*x/a/c^4-1/16*I/a/f/(c-I*c*tan(f*x+e))^4-1/12*I/a/c/f/(c-I*c*tan(f*x+e))^3-3/32*I/a/f/(c^2-I*c^2*tan(f*x+e))^2-1/8*I/a/f/(c^4-I*c^4*tan(f*x+e))+1/32*I/a/f/(c^4+I*c^4*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x,5,15/64*x/a^2/c^4-1/32*I/a^2/f/(c-I*c*tan(f*x+e))^4-1/16*I/a^2/c/f/(c-I*c*tan(f*x+e))^3-3/32*I/a^2/f/(c^2-I*c^2*tan(f*x+e))^2+1/64*I/a^2/f/(c^2+I*c^2*tan(f*x+e))^2-5/32*I/a^2/f/(c^4-I*c^4*tan(f*x+e))+5/64*I/a^2/f/(c^4+I*c^4*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x,5,35/128*x/a^3/c^4-1/64*I/a^3/f/(c-I*c*tan(f*x+e))^4-1/24*I/a^3/c/f/(c-I*c*tan(f*x+e))^3+1/96*I/a^3/c/f/(c+I*c*tan(f*x+e))^3-5/64*I/a^3/f/(c^2-I*c^2*tan(f*x+e))^2+5/128*I/a^3/f/(c^2+I*c^2*tan(f*x+e))^2-5/32*I/a^3/f/(c^4-I*c^4*tan(f*x+e))+15/128*I/a^3/f/(c^4+I*c^4*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*sqrt(c-I*c*tan(f*x+e)),x,4,8*I*a^3*sqrt(c-I*c*tan(f*x+e))/f-8/3*I*a^3*(c-I*c*tan(f*x+e))^(3/2)/c/f+2/5*I*a^3*(c-I*c*tan(f*x+e))^(5/2)/c^2/f,1],
[(a+I*a*tan(f*x+e))^2*sqrt(c-I*c*tan(f*x+e)),x,4,4*I*a^2*sqrt(c-I*c*tan(f*x+e))/f-2/3*I*a^2*(c-I*c*tan(f*x+e))^(3/2)/c/f,1],
[(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e)),x,3,2*I*a*sqrt(c-I*c*tan(f*x+e))/f,1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,5,1/2*I*sqrt(c)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a/f+1/2*I*sqrt(c-I*c*tan(f*x+e))/a/f/(1+I*tan(f*x+e)),1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,6,3/16*I*sqrt(c)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/f+1/4*I*sqrt(c-I*c*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))^2+3/16*I*sqrt(c-I*c*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e)),1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,7,5/64*I*sqrt(c)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/f+1/6*I*sqrt(c-I*c*tan(f*x+e))/a^3/f/(1+I*tan(f*x+e))^3+5/48*I*sqrt(c-I*c*tan(f*x+e))/a^3/f/(1+I*tan(f*x+e))^2+5/64*I*sqrt(c-I*c*tan(f*x+e))/a^3/f/(1+I*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(3/2),x,4,8/3*I*a^3*(c-I*c*tan(f*x+e))^(3/2)/f-8/5*I*a^3*(c-I*c*tan(f*x+e))^(5/2)/c/f+2/7*I*a^3*(c-I*c*tan(f*x+e))^(7/2)/c^2/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(3/2),x,4,4/3*I*a^2*(c-I*c*tan(f*x+e))^(3/2)/f-2/5*I*a^2*(c-I*c*tan(f*x+e))^(5/2)/c/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x,3,2/3*I*a*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x,5,-I*c^(3/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a/f+I*c^2*sqrt(c-I*c*tan(f*x+e))/a/f/(c+I*c*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x,6,-1/8*I*c^(3/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/f+1/2*I*c^3*sqrt(c-I*c*tan(f*x+e))/a^2/f/(c+I*c*tan(f*x+e))^2-1/8*I*c^3*sqrt(c-I*c*tan(f*x+e))/a^2/f/(c^2+I*c^2*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x,7,-1/32*I*c^(3/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/f+1/3*I*c^4*sqrt(c-I*c*tan(f*x+e))/a^3/f/(c+I*c*tan(f*x+e))^3-1/24*I*c^3*sqrt(c-I*c*tan(f*x+e))/a^3/f/(c+I*c*tan(f*x+e))^2-1/32*I*c^4*sqrt(c-I*c*tan(f*x+e))/a^3/f/(c^3+I*c^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(5/2),x,4,8/5*I*a^3*(c-I*c*tan(f*x+e))^(5/2)/f-8/7*I*a^3*(c-I*c*tan(f*x+e))^(7/2)/c/f+2/9*I*a^3*(c-I*c*tan(f*x+e))^(9/2)/c^2/f,1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(5/2),x,4,4/5*I*a^2*(c-I*c*tan(f*x+e))^(5/2)/f-2/7*I*a^2*(c-I*c*tan(f*x+e))^(7/2)/c/f,1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x,3,2/5*I*a*(c-I*c*tan(f*x+e))^(5/2)/f,1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x,6,-3*I*sqrt(2)*c^(5/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/a/f+3*I*c^2*sqrt(c-I*c*tan(f*x+e))/a/f+I*c^2*(c-I*c*tan(f*x+e))^(3/2)/a/f/(c+I*c*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x,6,3/4*I*c^(5/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/f+1/2*I*c^3*(c-I*c*tan(f*x+e))^(3/2)/a^2/f/(c+I*c*tan(f*x+e))^2-3/4*I*c^3*sqrt(c-I*c*tan(f*x+e))/a^2/f/(c+I*c*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x,7,1/16*I*c^(5/2)*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/f+1/3*I*c^4*(c-I*c*tan(f*x+e))^(3/2)/a^3/f/(c+I*c*tan(f*x+e))^3-1/4*I*c^4*sqrt(c-I*c*tan(f*x+e))/a^3/f/(c+I*c*tan(f*x+e))^2+1/16*I*c^4*sqrt(c-I*c*tan(f*x+e))/a^3/f/(c^2+I*c^2*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/sqrt(c-I*c*tan(f*x+e)),x,4,-8*I*a^3/f/sqrt(c-I*c*tan(f*x+e))-8*I*a^3*sqrt(c-I*c*tan(f*x+e))/c/f+2/3*I*a^3*(c-I*c*tan(f*x+e))^(3/2)/c^2/f,1],
[(a+I*a*tan(f*x+e))^2/sqrt(c-I*c*tan(f*x+e)),x,4,-4*I*a^2/f/sqrt(c-I*c*tan(f*x+e))-2*I*a^2*sqrt(c-I*c*tan(f*x+e))/c/f,1],
[(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),x,3,-2*I*a/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),x,6,3/4*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a/sqrt(c)/f-3/4*I/a/f/sqrt(c-I*c*tan(f*x+e))+1/2*I/a/f/(1+I*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/sqrt(c-I*c*tan(f*x+e)),x,7,15/32*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/sqrt(c)/f-15/32*I/a^2/f/sqrt(c-I*c*tan(f*x+e))+1/4*I/a^2/f/(1+I*tan(f*x+e))^2/sqrt(c-I*c*tan(f*x+e))+5/16*I/a^2/f/(1+I*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/sqrt(c-I*c*tan(f*x+e)),x,8,35/128*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/sqrt(c)/f-35/128*I/a^3/f/sqrt(c-I*c*tan(f*x+e))+1/6*I/a^3/f/(1+I*tan(f*x+e))^3/sqrt(c-I*c*tan(f*x+e))+7/48*I/a^3/f/(1+I*tan(f*x+e))^2/sqrt(c-I*c*tan(f*x+e))+35/192*I/a^3/f/(1+I*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x,4,-8/3*I*a^3/f/(c-I*c*tan(f*x+e))^(3/2)+8*I*a^3/c/f/sqrt(c-I*c*tan(f*x+e))+2*I*a^3*sqrt(c-I*c*tan(f*x+e))/c^2/f,1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x,4,-4/3*I*a^2/f/(c-I*c*tan(f*x+e))^(3/2)+2*I*a^2/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x,3,-2/3*I*a/f/(c-I*c*tan(f*x+e))^(3/2),1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x,7,5/8*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a/c^(3/2)/f-5/12*I/a/f/(c-I*c*tan(f*x+e))^(3/2)+1/2*I/a/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2)-5/8*I/a/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x,8,35/64*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/c^(3/2)/f-35/96*I/a^2/f/(c-I*c*tan(f*x+e))^(3/2)+1/4*I/a^2/f/(1+I*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2)+7/16*I/a^2/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2)-35/64*I/a^2/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x,9,105/256*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/c^(3/2)/f-35/128*I/a^3/f/(c-I*c*tan(f*x+e))^(3/2)+1/6*I/a^3/f/(1+I*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2)+3/16*I/a^3/f/(1+I*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2)+21/64*I/a^3/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2)-105/256*I/a^3/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x,4,-8/5*I*a^3/f/(c-I*c*tan(f*x+e))^(5/2)+8/3*I*a^3/c/f/(c-I*c*tan(f*x+e))^(3/2)-2*I*a^3/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x,4,-4/5*I*a^2/f/(c-I*c*tan(f*x+e))^(5/2)+2/3*I*a^2/c/f/(c-I*c*tan(f*x+e))^(3/2),1],
[(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x,3,-2/5*I*a/f/(c-I*c*tan(f*x+e))^(5/2),1],
[1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x,8,7/16*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a/c^(5/2)/f-7/20*I/a/f/(c-I*c*tan(f*x+e))^(5/2)+1/2*I/a/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2)-7/24*I/a/c/f/(c-I*c*tan(f*x+e))^(3/2)-7/16*I/a/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x,9,63/128*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^2/c^(5/2)/f-63/160*I/a^2/f/(c-I*c*tan(f*x+e))^(5/2)+1/4*I/a^2/f/(1+I*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2)+9/16*I/a^2/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2)-21/64*I/a^2/c/f/(c-I*c*tan(f*x+e))^(3/2)-63/128*I/a^2/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x,10,231/512*I*arctanh(sqrt(c-I*c*tan(f*x+e))/sqrt(2)/sqrt(c))/sqrt(2)/a^3/c^(5/2)/f-231/640*I/a^3/f/(c-I*c*tan(f*x+e))^(5/2)+1/6*I/a^3/f/(1+I*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2)+11/48*I/a^3/f/(1+I*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2)+33/64*I/a^3/f/(1+I*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2)-77/256*I/a^3/c/f/(c-I*c*tan(f*x+e))^(3/2)-231/512*I/a^3/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)*sqrt(c-I*c*tan(f*x+e)),x,5,-3*I*a^(5/2)*sqrt(c)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+3/2*I*a^2*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f+1/2*I*a*(a+I*a*tan(f*x+e))^(3/2)*sqrt(c-I*c*tan(f*x+e))/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*sqrt(c-I*c*tan(f*x+e)),x,4,-2*I*a^(3/2)*sqrt(c)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+I*a*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f,1],
[sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e)),x,3,-2*I*sqrt(a)*sqrt(c)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f,1],
[sqrt(c-I*c*tan(f*x+e))/sqrt(a+I*a*tan(f*x+e)),x,2,I*sqrt(c-I*c*tan(f*x+e))/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x,3,1/3*I*sqrt(c-I*c*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^(3/2)+1/3*I*sqrt(c-I*c*tan(f*x+e))/a/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2),x,4,1/5*I*sqrt(c-I*c*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^(5/2)+2/15*I*sqrt(c-I*c*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^(3/2)+2/15*I*sqrt(c-I*c*tan(f*x+e))/a^2/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^(7/2),x,5,1/7*I*sqrt(c-I*c*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^(7/2)+3/35*I*sqrt(c-I*c*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^(5/2)+2/35*I*sqrt(c-I*c*tan(f*x+e))/a^2/f/(a+I*a*tan(f*x+e))^(3/2)+2/35*I*sqrt(c-I*c*tan(f*x+e))/a^3/f/sqrt(a+I*a*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(3/2),x,5,-I*a^(5/2)*c^(3/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+1/2*a^2*c*tan(f*x+e)*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f+1/3*I*a*(a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2),x,4,-I*a^(3/2)*c^(3/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+1/2*a*c*tan(f*x+e)*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f,1],
[sqrt(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x,4,-2*I*sqrt(a)*c^(3/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f-I*c*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f,1],
[(c-I*c*tan(f*x+e))^(3/2)/sqrt(a+I*a*tan(f*x+e)),x,4,2*I*c^(3/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/sqrt(a)/f+2*I*c*sqrt(c-I*c*tan(f*x+e))/f/sqrt(a+I*a*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x,2,1/3*I*(c-I*c*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x,3,1/5*I*(c-I*c*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(5/2)+1/15*I*(c-I*c*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(7/2),x,4,1/7*I*(c-I*c*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(7/2)+2/35*I*(c-I*c*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^(5/2)+2/105*I*(c-I*c*tan(f*x+e))^(3/2)/a^2/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(9/2),x,5,1/9*I*(c-I*c*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(9/2)+1/21*I*(c-I*c*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^(7/2)+2/105*I*(c-I*c*tan(f*x+e))^(3/2)/a^2/f/(a+I*a*tan(f*x+e))^(5/2)+2/315*I*(c-I*c*tan(f*x+e))^(3/2)/a^3/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(5/2),x,5,-3/4*I*a^(5/2)*c^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+3/8*a^2*c^2*tan(f*x+e)*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f+1/4*a*c*tan(f*x+e)*(a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(5/2),x,5,-I*a^(3/2)*c^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f+1/2*a*c^2*tan(f*x+e)*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f-1/3*I*c*(a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[sqrt(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x,5,-3*I*sqrt(a)*c^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/f-3/2*I*c^2*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/f-1/2*I*c*sqrt(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[(c-I*c*tan(f*x+e))^(5/2)/sqrt(a+I*a*tan(f*x+e)),x,5,6*I*c^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/sqrt(a)/f+3*I*c^2*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/a/f+2*I*c*(c-I*c*tan(f*x+e))^(3/2)/f/sqrt(a+I*a*tan(f*x+e)),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x,5,-2*I*c^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/a^(3/2)/f-2*I*c^2*sqrt(c-I*c*tan(f*x+e))/a/f/sqrt(a+I*a*tan(f*x+e))+2/3*I*c*(c-I*c*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x,2,1/5*I*(c-I*c*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(7/2),x,3,1/7*I*(c-I*c*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^(7/2)+1/35*I*(c-I*c*tan(f*x+e))^(5/2)/a/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(9/2),x,4,1/9*I*(c-I*c*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^(9/2)+2/63*I*(c-I*c*tan(f*x+e))^(5/2)/a/f/(a+I*a*tan(f*x+e))^(7/2)+2/315*I*(c-I*c*tan(f*x+e))^(5/2)/a^2/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(11/2),x,5,1/11*I*(c-I*c*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^(11/2)+1/33*I*(c-I*c*tan(f*x+e))^(5/2)/a/f/(a+I*a*tan(f*x+e))^(9/2)+2/231*I*(c-I*c*tan(f*x+e))^(5/2)/a^2/f/(a+I*a*tan(f*x+e))^(7/2)+2/1155*I*(c-I*c*tan(f*x+e))^(5/2)/a^3/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^(7/2)/sqrt(c-I*c*tan(f*x+e)),x,6,15*I*a^(7/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/sqrt(c)/f-2*I*a*(a+I*a*tan(f*x+e))^(5/2)/f/sqrt(c-I*c*tan(f*x+e))-15/2*I*a^3*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c/f-5/2*I*a^2*(a+I*a*tan(f*x+e))^(3/2)*sqrt(c-I*c*tan(f*x+e))/c/f,1],
[(a+I*a*tan(f*x+e))^(5/2)/sqrt(c-I*c*tan(f*x+e)),x,5,6*I*a^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/sqrt(c)/f-2*I*a*(a+I*a*tan(f*x+e))^(3/2)/f/sqrt(c-I*c*tan(f*x+e))-3*I*a^2*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c/f,1],
[(a+I*a*tan(f*x+e))^(3/2)/sqrt(c-I*c*tan(f*x+e)),x,4,2*I*a^(3/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/sqrt(c)/f-2*I*a*sqrt(a+I*a*tan(f*x+e))/f/sqrt(c-I*c*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),x,2,-I*sqrt(a+I*a*tan(f*x+e))/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),x,2,tan(f*x+e)/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c-I*c*tan(f*x+e)),x,3,1/3*I/f/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c-I*c*tan(f*x+e))+2/3*tan(f*x+e)/a/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/sqrt(c-I*c*tan(f*x+e)),x,4,1/5*I/f/(a+I*a*tan(f*x+e))^(5/2)/sqrt(c-I*c*tan(f*x+e))+1/5*I/a/f/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c-I*c*tan(f*x+e))+2/5*tan(f*x+e)/a^2/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(7/2)/sqrt(c-I*c*tan(f*x+e)),x,5,1/7*I/f/(a+I*a*tan(f*x+e))^(7/2)/sqrt(c-I*c*tan(f*x+e))+4/35*I/a/f/(a+I*a*tan(f*x+e))^(5/2)/sqrt(c-I*c*tan(f*x+e))+4/35*I/a^2/f/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c-I*c*tan(f*x+e))+8/35*tan(f*x+e)/a^3/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(3/2),x,7,-35*I*a^(9/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(3/2)/f-2/3*I*a*(a+I*a*tan(f*x+e))^(7/2)/f/(c-I*c*tan(f*x+e))^(3/2)+14/3*I*a^2*(a+I*a*tan(f*x+e))^(5/2)/c/f/sqrt(c-I*c*tan(f*x+e))+35/2*I*a^4*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c^2/f+35/6*I*a^3*(a+I*a*tan(f*x+e))^(3/2)*sqrt(c-I*c*tan(f*x+e))/c^2/f,1],
[(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x,6,-10*I*a^(7/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(3/2)/f-2/3*I*a*(a+I*a*tan(f*x+e))^(5/2)/f/(c-I*c*tan(f*x+e))^(3/2)+10/3*I*a^2*(a+I*a*tan(f*x+e))^(3/2)/c/f/sqrt(c-I*c*tan(f*x+e))+5*I*a^3*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c^2/f,1],
[(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x,5,-2*I*a^(5/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(3/2)/f-2/3*I*a*(a+I*a*tan(f*x+e))^(3/2)/f/(c-I*c*tan(f*x+e))^(3/2)+2*I*a^2*sqrt(a+I*a*tan(f*x+e))/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x,2,-1/3*I*(a+I*a*tan(f*x+e))^(3/2)/f/(c-I*c*tan(f*x+e))^(3/2),1],
[sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x,3,-1/3*I*sqrt(a+I*a*tan(f*x+e))/f/(c-I*c*tan(f*x+e))^(3/2)-1/3*I*sqrt(a+I*a*tan(f*x+e))/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x,4,I/f/sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2)-2/3*I*sqrt(a+I*a*tan(f*x+e))/a/f/(c-I*c*tan(f*x+e))^(3/2)-2/3*I*sqrt(a+I*a*tan(f*x+e))/a/c/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x,3,1/3*tan(f*x+e)/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2)+2/3*tan(f*x+e)/a/c/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x,4,1/5*I/f/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2)+4/15*tan(f*x+e)/a/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2)+8/15*tan(f*x+e)/a^2/c/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x,5,1/7*I/f/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2)+1/7*I/a/f/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2)+4/21*tan(f*x+e)/a^2/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2)+8/21*tan(f*x+e)/a^3/c/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(11/2)/(c-I*c*tan(f*x+e))^(5/2),x,8,63*I*a^(11/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(5/2)/f-2/5*I*a*(a+I*a*tan(f*x+e))^(9/2)/f/(c-I*c*tan(f*x+e))^(5/2)+6/5*I*a^2*(a+I*a*tan(f*x+e))^(7/2)/c/f/(c-I*c*tan(f*x+e))^(3/2)-42/5*I*a^3*(a+I*a*tan(f*x+e))^(5/2)/c^2/f/sqrt(c-I*c*tan(f*x+e))-63/2*I*a^5*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c^3/f-21/2*I*a^4*(a+I*a*tan(f*x+e))^(3/2)*sqrt(c-I*c*tan(f*x+e))/c^3/f,1],
[(a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(5/2),x,7,14*I*a^(9/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(5/2)/f-2/5*I*a*(a+I*a*tan(f*x+e))^(7/2)/f/(c-I*c*tan(f*x+e))^(5/2)+14/15*I*a^2*(a+I*a*tan(f*x+e))^(5/2)/c/f/(c-I*c*tan(f*x+e))^(3/2)-14/3*I*a^3*(a+I*a*tan(f*x+e))^(3/2)/c^2/f/sqrt(c-I*c*tan(f*x+e))-7*I*a^4*sqrt(a+I*a*tan(f*x+e))*sqrt(c-I*c*tan(f*x+e))/c^3/f,1],
[(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x,6,2*I*a^(7/2)*arctan(sqrt(c)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c-I*c*tan(f*x+e)))/c^(5/2)/f-2/5*I*a*(a+I*a*tan(f*x+e))^(5/2)/f/(c-I*c*tan(f*x+e))^(5/2)+2/3*I*a^2*(a+I*a*tan(f*x+e))^(3/2)/c/f/(c-I*c*tan(f*x+e))^(3/2)-2*I*a^3*sqrt(a+I*a*tan(f*x+e))/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x,2,-1/5*I*(a+I*a*tan(f*x+e))^(5/2)/f/(c-I*c*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x,3,-1/5*I*(a+I*a*tan(f*x+e))^(3/2)/f/(c-I*c*tan(f*x+e))^(5/2)-1/15*I*(a+I*a*tan(f*x+e))^(3/2)/c/f/(c-I*c*tan(f*x+e))^(3/2),1],
[sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x,4,-1/5*I*sqrt(a+I*a*tan(f*x+e))/f/(c-I*c*tan(f*x+e))^(5/2)-2/15*I*sqrt(a+I*a*tan(f*x+e))/c/f/(c-I*c*tan(f*x+e))^(3/2)-2/15*I*sqrt(a+I*a*tan(f*x+e))/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x,5,I/f/sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2)-3/5*I*sqrt(a+I*a*tan(f*x+e))/a/f/(c-I*c*tan(f*x+e))^(5/2)-2/5*I*sqrt(a+I*a*tan(f*x+e))/a/c/f/(c-I*c*tan(f*x+e))^(3/2)-2/5*I*sqrt(a+I*a*tan(f*x+e))/a/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x,6,1/3*I/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2)+4/3*I/a/f/sqrt(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2)-4/5*I*sqrt(a+I*a*tan(f*x+e))/a^2/f/(c-I*c*tan(f*x+e))^(5/2)-8/15*I*sqrt(a+I*a*tan(f*x+e))/a^2/c/f/(c-I*c*tan(f*x+e))^(3/2)-8/15*I*sqrt(a+I*a*tan(f*x+e))/a^2/c^2/f/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x,4,1/5*tan(f*x+e)/f/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2)+4/15*tan(f*x+e)/a/c/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2)+8/15*tan(f*x+e)/a^2/c^2/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x,5,1/7*I/f/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2)+6/35*tan(f*x+e)/a/f/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2)+8/35*tan(f*x+e)/a^2/c/f/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2)+16/35*tan(f*x+e)/a^3/c^2/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^n,x,4,8*I*a^4*(c-I*c*tan(f*x+e))^n/f/n-12*I*a^4*(c-I*c*tan(f*x+e))^(1+n)/c/f/(1+n)+6*I*a^4*(c-I*c*tan(f*x+e))^(2+n)/c^2/f/(2+n)-I*a^4*(c-I*c*tan(f*x+e))^(3+n)/c^3/f/(3+n),1],
[(a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^n,x,4,4*I*a^3*(c-I*c*tan(f*x+e))^n/f/n-4*I*a^3*(c-I*c*tan(f*x+e))^(1+n)/c/f/(1+n)+I*a^3*(c-I*c*tan(f*x+e))^(2+n)/c^2/f/(2+n),1],
[(a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^n,x,4,2*I*a^2*(c-I*c*tan(f*x+e))^n/f/n-I*a^2*(c-I*c*tan(f*x+e))^(1+n)/c/f/(1+n),1],
[(a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x,3,I*a*(c-I*c*tan(f*x+e))^n/f/n,1],
[(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x,3,1/4*I*hypergeom([2, n],[1+n],1/2-1/2*I*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/a/f/n,1],
[(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x,3,1/8*I*hypergeom([3, n],[1+n],1/2-1/2*I*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/a^2/f/n,1],
[(c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x,3,1/16*I*hypergeom([4, n],[1+n],1/2-1/2*I*tan(f*x+e))*(c-I*c*tan(f*x+e))^n/a^3/f/n,1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n,x,3,1/2*I*hypergeom([1, m+n],[1+n],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n/f/n,1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^4,x,4,-8*I*c^4*(a+I*a*tan(f*x+e))^m/f/m+12*I*c^4*(a+I*a*tan(f*x+e))^(1+m)/a/f/(1+m)-6*I*c^4*(a+I*a*tan(f*x+e))^(2+m)/a^2/f/(2+m)+I*c^4*(a+I*a*tan(f*x+e))^(3+m)/a^3/f/(3+m),1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^3,x,4,-4*I*c^3*(a+I*a*tan(f*x+e))^m/f/m+4*I*c^3*(a+I*a*tan(f*x+e))^(1+m)/a/f/(1+m)-I*c^3*(a+I*a*tan(f*x+e))^(2+m)/a^2/f/(2+m),1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^2,x,4,-2*I*c^2*(a+I*a*tan(f*x+e))^m/f/m+I*c^2*(a+I*a*tan(f*x+e))^(1+m)/a/f/(1+m),1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),x,3,-I*c*(a+I*a*tan(f*x+e))^m/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x,3,-1/4*I*hypergeom([2, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/c/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x,3,-1/8*I*hypergeom([3, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/c^2/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x,3,-1/16*I*hypergeom([4, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/c^3/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x,3,-1/32*I*hypergeom([5, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/c^4/f/m,1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2),x,3,1/5*I*hypergeom([1, 5/2+m],[7/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2)/f,1],
[(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2),x,3,1/3*I*hypergeom([1, 3/2+m],[5/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2)/f,1],
[(a+I*a*tan(f*x+e))^m*sqrt(c-I*c*tan(f*x+e)),x,3,I*hypergeom([1, 1/2+m],[3/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m*sqrt(c-I*c*tan(f*x+e))/f,1],
[(a+I*a*tan(f*x+e))^m/sqrt(c-I*c*tan(f*x+e)),x,3,-I*hypergeom([1, -1/2+m],[1/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/sqrt(c-I*c*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x,3,-1/3*I*hypergeom([1, -3/2+m],[-1/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/(c-I*c*tan(f*x+e))^(3/2),1],
[(a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x,3,-1/5*I*hypergeom([1, -5/2+m],[-3/2],1/2-1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/(c-I*c*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e)),x,4,4*a^3*(c-I*d)*x-4*a^3*(I*c+d)*ln(cos(f*x+e))/f-2*a^3*(c-I*d)*tan(f*x+e)/f+1/2*a*(I*c+d)*(a+I*a*tan(f*x+e))^2/f+1/3*d*(a+I*a*tan(f*x+e))^3/f,1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e)),x,3,2*a^2*(c-I*d)*x-2*a^2*(I*c+d)*ln(cos(f*x+e))/f-a^2*(c-I*d)*tan(f*x+e)/f+1/2*d*(a+I*a*tan(f*x+e))^2/f,1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x,2,a*(c-I*d)*x-a*(I*c+d)*ln(cos(f*x+e))/f+I*a*d*tan(f*x+e)/f,1],
[(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,2,1/2*(c-I*d)*x/a+1/2*(I*c-d)/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,3,1/4*(c-I*d)*x/a^2+1/4*(I*c-d)/f/(a+I*a*tan(f*x+e))^2+1/4*(I*c+d)/f/(a^2+I*a^2*tan(f*x+e)),1],
[(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,4,1/8*(c-I*d)*x/a^3+1/6*(I*c-d)/f/(a+I*a*tan(f*x+e))^3+1/8*(I*c+d)/a/f/(a+I*a*tan(f*x+e))^2+1/8*(I*c+d)/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x,5,4*a^3*(c-I*d)^2*x-4*I*a^3*(c-I*d)^2*ln(cos(f*x+e))/f-2*a^3*(c-I*d)^2*tan(f*x+e)/f+1/2*I*a*(c-I*d)^2*(a+I*a*tan(f*x+e))^2/f+2/3*c*d*(a+I*a*tan(f*x+e))^3/f-1/4*I*d^2*(a+I*a*tan(f*x+e))^4/a/f,1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x,4,2*a^2*(c-I*d)^2*x-2*I*a^2*(c-I*d)^2*ln(cos(f*x+e))/f-a^2*(c-I*d)^2*tan(f*x+e)/f+c*d*(a+I*a*tan(f*x+e))^2/f-1/3*I*d^2*(a+I*a*tan(f*x+e))^3/a/f,1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^2,x,3,a*(c-I*d)^2*x-I*a*(c-I*d)^2*ln(cos(f*x+e))/f+a*d*(I*c+d)*tan(f*x+e)/f+1/2*I*a*(c+d*tan(f*x+e))^2/f,1],
[(c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x,3,1/2*(c^2-2*I*c*d+d^2)*x/a+I*d^2*ln(cos(f*x+e))/a/f+1/2*I*(c+I*d)^2/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x,3,1/4*(c-I*d)^2*x/a^2+1/4*(c+I*d)*(I*c+3*d)/a^2/f/(1+I*tan(f*x+e))+1/4*I*(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2,1],
[(c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x,4,1/8*(c-I*d)^2*x/a^3+1/6*I*(c+I*d)^2/f/(a+I*a*tan(f*x+e))^3+1/8*(c+I*d)*(I*c+3*d)/a/f/(a+I*a*tan(f*x+e))^2+1/8*I*(c-I*d)^2/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x,6,4*a^3*(c-I*d)^3*x+4*a^3*(I*c+d)^3*ln(cos(f*x+e))/f+4*I*a^3*(c-I*d)^2*d*tan(f*x+e)/f+2*a^3*(I*c+d)*(c+d*tan(f*x+e))^2/f+4/3*I*a^3*(c+d*tan(f*x+e))^3/f+1/20*a^3*(I*c-11*d)*(c+d*tan(f*x+e))^4/d^2/f-1/5*(a^3+I*a^3*tan(f*x+e))*(c+d*tan(f*x+e))^4/d/f,1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x,5,2*a^2*(c-I*d)^3*x+2*a^2*(I*c+d)^3*ln(cos(f*x+e))/f+2*I*a^2*(c-I*d)^2*d*tan(f*x+e)/f+a^2*(I*c+d)*(c+d*tan(f*x+e))^2/f+2/3*I*a^2*(c+d*tan(f*x+e))^3/f-1/4*a^2*(c+d*tan(f*x+e))^4/d/f,1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^3,x,4,a*(c-I*d)^3*x+a*(I*c+d)^3*ln(cos(f*x+e))/f+I*a*(c-I*d)^2*d*tan(f*x+e)/f+1/2*a*(I*c+d)*(c+d*tan(f*x+e))^2/f+1/3*I*a*(c+d*tan(f*x+e))^3/f,1],
[(c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x,3,1/2*(c^3-3*I*c^2*d+3*c*d^2+3*I*d^3)*x/a+(3*I*c-d)*d^2*ln(cos(f*x+e))/a/f-1/2*(c+3*I*d)*d^2*tan(f*x+e)/a/f+1/2*(I*c-d)*(c+d*tan(f*x+e))^2/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x,5,1/4*(c^3-3*I*c^2*d-3*c*d^2-3*I*d^3)*x/a^2+d^3*ln(cos(f*x+e))/a^2/f+1/4*(c+I*d)^2*(I*c+3*d)/a^2/f/(1+I*tan(f*x+e))+1/4*(I*c-d)*(c+d*tan(f*x+e))^2/f/(a+I*a*tan(f*x+e))^2,1],
[(c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x,4,1/8*(c-I*d)^3*x/a^3+1/8*(c+I*d)*(c-3*I*d)*(I*c+d)/a^3/f/(1+I*tan(f*x+e))+1/8*(c+I*d)^2*(I*c+d)/a/f/(a+I*a*tan(f*x+e))^2+1/6*I*(c+d*tan(f*x+e))^3/f/(a+I*a*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x,5,4*a^3*x/(c-I*d)-a^3*(I*c-3*d)*ln(cos(f*x+e))/d^2/f-a^3*(c+I*d)^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/d^2/(I*c+d)/f-(a^3+I*a^3*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x,4,-a^2*c*(c+I*d)*x/(c-I*d)/d^2+a^2*(c+2*I*d)*x/d^2+a^2*ln(cos(f*x+e))/d/f-a^2*(I*c-d)*ln(c*cos(f*x+e)+d*sin(f*x+e))/d/(I*c+d)/f,1],
[(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x,2,a*x/(c-I*d)+a*ln(c*cos(f*x+e)+d*sin(f*x+e))/(I*c+d)/f,1],
[1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x,5,1/2*x/a/(c+I*d)-c*d*x/a/(I*c-d)/(c^2+d^2)-d^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/a/(I*c-d)/(c^2+d^2)/f-1/2/(I*c-d)/f/(a+I*a*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x,4,1/4*(c^3+3*I*c^2*d-3*c*d^2+3*I*d^3)*x/a^2/(c-I*d)/(c+I*d)^3-d^3*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^2/(c-I*d)/(c+I*d)^3/f+1/4*(I*c-3*d)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))-1/4/(I*c-d)/f/(a+I*a*tan(f*x+e))^2,1],
[1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x,5,1/8*(c^4+4*I*c^3*d-6*c^2*d^2-4*I*c*d^3-7*d^4)*x/a^3/(c-I*d)/(c+I*d)^4+d^4*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^3/(c+I*d)^4/(I*c+d)/f-1/6/(I*c-d)/f/(a+I*a*tan(f*x+e))^3+1/8*(I*c-3*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2+1/8*(c^2+4*I*c*d-7*d^2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x,5,4*a^3*x/(c-I*d)^2+I*a^3*ln(cos(f*x+e))/d^2/f-a^3*(I*c-d)*(c-3*I*d)*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c-I*d)^2/d^2/f+(c+I*d)*(a^3+I*a^3*tan(f*x+e))/(c-I*d)/d/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x,3,2*a^2*x/(c-I*d)^2-2*I*a^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c-I*d)^2/f+a^2*(I*c-d)/d/(I*c+d)/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x,3,a*x/(c-I*d)^2-I*a*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c-I*d)^2/f-a/(I*c+d)/f/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x,4,1/2*(c^3+3*I*c^2*d+3*c*d^2-3*I*d^3)*x/a/(c-I*d)^2/(c+I*d)^3+(3*c-I*d)*d^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/a/(I*c-d)^3/(c-I*d)^2/f+1/2*(c-3*I*d)*d/a/(c-I*d)/(c+I*d)^2/f/(c+d*tan(f*x+e))-1/2/(I*c-d)/f/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x,5,1/4*(c^4+4*I*c^3*d-6*c^2*d^2+12*I*c*d^3+9*d^4)*x/a^2/(c-I*d)^2/(c+I*d)^4-2*(2*c-I*d)*d^3*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^2/(c-I*d)^2/(c+I*d)^4/f+1/4*d*(c^2+4*I*c*d+9*d^2)/a^2/(c-I*d)/(c+I*d)^3/f/(c+d*tan(f*x+e))+1/4*(I*c-4*d)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))/(c+d*tan(f*x+e))-1/4/(I*c-d)/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x,6,1/8*(c^5+5*I*c^4*d-10*c^3*d^2-10*I*c^2*d^3-35*c*d^4+25*I*d^5)*x/a^3/(c-I*d)^2/(c+I*d)^5+(5*c-3*I*d)*d^4*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^3/(I*c-d)^5/(c-I*d)^2/f+1/8*d*(c^3+5*I*c^2*d-11*c*d^2+25*I*d^3)/a^3/(c-I*d)/(c+I*d)^4/f/(c+d*tan(f*x+e))-1/6/(I*c-d)/f/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))+1/24*(3*I*c-11*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))+1/8*(c^2+5*I*c*d-12*d^2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e))/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x,4,4*a^3*x/(c-I*d)^3-4*a^3*ln(c*cos(f*x+e)+d*sin(f*x+e))/(I*c+d)^3/f-1/2*a*(a+I*a*tan(f*x+e))^2/(I*c+d)/f/(c+d*tan(f*x+e))^2+2*a^3*(c+I*d)/(c-I*d)^2/d/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x,4,2*a^2*x/(c-I*d)^3-2*a^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/(I*c+d)^3/f+1/2*a^2*(I*c-d)/d/(I*c+d)/f/(c+d*tan(f*x+e))^2+2*I*a^2/(c-I*d)^2/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x,4,a*x/(c-I*d)^3-a*ln(c*cos(f*x+e)+d*sin(f*x+e))/(I*c+d)^3/f-1/2*a/(I*c+d)/f/(c+d*tan(f*x+e))^2+I*a/(c-I*d)^2/f/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x,5,1/2*(c^4+4*I*c^3*d+6*c^2*d^2-12*I*c*d^3-3*d^4)*x/a/(c-I*d)^3/(c+I*d)^4+2*d^2*(3*c^2-2*I*c*d-d^2)*ln(c*cos(f*x+e)+d*sin(f*x+e))/a/(c+I*d)^4/(I*c+d)^3/f+1/2*(c-2*I*d)*d/a/(c-I*d)/(c+I*d)^2/f/(c+d*tan(f*x+e))^2-1/2/(I*c-d)/f/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2+1/2*d*(c^2-8*I*c*d-3*d^2)/a/(c-I*d)^2/(c+I*d)^3/f/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x,6,1/4*(c^5+5*I*c^4*d-10*c^3*d^2+30*I*c^2*d^3+45*c*d^4-15*I*d^5)*x/a^2/(c-I*d)^3/(c+I*d)^5-2*d^3*(5*c^2-5*I*c*d-2*d^2)*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^2/(I*c-d)^5/(I*c+d)^3/f+1/4*d*(c^2+5*I*c*d+8*d^2)/a^2/(c-I*d)/(c+I*d)^3/f/(c+d*tan(f*x+e))^2+1/4*(I*c-5*d)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))/(c+d*tan(f*x+e))^2-1/4/(I*c-d)/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2+1/4*(c-3*I*d)*d*(c^2+8*I*c*d+5*d^2)/a^2/(c-I*d)^2/(c+I*d)^4/f/(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x,7,1/8*(c^6+6*I*c^5*d-15*c^4*d^2-20*I*c^3*d^3-105*c^2*d^4+150*I*c*d^5+55*d^6)*x/a^3/(c-I*d)^3/(c+I*d)^6-d^4*(15*c^2-18*I*c*d-7*d^2)*ln(c*cos(f*x+e)+d*sin(f*x+e))/a^3/(c+I*d)^6/(I*c+d)^3/f+1/8*d*(c^3+6*I*c^2*d-17*c*d^2+28*I*d^3)/a^3/(c-I*d)/(c+I*d)^4/f/(c+d*tan(f*x+e))^2-1/6/(I*c-d)/f/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2+1/24*(3*I*c-13*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2+1/24*(3*c^2+18*I*c*d-55*d^2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e))/(c+d*tan(f*x+e))^2+1/8*d*(c^4+6*I*c^3*d-16*c^2*d^2+94*I*c*d^3+55*d^4)/a^3/(c-I*d)^2/(c+I*d)^5/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*sqrt(c+d*tan(f*x+e)),x,6,-8*I*a^3*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+8*I*a^3*sqrt(c+d*tan(f*x+e))/f+4/15*a^3*(I*c-6*d)*(c+d*tan(f*x+e))^(3/2)/d^2/f-2/5*(a^3+I*a^3*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+I*a*tan(f*x+e))^2*sqrt(c+d*tan(f*x+e)),x,5,-4*I*a^2*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+4*I*a^2*sqrt(c+d*tan(f*x+e))/f-2/3*a^2*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e)),x,4,-2*I*a*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+2*I*a*sqrt(c+d*tan(f*x+e))/f,1],
[sqrt(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x,8,-1/2*I*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/f+1/2*I*c*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/sqrt(c+I*d)/f+1/2*I*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e)),1],
[sqrt(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x,9,-1/4*I*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/f-1/8*(2*c*d-I*(2*c^2+d^2))*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/(c+I*d)^(3/2)/f+1/8*(2*I*c-d)*sqrt(c+d*tan(f*x+e))/a^2/(c+I*d)/f/(1+I*tan(f*x+e))+1/4*I*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^2,1],
[sqrt(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x,10,-1/8*I*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/f+1/16*(2*I*c^3-4*c^2*d-I*c*d^2-2*d^3)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/(c+I*d)^(5/2)/f+1/6*I*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^3+1/24*(3*I*c-2*d)*sqrt(c+d*tan(f*x+e))/a/(c+I*d)/f/(a+I*a*tan(f*x+e))^2+1/16*c*(2*I*c-3*d)*sqrt(c+d*tan(f*x+e))/(c+I*d)^2/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x,7,-8*I*a^3*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+8*a^3*(I*c+d)*sqrt(c+d*tan(f*x+e))/f+8/3*I*a^3*(c+d*tan(f*x+e))^(3/2)/f+4/35*a^3*(I*c-8*d)*(c+d*tan(f*x+e))^(5/2)/d^2/f-2/7*(a^3+I*a^3*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)/d/f,1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x,6,-4*I*a^2*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+4*a^2*(I*c+d)*sqrt(c+d*tan(f*x+e))/f+4/3*I*a^2*(c+d*tan(f*x+e))^(3/2)/f-2/5*a^2*(c+d*tan(f*x+e))^(5/2)/d/f,1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x,5,-2*I*a*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+2*a*(I*c+d)*sqrt(c+d*tan(f*x+e))/f+2/3*I*a*(c+d*tan(f*x+e))^(3/2)/f,1],
[(c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x,8,-1/2*I*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/f+1/2*sqrt(c+I*d)*(I*c+2*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/f+1/2*(I*c-d)*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x,9,-1/4*I*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/f+1/8*(2*c*d+I*(2*c^2+d^2))*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/sqrt(c+I*d)/f+1/8*(2*I*c+3*d)*sqrt(c+d*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))+1/4*(I*c-d)*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^2,1],
[(c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x,10,-1/8*I*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/f+1/16*I*c*(2*c^2+3*d^2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/(c+I*d)^(3/2)/f+1/6*(I*c-d)*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^3+1/24*(3*I*c+4*d)*sqrt(c+d*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^2-1/16*(2*c^2-I*c*d+2*d^2)*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x,8,-8*I*a^3*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+8*I*a^3*(c-I*d)^2*sqrt(c+d*tan(f*x+e))/f+8/3*a^3*(I*c+d)*(c+d*tan(f*x+e))^(3/2)/f+8/5*I*a^3*(c+d*tan(f*x+e))^(5/2)/f+4/63*a^3*(I*c-10*d)*(c+d*tan(f*x+e))^(7/2)/d^2/f-2/9*(a^3+I*a^3*tan(f*x+e))*(c+d*tan(f*x+e))^(7/2)/d/f,1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x,7,-4*I*a^2*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+4*I*a^2*(c-I*d)^2*sqrt(c+d*tan(f*x+e))/f+4/3*a^2*(I*c+d)*(c+d*tan(f*x+e))^(3/2)/f+4/5*I*a^2*(c+d*tan(f*x+e))^(5/2)/f-2/7*a^2*(c+d*tan(f*x+e))^(7/2)/d/f,1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x,6,-2*I*a*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+2*I*a*(c-I*d)^2*sqrt(c+d*tan(f*x+e))/f+2/3*a*(I*c+d)*(c+d*tan(f*x+e))^(3/2)/f+2/5*I*a*(c+d*tan(f*x+e))^(5/2)/f,1],
[(c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x,9,-1/2*I*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/f+1/2*(c+I*d)^(3/2)*(I*c+4*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/f-1/2*(c+5*I*d)*d*sqrt(c+d*tan(f*x+e))/a/f+1/2*(I*c-d)*(c+d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x,9,-1/4*I*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/f+1/8*sqrt(c+I*d)*(2*I*c^2+6*c*d-7*I*d^2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/f+1/8*(c+I*d)*(2*I*c+5*d)*sqrt(c+d*tan(f*x+e))/a^2/f/(1+I*tan(f*x+e))+1/4*(I*c-d)*(c+d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^2,1],
[(c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x,10,-1/8*I*(c-I*d)^(5/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/f+1/16*(2*I*c^3+4*c^2*d-I*c*d^2+2*d^3)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/sqrt(c+I*d)/f+1/8*(c+I*d)*(I*c+2*d)*sqrt(c+d*tan(f*x+e))/a/f/(a+I*a*tan(f*x+e))^2+1/16*(2*I*c^2+5*c*d-4*I*d^2)*sqrt(c+d*tan(f*x+e))/f/(a^3+I*a^3*tan(f*x+e))+1/6*(I*c-d)*(c+d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^3,1],
[(a+I*a*tan(f*x+e))^3/sqrt(c+d*tan(f*x+e)),x,5,-8*I*a^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f+4/3*a^3*(I*c-4*d)*sqrt(c+d*tan(f*x+e))/d^2/f-2/3*(a^3+I*a^3*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e)),x,4,-4*I*a^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f-2*a^2*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,3,-2*I*a*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f,1],
[1/(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,8,-1/2*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/sqrt(c-I*d)/f+1/2*(I*c-2*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/(c+I*d)^(3/2)/f-1/2*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a+I*a*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e)),x,9,-1/4*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/sqrt(c-I*d)/f+1/8*(2*I*c^2-6*c*d-7*I*d^2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/(c+I*d)^(5/2)/f+1/8*(2*I*c-5*d)*sqrt(c+d*tan(f*x+e))/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))-1/4*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a+I*a*tan(f*x+e))^2,1],
[1/(a+I*a*tan(f*x+e))^3/sqrt(c+d*tan(f*x+e)),x,10,-1/8*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/sqrt(c-I*d)/f+1/16*(2*I*c^3-8*c^2*d-13*I*c*d^2+12*d^3)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/(c+I*d)^(7/2)/f-1/6*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a+I*a*tan(f*x+e))^3+1/24*(3*I*c-8*d)*sqrt(c+d*tan(f*x+e))/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2+1/16*(2*c^2+7*I*c*d-10*d^2)*sqrt(c+d*tan(f*x+e))/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x,5,-8*I*a^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f+2*(c+I*d)*(a^3+I*a^3*tan(f*x+e))/(c-I*d)/d/f/sqrt(c+d*tan(f*x+e))+4*a^3*c*sqrt(c+d*tan(f*x+e))/d^2/(I*c+d)/f,1],
[(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x,4,-4*I*a^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f+2*a^2*(I*c-d)/d/(I*c+d)/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,4,-2*I*a*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f-2*a/(I*c+d)/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,9,-1/2*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/(c-I*d)^(3/2)/f+1/2*(I*c-4*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/(c+I*d)^(5/2)/f+1/2*(c-5*I*d)*d/a/(c-I*d)/(c+I*d)^2/f/sqrt(c+d*tan(f*x+e))-1/2/(I*c-d)/f/(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x,10,-1/4*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/(c-I*d)^(3/2)/f+1/8*(2*I*c^2-10*c*d-23*I*d^2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/(c+I*d)^(7/2)/f+1/8*d*(2*c^2+7*I*c*d+25*d^2)/a^2/(c-I*d)/(c+I*d)^3/f/sqrt(c+d*tan(f*x+e))+1/8*(2*I*c-7*d)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))/sqrt(c+d*tan(f*x+e))-1/4/(I*c-d)/f/(a+I*a*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x,11,-1/8*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/(c-I*d)^(3/2)/f+1/16*(2*I*c^3-12*c^2*d-33*I*c*d^2+58*d^3)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/(c+I*d)^(9/2)/f+1/16*d*(2*c^3+9*I*c^2*d-17*c*d^2+60*I*d^3)/a^3/(c-I*d)/(c+I*d)^4/f/sqrt(c+d*tan(f*x+e))-1/6/(I*c-d)/f/(a+I*a*tan(f*x+e))^3/sqrt(c+d*tan(f*x+e))+1/24*(3*I*c-10*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e))+1/48*(6*c^2+27*I*c*d-56*d^2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x,5,-8*I*a^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f+2/3*(c+I*d)*(a^3+I*a^3*tan(f*x+e))/(c-I*d)/d/f/(c+d*tan(f*x+e))^(3/2)+4/3*a^3*(I*c-d)*(c-4*I*d)/(c-I*d)^2/d^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x,5,-4*I*a^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f+2/3*a^2*(I*c-d)/d/(I*c+d)/f/(c+d*tan(f*x+e))^(3/2)+4*I*a^2/(c-I*d)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,5,-2*I*a*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f-2/3*a/(I*c+d)/f/(c+d*tan(f*x+e))^(3/2)+2*I*a/(c-I*d)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,10,-1/2*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a/(c-I*d)^(5/2)/f+1/2*(I*c-6*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a/(c+I*d)^(7/2)/f+1/6*d*(3*I*c+7*d)/a/(I*c-d)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-1/2/(I*c-d)/f/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+1/2*d*(c^2-14*I*c*d-5*d^2)/a/(c-I*d)^2/(c+I*d)^3/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x,11,-1/4*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^2/(c-I*d)^(5/2)/f+1/8*(2*I*c^2-14*c*d-47*I*d^2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^2/(c+I*d)^(9/2)/f+1/24*d*(6*c^2+27*I*c*d+49*d^2)/a^2/(c-I*d)/(c+I*d)^3/f/(c+d*tan(f*x+e))^(3/2)+1/8*(2*I*c-9*d)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)-1/4/(I*c-d)/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2)+1/8*d*(2*c^3+9*I*c^2*d+88*c*d^2-45*I*d^3)/a^2/(c-I*d)^2/(c+I*d)^4/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x,12,-1/8*I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/a^3/(c-I*d)^(5/2)/f+1/16*(2*I*c^3-16*c^2*d-61*I*c*d^2+152*d^3)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/a^3/(c+I*d)^(11/2)/f+1/48*d*(6*c^3+33*I*c^2*d-83*c*d^2+154*I*d^3)/a^3/(c-I*d)/(c+I*d)^4/f/(c+d*tan(f*x+e))^(3/2)-1/6/(I*c-d)/f/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2)+1/8*(I*c-4*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2)+1/16*(2*c^2+11*I*c*d-30*d^2)/(I*c-d)^3/f/(a^3+I*a^3*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+1/16*d*(2*c^4+11*I*c^3*d-26*c^2*d^2+253*I*c*d^3+150*d^4)/a^3/(c-I*d)^2/(c+I*d)^5/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)*sqrt(c+d*tan(f*x+e)),x,8,-1/4*(-1)^(1/4)*a^(5/2)*(c^2+10*I*c*d+23*d^2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-4*I*sqrt(2)*a^(5/2)*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/4*a^2*(c+9*I*d)*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f-1/2*a^2*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*sqrt(c+d*tan(f*x+e)),x,8,-(-1)^(1/4)*a^(3/2)*(I*c+3*d)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f-2*I*sqrt(2)*a^(3/2)*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+a^2*(c+I*d)*sqrt(c+d*tan(f*x+e))/d/f/sqrt(a+I*a*tan(f*x+e))-a^2*(c+d*tan(f*x+e))^(3/2)/d/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e)),x,6,-2*(-1)^(1/4)*sqrt(a)*sqrt(d)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/f-I*sqrt(2)*sqrt(a)*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f,1],
[sqrt(c+d*tan(f*x+e))/sqrt(a+I*a*tan(f*x+e)),x,3,-I*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/f+I*sqrt(c+d*tan(f*x+e))/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x,4,-1/2*I*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/f+1/2*I*sqrt(c+d*tan(f*x+e))/a/f/sqrt(a+I*a*tan(f*x+e))-1/3*(c+d*tan(f*x+e))^(3/2)/(I*c-d)/f/(a+I*a*tan(f*x+e))^(3/2),1],
[sqrt(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2),x,6,-1/4*I*sqrt(c-I*d)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/f+1/5*I*sqrt(c+d*tan(f*x+e))/f/(a+I*a*tan(f*x+e))^(5/2)+1/30*(5*I*c-3*d)*sqrt(c+d*tan(f*x+e))/a/(c+I*d)/f/(a+I*a*tan(f*x+e))^(3/2)-1/60*(20*c*d-I*(15*c^2+3*d^2))*sqrt(c+d*tan(f*x+e))/a^2/(c+I*d)^2/f/sqrt(a+I*a*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(3/2),x,9,-1/8*(-1)^(1/4)*a^(5/2)*(c-3*I*d)*(c^2+18*I*c*d+15*d^2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-4*I*sqrt(2)*a^(5/2)*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/8*a^2*(c^2+14*I*c*d+19*d^2)*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f+1/12*a^2*(c+13*I*d)*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f-1/3*a^2*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)/d/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x,9,-1/4*(-1)^(1/4)*a^(3/2)*(3*I*c^2+18*c*d-11*I*d^2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f-2*I*sqrt(2)*a^(3/2)*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/4*a*(3*I*c+5*d)*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f+1/2*a^2*(c+I*d)*(c+d*tan(f*x+e))^(3/2)/d/f/sqrt(a+I*a*tan(f*x+e))-1/2*a^2*(c+d*tan(f*x+e))^(5/2)/d/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x,7,-(-1)^(1/4)*sqrt(a)*(3*c-I*d)*sqrt(d)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/f-I*sqrt(2)*sqrt(a)*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+d*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f,1],
[(c+d*tan(f*x+e))^(3/2)/sqrt(a+I*a*tan(f*x+e)),x,7,2*(-1)^(3/4)*d^(3/2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(a)/f-I*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/f+(I*c-d)*sqrt(c+d*tan(f*x+e))/f/sqrt(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x,4,-1/2*I*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/f+1/2*(I*c+d)*sqrt(c+d*tan(f*x+e))/a/f/sqrt(a+I*a*tan(f*x+e))+1/3*I*(c+d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x,5,-1/4*I*(c-I*d)^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/f+1/4*(I*c+d)*sqrt(c+d*tan(f*x+e))/a^2/f/sqrt(a+I*a*tan(f*x+e))+1/6*I*(c+d*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^(3/2)-1/5*(c+d*tan(f*x+e))^(5/2)/(I*c-d)/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(5/2),x,10,-1/64*(-1)^(1/4)*a^(5/2)*(5*c^4+100*I*c^3*d+690*c^2*d^2-900*I*c*d^3-363*d^4)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-4*I*sqrt(2)*a^(5/2)*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/64*a^2*(5*c^3+95*I*c^2*d+273*c*d^2-149*I*d^3)*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f+1/96*a^2*(5*c^2+90*I*c*d+107*d^2)*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f+1/24*a^2*(c+17*I*d)*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)/d/f-1/4*a^2*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(7/2)/d/f,1],
[(a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x,10,-1/8*(-1)^(1/4)*a^(3/2)*(5*I*c^3+45*c^2*d-55*I*c*d^2-23*d^3)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f-2*I*sqrt(2)*a^(3/2)*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/8*a*(c-3*I*d)*(5*I*c+3*d)*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f+1/12*a*(5*I*c+7*d)*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/f+1/3*a^2*(c+I*d)*(c+d*tan(f*x+e))^(5/2)/d/f/sqrt(a+I*a*tan(f*x+e))-1/3*a^2*(c+d*tan(f*x+e))^(7/2)/d/f/sqrt(a+I*a*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x,8,-1/4*(-1)^(1/4)*sqrt(a)*sqrt(d)*(15*c^2-10*I*c*d-7*d^2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/f-I*sqrt(2)*sqrt(a)*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/f+1/4*(7*c-I*d)*d*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f+1/2*d*sqrt(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/f,1],
[(c+d*tan(f*x+e))^(5/2)/sqrt(a+I*a*tan(f*x+e)),x,8,(-1)^(1/4)*(5*I*c-d)*d^(3/2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(a)/f-I*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/f-(c+2*I*d)*d*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/a/f+(I*c-d)*(c+d*tan(f*x+e))^(3/2)/f/sqrt(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x,8,2*(-1)^(1/4)*d^(5/2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/a^(3/2)/f-1/2*I*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/f+1/2*(c+I*d)*(I*c+3*d)*sqrt(c+d*tan(f*x+e))/a/f/sqrt(a+I*a*tan(f*x+e))+1/3*(I*c-d)*(c+d*tan(f*x+e))^(3/2)/f/(a+I*a*tan(f*x+e))^(3/2),1],
[(c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x,5,-1/4*I*(c-I*d)^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/f+1/4*I*(c-I*d)^2*sqrt(c+d*tan(f*x+e))/a^2/f/sqrt(a+I*a*tan(f*x+e))+1/6*(I*c+d)*(c+d*tan(f*x+e))^(3/2)/a/f/(a+I*a*tan(f*x+e))^(3/2)+1/5*I*(c+d*tan(f*x+e))^(5/2)/f/(a+I*a*tan(f*x+e))^(5/2),1],
[(a+I*a*tan(f*x+e))^(5/2)/sqrt(c+d*tan(f*x+e)),x,7,-(-1)^(1/4)*a^(5/2)*(c+5*I*d)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(c-I*d)/f-a^2*sqrt(a+I*a*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+I*a*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e)),x,6,-2*(-1)^(3/4)*a^(3/2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f-2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(c-I*d)/f,1],
[sqrt(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,2,-I*sqrt(2)*sqrt(a)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(c-I*d)/f,1],
[1/sqrt(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,4,-I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/sqrt(c-I*d)/f-sqrt(c+d*tan(f*x+e))/(I*c+d)/f/sqrt(a+I*a*tan(f*x+e))+2*d*sqrt(c+d*tan(f*x+e))/(c^2+d^2)/f/sqrt(a+I*a*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e)),x,5,-1/2*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/sqrt(c-I*d)/f-1/3*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a+I*a*tan(f*x+e))^(3/2)+1/6*(3*I*c-7*d)*sqrt(c+d*tan(f*x+e))/a/(c+I*d)^2/f/sqrt(a+I*a*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/sqrt(c+d*tan(f*x+e)),x,6,-1/4*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/sqrt(c-I*d)/f-1/5*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/(a+I*a*tan(f*x+e))^(5/2)+1/30*(5*I*c-13*d)*sqrt(c+d*tan(f*x+e))/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^(3/2)+1/60*(15*c^2+50*I*c*d-67*d^2)*sqrt(c+d*tan(f*x+e))/a^2/(I*c-d)^3/f/sqrt(a+I*a*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x,7,2*(-1)^(1/4)*a^(5/2)*arctanh((-1)^(3/4)*sqrt(d)*sqrt(a+I*a*tan(f*x+e))/sqrt(a)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(3/2)/f+2*a^2*(c+I*d)*sqrt(a+I*a*tan(f*x+e))/(c-I*d)/d/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x,3,-2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(3/2)/f-2*a*sqrt(a+I*a*tan(f*x+e))/(I*c+d)/f/sqrt(c+d*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,3,-I*sqrt(2)*sqrt(a)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(3/2)/f-2*d*sqrt(a+I*a*tan(f*x+e))/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,5,-I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/(c-I*d)^(3/2)/f-1/(I*c-d)/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e))+(c-3*I*d)*d*sqrt(a+I*a*tan(f*x+e))/a/(c-I*d)/(c+I*d)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x,6,-1/2*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/(c-I*d)^(3/2)/f-1/3/(I*c-d)/f/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e))+1/6*(3*I*c-11*d)/a/(c+I*d)^2/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e))+1/6*(3*c-5*I*d)*(c+5*I*d)*d*sqrt(a+I*a*tan(f*x+e))/a^2/(c-I*d)/(c+I*d)^3/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x,7,-1/4*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/(c-I*d)^(3/2)/f-1/5/(I*c-d)/f/(a+I*a*tan(f*x+e))^(5/2)/sqrt(c+d*tan(f*x+e))+1/30*(5*I*c-17*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e))+1/60*(15*c^2+70*I*c*d-151*d^2)/a^2/(I*c-d)^3/f/sqrt(a+I*a*tan(f*x+e))/sqrt(c+d*tan(f*x+e))+1/60*d*(15*c^3+65*I*c^2*d-117*c*d^2+317*I*d^3)*sqrt(a+I*a*tan(f*x+e))/a^3/(c-I*d)/(c+I*d)^4/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x,4,-4*I*sqrt(2)*a^(5/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(5/2)/f-2/3*a*(a+I*a*tan(f*x+e))^(3/2)/(I*c+d)/f/(c+d*tan(f*x+e))^(3/2)+4*I*a^2*sqrt(a+I*a*tan(f*x+e))/(c-I*d)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x,4,-2*I*sqrt(2)*a^(3/2)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(5/2)/f-2/3*d*(a+I*a*tan(f*x+e))^(3/2)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+2*I*a*sqrt(a+I*a*tan(f*x+e))/(c-I*d)^2/f/sqrt(c+d*tan(f*x+e)),1],
[sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,5,-I*sqrt(2)*sqrt(a)*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/(c-I*d)^(5/2)/f-2/3*d*sqrt(a+I*a*tan(f*x+e))/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-2/3*(5*c+I*d)*d*sqrt(a+I*a*tan(f*x+e))/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,6,-I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/sqrt(a)/(c-I*d)^(5/2)/f-1/(I*c-d)/f/sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+1/3*d*(3*I*c+5*d)*sqrt(a+I*a*tan(f*x+e))/a/(I*c-d)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+1/3*(3*c-I*d)*(c-7*I*d)*d*sqrt(a+I*a*tan(f*x+e))/a/(c-I*d)^2/(c+I*d)^3/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x,7,-1/2*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(3/2)/(c-I*d)^(5/2)/f-1/3/(I*c-d)/f/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2)+1/2*(I*c-5*d)/a/(c+I*d)^2/f/sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+1/6*d*(3*c^2+14*I*c*d+21*d^2)*sqrt(a+I*a*tan(f*x+e))/a^2/(c-I*d)/(c+I*d)^3/f/(c+d*tan(f*x+e))^(3/2)+1/6*(c-3*I*d)*d*(3*c^2+22*I*c*d+13*d^2)*sqrt(a+I*a*tan(f*x+e))/a^2/(c-I*d)^2/(c+I*d)^4/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x,8,-1/4*I*arctanh(sqrt(2)*sqrt(a)*sqrt(c+d*tan(f*x+e))/sqrt(c-I*d)/sqrt(a+I*a*tan(f*x+e)))/sqrt(2)/a^(5/2)/(c-I*d)^(5/2)/f-1/5/(I*c-d)/f/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2)+1/30*(5*I*c-21*d)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2)+1/20*(5*c^2+30*I*c*d-89*d^2)/a^2/(I*c-d)^3/f/sqrt(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+1/60*d*(15*c^3+85*I*c^2*d-221*c*d^2+361*I*d^3)*sqrt(a+I*a*tan(f*x+e))/a^3/(c-I*d)/(c+I*d)^4/f/(c+d*tan(f*x+e))^(3/2)+1/60*d*(15*c^4+80*I*c^3*d-182*c^2*d^2+1224*I*c*d^3+707*d^4)*sqrt(a+I*a*tan(f*x+e))/a^3/(c-I*d)^2/(c+I*d)^5/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x,3,-1/2*I*AppellF1(m,-n,1,1+m,-d*(1+I*tan(f*x+e))/(I*c-d),1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n/f/m/(((c+d*tan(f*x+e))/(c+I*d))^n),1],
[(a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^n,x,4,a^3*(I*c-d*(5+2*n))*(c+d*tan(f*x+e))^(1+n)/d^2/f/(1+n)/(2+n)+4*a^3*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/(I*c+d)/f/(1+n)-(a^3+I*a^3*tan(f*x+e))*(c+d*tan(f*x+e))^(1+n)/d/f/(2+n),1],
[(a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^n,x,3,-a^2*(c+d*tan(f*x+e))^(1+n)/d/f/(1+n)+2*a^2*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/(I*c+d)/f/(1+n),1],
[(a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^n,x,2,a*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/(I*c+d)/f/(1+n),1],
[(c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x,6,1/4*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/a/(I*c+d)/f/(1+n)+1/4*(I*c-d+2*d*n)*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c+I*d))*(c+d*tan(f*x+e))^(1+n)/a/(c+I*d)^2/f/(1+n)-1/2*(c+d*tan(f*x+e))^(1+n)/(I*c-d)/f/(a+I*a*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x,7,1/8*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/a^2/(I*c+d)/f/(1+n)+1/8*(c^2+2*I*c*d*(1-n)-d^2*(2*n^2-4*n+1))*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c+I*d))*(c+d*tan(f*x+e))^(1+n)/a^2/(I*c-d)^3/f/(1+n)+1/4*(I*c-d*(2-n))*(c+d*tan(f*x+e))^(1+n)/a^2/(c+I*d)^2/f/(1+I*tan(f*x+e))-1/4*(c+d*tan(f*x+e))^(1+n)/(I*c-d)/f/(a+I*a*tan(f*x+e))^2,1],
[(c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x,8,1/16*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c-I*d))*(c+d*tan(f*x+e))^(1+n)/a^3/(I*c+d)/f/(1+n)+1/48*(3*I*c^3-c^2*d*(9-6*n)-3*I*c*d^2*(2*n^2-6*n+3)+d^3*(-4*n^3+18*n^2-20*n+3))*hypergeom([1, 1+n],[2+n],(c+d*tan(f*x+e))/(c+I*d))*(c+d*tan(f*x+e))^(1+n)/a^3/(c+I*d)^4/f/(1+n)-1/6*(c+d*tan(f*x+e))^(1+n)/(I*c-d)/f/(a+I*a*tan(f*x+e))^3+1/24*(3*I*c-d*(7-2*n))*(c+d*tan(f*x+e))^(1+n)/a/(c+I*d)^2/f/(a+I*a*tan(f*x+e))^2+1/24*(3*I*c^2-3*c*d*(3-n)-I*d^2*(2*n^2-9*n+10))*(c+d*tan(f*x+e))^(1+n)/(c+I*d)^3/f/(a^3+I*a^3*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x,5,-2*d*(d^2+I*c*d*m-c^2*(3+m))*(a+I*a*tan(f*x+e))^m/f/m/(2+m)+1/2*(I*c+d)^3*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/m-d^2*(d*m+I*c*(4+m))*(a+I*a*tan(f*x+e))^(1+m)/a/f/(1+m)/(2+m)+d*(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2/f/(2+m),1],
[(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x,4,2*c*d*(a+I*a*tan(f*x+e))^m/f/m-1/2*I*(c-I*d)^2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/m-I*d^2*(a+I*a*tan(f*x+e))^(1+m)/a/f/(1+m),1],
[(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e)),x,3,d*(a+I*a*tan(f*x+e))^m/f/m-1/2*(I*c+d)*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e)),x,5,1/2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/(I*c+d)/f/m-d*hypergeom([1, m],[1+m],-d*(1+I*tan(f*x+e))/(I*c-d))*(a+I*a*tan(f*x+e))^m/(c^2+d^2)/f/m,1],
[(a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x,6,-1/2*I*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/(c-I*d)^2/f/m-d*(c*(2-m)+I*d*m)*hypergeom([1, m],[1+m],-d*(1+I*tan(f*x+e))/(I*c-d))*(a+I*a*tan(f*x+e))^m/(c^2+d^2)^2/f/m-d*(a+I*a*tan(f*x+e))^m/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x,7,-1/2*hypergeom([1, m],[1+m],1/2+1/2*I*tan(f*x+e))*(a+I*a*tan(f*x+e))^m/(I*c+d)^3/f/m-1/2*d*(2*I*c*d*(3-m)*m+c^2*(m^2-5*m+6)-d^2*(m^2-m+2))*hypergeom([1, m],[1+m],-d*(1+I*tan(f*x+e))/(I*c-d))*(a+I*a*tan(f*x+e))^m/(c^2+d^2)^3/f/m-1/2*d*(a+I*a*tan(f*x+e))^m/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-1/2*d*(c*(4-m)+I*d*m)*(a+I*a*tan(f*x+e))^m/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x,3,2/5*a*AppellF1(5/2,1-m,1,7/2,(c+d*tan(f*x+e))/(c+I*d),(c+d*tan(f*x+e))/(c-I*d))*(-d*(1+I*tan(f*x+e))/(I*c-d))^(1-m)*(a+I*a*tan(f*x+e))^(-1+m)*(c+d*tan(f*x+e))^(5/2)/(I*c+d)/f,1],
[(a+I*a*tan(f*x+e))^m*sqrt(c+d*tan(f*x+e)),x,3,2/3*a*AppellF1(3/2,1-m,1,5/2,(c+d*tan(f*x+e))/(c+I*d),(c+d*tan(f*x+e))/(c-I*d))*(-d*(1+I*tan(f*x+e))/(I*c-d))^(1-m)*(a+I*a*tan(f*x+e))^(-1+m)*(c+d*tan(f*x+e))^(3/2)/(I*c+d)/f,1],
[(a+I*a*tan(f*x+e))^m/sqrt(c+d*tan(f*x+e)),x,3,2*a*AppellF1(1/2,1-m,1,3/2,(c+d*tan(f*x+e))/(c+I*d),(c+d*tan(f*x+e))/(c-I*d))*(-d*(1+I*tan(f*x+e))/(I*c-d))^(1-m)*(a+I*a*tan(f*x+e))^(-1+m)*sqrt(c+d*tan(f*x+e))/(I*c+d)/f,1],
[(a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x,3,-2*a*AppellF1(-1/2,1-m,1,1/2,(c+d*tan(f*x+e))/(c+I*d),(c+d*tan(f*x+e))/(c-I*d))*(-d*(1+I*tan(f*x+e))/(I*c-d))^(1-m)*(a+I*a*tan(f*x+e))^(-1+m)/(I*c+d)/f/sqrt(c+d*tan(f*x+e)),1],
[(a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x,3,-2/3*a*AppellF1(-3/2,1-m,1,-1/2,(c+d*tan(f*x+e))/(c+I*d),(c+d*tan(f*x+e))/(c-I*d))*(-d*(1+I*tan(f*x+e))/(I*c-d))^(1-m)*(a+I*a*tan(f*x+e))^(-1+m)/(I*c+d)/f/(c+d*tan(f*x+e))^(3/2),1],
[(a+b*tan(f*x+e))^3*(c+d*tan(f*x+e)),x,4,(a^3*c-3*a^2*b*d-3*a*b^2*c+b^3*d)*x-(a^3*d+3*a^2*b*c-3*a*b^2*d-b^3*c)*ln(cos(f*x+e))/f+b*(a^2*d+2*a*b*c-b^2*d)*tan(f*x+e)/f+1/2*(a*d+b*c)*(a+b*tan(f*x+e))^2/f+1/3*d*(a+b*tan(f*x+e))^3/f,1],
[(a+b*tan(f*x+e))^2*(c+d*tan(f*x+e)),x,3,(a^2*c-2*a*b*d-b^2*c)*x-(a^2*d+2*a*b*c-b^2*d)*ln(cos(f*x+e))/f+b*(a*d+b*c)*tan(f*x+e)/f+1/2*d*(a+b*tan(f*x+e))^2/f,1],
[(a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x,2,(a*c-b*d)*x-(a*d+b*c)*ln(cos(f*x+e))/f+b*d*tan(f*x+e)/f,1],
[(c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x,2,(a*c+b*d)*x/(a^2+b^2)+(-a*d+b*c)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)/f,1],
[(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x,3,(a^2*c+2*a*b*d-b^2*c)*x/(a^2+b^2)^2+(-a^2*d+2*a*b*c+b^2*d)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/f-(-a*d+b*c)/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x,4,(a^3*c+3*a^2*b*d-3*a*b^2*c-b^3*d)*x/(a^2+b^2)^3+(-a^3*d+3*a^2*b*c+3*a*b^2*d-b^3*c)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/f-1/2*(-a*d+b*c)/(a^2+b^2)/f/(a+b*tan(f*x+e))^2-(-a^2*d+2*a*b*c+b^2*d)/(a^2+b^2)^2/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x,5,-(6*a^2*b*c*d-2*b^3*c*d-a^3*(c^2-d^2)+3*a*b^2*(c^2-d^2))*x-(2*a^3*c*d-6*a*b^2*c*d+3*a^2*b*(c^2-d^2)-b^3*(c^2-d^2))*ln(cos(f*x+e))/f+2*b*(a*d+b*c)*(a*c-b*d)*tan(f*x+e)/f+1/2*(2*a*c*d+b*(c^2-d^2))*(a+b*tan(f*x+e))^2/f+2/3*c*d*(a+b*tan(f*x+e))^3/f+1/4*d^2*(a+b*tan(f*x+e))^4/b/f,1],
[(a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x,4,(a*c-a*d-b*c-b*d)*(a*c+a*d+b*c-b*d)*x-2*(a*d+b*c)*(a*c-b*d)*ln(cos(f*x+e))/f+b*(2*a*c*d+b*(c^2-d^2))*tan(f*x+e)/f+c*d*(a+b*tan(f*x+e))^2/f+1/3*d^2*(a+b*tan(f*x+e))^3/b/f,1],
[(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2,x,3,-(2*b*c*d-a*(c^2-d^2))*x-(2*a*c*d+b*(c^2-d^2))*ln(cos(f*x+e))/f+d*(a*d+b*c)*tan(f*x+e)/f+1/2*b*(c+d*tan(f*x+e))^2/f,1],
[(c+d*tan(f*x+e))^2/(a+b*tan(f*x+e)),x,4,a*(-a*d+b*c)^2*x/b^2/(a^2+b^2)+d*(-a*d+2*b*c)*x/b^2-d^2*ln(cos(f*x+e))/b/f+(-a*d+b*c)^2*ln(a*cos(f*x+e)+b*sin(f*x+e))/b/(a^2+b^2)/f,1],
[(c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^2,x,3,-(b*(c-d)-a*(c+d))*(a*(c-d)+b*(c+d))*x/(a^2+b^2)^2+2*(-a*d+b*c)*(a*c+b*d)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/f-(-a*d+b*c)^2/b/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^3,x,4,(6*a^2*b*c*d-2*b^3*c*d+a^3*(c^2-d^2)-3*a*b^2*(c^2-d^2))*x/(a^2+b^2)^3-(2*a^3*c*d-6*a*b^2*c*d-3*a^2*b*(c^2-d^2)+b^3*(c^2-d^2))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/f-1/2*(-a*d+b*c)^2/b/(a^2+b^2)/f/(a+b*tan(f*x+e))^2-2*(-a*d+b*c)*(a*c+b*d)/(a^2+b^2)^2/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x,6,-(a*c-b*d)*(8*a*b*c*d-a^2*(c^2-3*d^2)+b^2*(3*c^2-d^2))*x+(a*d+b*c)*(8*a*b*c*d+b^2*(c^2-3*d^2)-a^2*(3*c^2-d^2))*ln(cos(f*x+e))/f+d*(2*a^3*c*d-6*a*b^2*c*d+3*a^2*b*(c^2-d^2)-b^3*(c^2-d^2))*tan(f*x+e)/f+1/2*(a^3*d+3*a^2*b*c-3*a*b^2*d-b^3*c)*(c+d*tan(f*x+e))^2/f+1/3*b*(3*a^2-b^2)*(c+d*tan(f*x+e))^3/f-1/20*b^2*(-11*a*d+b*c)*(c+d*tan(f*x+e))^4/d^2/f+1/5*b^2*(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^4/d/f,1],
[(a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x,5,-(b^2*c*(c^2-3*d^2)+2*a*b*d*(3*c^2-d^2)-a^2*(c^3-3*c*d^2))*x-(2*a*b*c*(c^2-3*d^2)-b^2*d*(3*c^2-d^2)+a^2*(3*c^2*d-d^3))*ln(cos(f*x+e))/f+2*d*(a*d+b*c)*(a*c-b*d)*tan(f*x+e)/f+1/2*(a^2*d+2*a*b*c-b^2*d)*(c+d*tan(f*x+e))^2/f+2/3*a*b*(c+d*tan(f*x+e))^3/f+1/4*b^2*(c+d*tan(f*x+e))^4/d/f,1],
[(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3,x,4,-(b*d*(3*c^2-d^2)-a*(c^3-3*c*d^2))*x-(3*a*c^2*d-a*d^3+b*c^3-3*b*c*d^2)*ln(cos(f*x+e))/f+d*(2*a*c*d+b*(c^2-d^2))*tan(f*x+e)/f+1/2*(a*d+b*c)*(c+d*tan(f*x+e))^2/f+1/3*b*(c+d*tan(f*x+e))^3/f,1],
[(c+d*tan(f*x+e))^3/(a+b*tan(f*x+e)),x,5,(a*c^3-3*a*c*d^2+3*b*c^2*d-b*d^3)*x/(a^2+b^2)+(-3*a*c^2*d+a*d^3+b*c^3-3*b*c*d^2)*ln(cos(f*x+e))/(a^2+b^2)/f+(-a*d+b*c)^3*ln(a+b*tan(f*x+e))/b^2/(a^2+b^2)/f+d^2*(c+d*tan(f*x+e))/b/f,1],
[(c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^2,x,5,-(b^2*c*(c^2-3*d^2)-2*a*b*d*(3*c^2-d^2)-a^2*(c^3-3*c*d^2))*x/(a^2+b^2)^2+(2*a*b*c*(c^2-3*d^2)+b^2*d*(3*c^2-d^2)-a^2*(3*c^2*d-d^3))*ln(cos(f*x+e))/(a^2+b^2)^2/f+(-a*d+b*c)^2*(a^2*d+2*a*b*c+3*b^2*d)*ln(a+b*tan(f*x+e))/b^2/(a^2+b^2)^2/f-(-a*d+b*c)^2*(c+d*tan(f*x+e))/b/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^3,x,4,(a*c+b*d)*(8*a*b*c*d+a^2*(c^2-3*d^2)-b^2*(3*c^2-d^2))*x/(a^2+b^2)^3+(-a*d+b*c)*(8*a*b*c*d-b^2*(c^2-3*d^2)+a^2*(3*c^2-d^2))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/f-1/2*(-a*d+b*c)^2*(a^2*d+4*a*b*c+5*b^2*d)/b^2/(a^2+b^2)^2/f/(a+b*tan(f*x+e))-1/2*(-a*d+b*c)^2*(c+d*tan(f*x+e))/b/(a^2+b^2)/f/(a+b*tan(f*x+e))^2,1],
[(a+b*tan(f*x+e))^4/(c+d*tan(f*x+e)),x,6,(a^4*c+4*a^3*b*d-6*a^2*b^2*c-4*a*b^3*d+b^4*c)*x/(c^2+d^2)-(-a^4*d+4*a^3*b*c+6*a^2*b^2*d-4*a*b^3*c-b^4*d)*ln(cos(f*x+e))/(c^2+d^2)/f+(-a*d+b*c)^4*ln(c+d*tan(f*x+e))/d^3/(c^2+d^2)/f-b^3*(-3*a*d+b*c)*tan(f*x+e)/d^2/f+1/2*b^2*(a+b*tan(f*x+e))^2/d/f,1],
[(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x,5,(a^3*c+3*a^2*b*d-3*a*b^2*c-b^3*d)*x/(c^2+d^2)-(-a^3*d+3*a^2*b*c+3*a*b^2*d-b^3*c)*ln(cos(f*x+e))/(c^2+d^2)/f-(-a*d+b*c)^3*ln(c+d*tan(f*x+e))/d^2/(c^2+d^2)/f+b^2*(a+b*tan(f*x+e))/d/f,1],
[(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x,4,-b*(-2*a*d+b*c)*x/d^2+c*(-a*d+b*c)^2*x/d^2/(c^2+d^2)-b^2*ln(cos(f*x+e))/d/f+(-a*d+b*c)^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/d/(c^2+d^2)/f,1],
[(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x,2,(a*c+b*d)*x/(c^2+d^2)-(-a*d+b*c)*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)/f,1],
[1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x,3,(a*c-b*d)*x/(a^2+b^2)/(c^2+d^2)+b^2*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)/(-a*d+b*c)/f-d^2*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)/(c^2+d^2)/f,1],
[1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x,4,(a^2*c-2*a*b*d-b^2*c)*x/(a^2+b^2)^2/(c^2+d^2)+b^2*(-3*a^2*d+2*a*b*c-b^2*d)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^2/f+d^3*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^2/(c^2+d^2)/f-b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x,5,(a^3*c-3*a^2*b*d-3*a*b^2*c+b^3*d)*x/(a^2+b^2)^3/(c^2+d^2)-b^2*(8*a^3*b*c*d-6*a^4*d^2+b^4*(c^2-d^2)-3*a^2*b^2*(c^2+d^2))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/(-a*d+b*c)^3/f-d^4*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^3/(c^2+d^2)/f-1/2*b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^2-b^2*(-3*a^2*d+2*a*b*c-b^2*d)/(a^2+b^2)^2/(-a*d+b*c)^2/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^2,x,6,(8*a^3*b*c*d-8*a*b^3*c*d+a^4*(c^2-d^2)-6*a^2*b^2*(c^2-d^2)+b^4*(c^2-d^2))*x/(c^2+d^2)^2-2*(a^2*c+2*a*b*d-b^2*c)*(-a^2*d+2*a*b*c+b^2*d)*ln(cos(f*x+e))/(c^2+d^2)^2/f-2*(-a*d+b*c)^3*(a*c*d+b*(c^2+2*d^2))*ln(c+d*tan(f*x+e))/d^3/(c^2+d^2)^2/f-b^2*(a*d*(-a*d+2*b*c)-b^2*(2*c^2+d^2))*tan(f*x+e)/d^2/(c^2+d^2)/f-(-a*d+b*c)^2*(a+b*tan(f*x+e))^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x,5,(6*a^2*b*c*d-2*b^3*c*d+a^3*(c^2-d^2)-3*a*b^2*(c^2-d^2))*x/(c^2+d^2)^2+(2*a^3*c*d-6*a*b^2*c*d-3*a^2*b*(c^2-d^2)+b^3*(c^2-d^2))*ln(cos(f*x+e))/(c^2+d^2)^2/f+(-a*d+b*c)^2*(2*a*c*d+b*(c^2+3*d^2))*ln(c+d*tan(f*x+e))/d^2/(c^2+d^2)^2/f-(-a*d+b*c)^2*(a+b*tan(f*x+e))/d/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x,3,-(b*(c-d)-a*(c+d))*(a*(c-d)+b*(c+d))*x/(c^2+d^2)^2-2*(-a*d+b*c)*(a*c+b*d)*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)^2/f-(-a*d+b*c)^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x,3,(2*b*c*d+a*(c^2-d^2))*x/(c^2+d^2)^2+(2*a*c*d-b*(c^2-d^2))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)^2/f+(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x,4,-(2*b*c*d-a*(c^2-d^2))*x/(a^2+b^2)/(c^2+d^2)^2+b^3*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)/(-a*d+b*c)^2/f+d^2*(2*a*c*d-b*(3*c^2+d^2))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^2/(c^2+d^2)^2/f+d^2/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x,5,(b*(c-d)+a*(c+d))*(a*(c-d)-b*(c+d))*x/(a^2+b^2)^2/(c^2+d^2)^2+2*b^3*(-2*a^2*d+a*b*c-b^2*d)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^3/f-2*d^3*(a*c*d-b*(2*c^2+d^2))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^3/(c^2+d^2)^2/f-d*(a^2*d^2+b^2*(c^2+2*d^2))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/(c+d*tan(f*x+e))-b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x,6,-(6*a^2*b*c*d-2*b^3*c*d-a^3*(c^2-d^2)+3*a*b^2*(c^2-d^2))*x/(a^2+b^2)^3/(c^2+d^2)^2-b^3*(10*a^3*b*c*d+2*a*b^3*c*d-10*a^4*d^2+b^4*(c^2-3*d^2)-3*a^2*b^2*(c^2+3*d^2))*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^3/(-a*d+b*c)^4/f-d^4*(-2*a*c*d+5*b*c^2+3*b*d^2)*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^4/(c^2+d^2)^2/f+d*(a^4*d^3-2*a*b^3*c*(c^2+d^2)+2*a^2*b^2*d*(2*c^2+3*d^2)+b^4*d*(2*c^2+3*d^2))/(a^2+b^2)^2/(-a*d+b*c)^3/(c^2+d^2)/f/(c+d*tan(f*x+e))-1/2*b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))-1/2*b^2*(-7*a^2*d+4*a*b*c-3*b^2*d)/(a^2+b^2)^2/(-a*d+b*c)^2/f/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^3,x,6,-(6*a^2*b^2*c*(c^2-3*d^2)-b^4*c*(c^2-3*d^2)-4*a^3*b*d*(3*c^2-d^2)+4*a*b^3*d*(3*c^2-d^2)-a^4*(c^3-3*c*d^2))*x/(c^2+d^2)^3-(4*a^3*b*c*(c^2-3*d^2)-4*a*b^3*c*(c^2-3*d^2)+6*a^2*b^2*d*(3*c^2-d^2)-b^4*d*(3*c^2-d^2)-a^4*(3*c^2*d-d^3))*ln(cos(f*x+e))/(c^2+d^2)^3/f+(-a*d+b*c)^2*(a^2*d^2*(3*c^2-d^2)+2*a*b*c*d*(c^2+5*d^2)+b^2*(c^4+3*c^2*d^2+6*d^4))*ln(c+d*tan(f*x+e))/d^3/(c^2+d^2)^3/f-1/2*(-a*d+b*c)^2*(a+b*tan(f*x+e))^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^2+(-a*d+b*c)^3*(2*a*c*d+b*(c^2+3*d^2))/d^3/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x,4,(a*c+b*d)*(8*a*b*c*d+a^2*(c^2-3*d^2)-b^2*(3*c^2-d^2))*x/(c^2+d^2)^3-(-a*d+b*c)*(8*a*b*c*d-b^2*(c^2-3*d^2)+a^2*(3*c^2-d^2))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)^3/f-1/2*(-a*d+b*c)^2*(a+b*tan(f*x+e))/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-1/2*(-a*d+b*c)^2*(4*a*c*d+b*(c^2+5*d^2))/d^2/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x,4,-(b^2*c*(c^2-3*d^2)-2*a*b*d*(3*c^2-d^2)-a^2*(c^3-3*c*d^2))*x/(c^2+d^2)^3-(2*a*b*c*(c^2-3*d^2)+b^2*d*(3*c^2-d^2)-a^2*(3*c^2*d-d^3))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)^3/f-1/2*(-a*d+b*c)^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^2+2*(-a*d+b*c)*(a*c+b*d)/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x,4,(a*c^3-3*a*c*d^2+3*b*c^2*d-b*d^3)*x/(c^2+d^2)^3+(a*d*(3*c^2-d^2)-b*(c^3-3*c*d^2))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(c^2+d^2)^3/f+1/2*(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-(2*a*c*d-b*(c^2-d^2))/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x,5,-(b*d*(3*c^2-d^2)-a*(c^3-3*c*d^2))*x/(a^2+b^2)/(c^2+d^2)^3+b^4*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)/(-a*d+b*c)^3/f+d^2*(8*a*b*c^3*d-a^2*d^2*(3*c^2-d^2)-b^2*(6*c^4+3*c^2*d^2+d^4))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^3/(c^2+d^2)^3/f+1/2*d^2/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-d^2*(2*a*c*d-b*(3*c^2+d^2))/(-a*d+b*c)^2/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x,6,-(b^2*c*(c^2-3*d^2)-a^2*(c^3-3*c*d^2)+a*b*(6*c^2*d-2*d^3))*x/(a^2+b^2)^2/(c^2+d^2)^3+b^4*(-5*a^2*d+2*a*b*c-3*b^2*d)*ln(a*cos(f*x+e)+b*sin(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^4/f+d^3*(a^2*d^2*(3*c^2-d^2)-2*a*b*c*d*(5*c^2+d^2)+b^2*(10*c^4+9*c^2*d^2+3*d^4))*ln(c*cos(f*x+e)+d*sin(f*x+e))/(-a*d+b*c)^4/(c^2+d^2)^3/f-1/2*d*(a^2*d^2+b^2*(2*c^2+3*d^2))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2+d*(2*a^3*c*d^3+2*a*b^2*c*d^3-2*a^2*b*d^2*(2*c^2+d^2)-b^3*(c^4+6*c^2*d^2+3*d^4))/(a^2+b^2)/(-a*d+b*c)^3/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3*sqrt(c+d*tan(f*x+e)),x,10,(I*a+b)^3*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f-(I*a-b)^3*sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+2*b*(3*a^2-b^2)*sqrt(c+d*tan(f*x+e))/f-4/15*b^2*(-6*a*d+b*c)*(c+d*tan(f*x+e))^(3/2)/d^2/f+2/5*b^2*(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+b*tan(f*x+e))^2*sqrt(c+d*tan(f*x+e)),x,9,-I*(a-I*b)^2*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+I*(a+I*b)^2*sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+4*a*b*sqrt(c+d*tan(f*x+e))/f+2/3*b^2*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e)),x,8,-(I*a+b)*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+(I*a-b)*sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+2*b*sqrt(c+d*tan(f*x+e))/f,1],
[sqrt(c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x,11,sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)/f-sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)/f-2*sqrt(b)*sqrt(-a*d+b*c)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)/f,1],
[sqrt(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x,12,-I*sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(a-I*b)^2/f+I*sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(a+I*b)^2/f-sqrt(b)*(-3*a^2*d+4*a*b*c+b^2*d)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)^2/sqrt(-a*d+b*c)/f-b*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[sqrt(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x,13,-sqrt(c-I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)^3/f+sqrt(c+I*d)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)^3/f+1/4*sqrt(b)*(40*a^3*b*c*d-24*a*b^3*c*d-15*a^4*d^2-6*a^2*b^2*(4*c^2-3*d^2)+b^4*(8*c^2+d^2))*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)^3/(-a*d+b*c)^(3/2)/f-1/2*b*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^2-1/4*b*(-7*a^2*d+8*a*b*c+b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x,11,(I*a+b)^3*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f-(I*a-b)^3*(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+2*(a^3*d+3*a^2*b*c-3*a*b^2*d-b^3*c)*sqrt(c+d*tan(f*x+e))/f+2/3*b*(3*a^2-b^2)*(c+d*tan(f*x+e))^(3/2)/f-4/35*b^2*(-8*a*d+b*c)*(c+d*tan(f*x+e))^(5/2)/d^2/f+2/7*b^2*(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2)/d/f,1],
[(a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x,10,-I*(a-I*b)^2*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+I*(a+I*b)^2*(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+2*(a^2*d+2*a*b*c-b^2*d)*sqrt(c+d*tan(f*x+e))/f+4/3*a*b*(c+d*tan(f*x+e))^(3/2)/f+2/5*b^2*(c+d*tan(f*x+e))^(5/2)/d/f,1],
[(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x,9,-(I*a+b)*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/f+(I*a-b)*(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/f+2*(a*d+b*c)*sqrt(c+d*tan(f*x+e))/f+2/3*b*(c+d*tan(f*x+e))^(3/2)/f,1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x,11,(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)/f-(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)/f-2*(-a*d+b*c)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/sqrt(b)/(a^2+b^2)/f,1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x,12,-I*(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(a-I*b)^2/f+I*(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(a+I*b)^2/f-sqrt(-a*d+b*c)*(-a^2*d+4*a*b*c+3*b^2*d)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/sqrt(b)/(a^2+b^2)^2/f-(-a*d+b*c)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x,13,-(c-I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)^3/f+(c+I*d)^(3/2)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)^3/f+1/4*(24*a^3*b*c*d-40*a*b^3*c*d-3*a^4*d^2-2*a^2*b^2*(12*c^2-13*d^2)+b^4*(8*c^2-3*d^2))*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/sqrt(b)/(a^2+b^2)^3/sqrt(-a*d+b*c)/f-1/2*(-a*d+b*c)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^2-1/4*(-3*a^2*d+8*a*b*c+5*b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/f/(a+b*tan(f*x+e)),1],
[sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e))^4,x,9,-2*(a^4-2*a^3*b-6*a^2*b^2+2*a*b^3+b^4)*arctan((a^4-2*a^3*b-6*a^2*b^2+2*a*b^3+b^4-2*(a^4-2*a^3*b-6*a^2*b^2+2*a*b^3+b^4)*tan(f*x+e))/(a^4-2*a^3*b-6*a^2*b^2+2*a*b^3+b^4)/sqrt(3+4*tan(f*x+e)))/f-(a^4+8*a^3*b-6*a^2*b^2-8*a*b^3+b^4)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+8*a*b*(a^2-b^2)*sqrt(3+4*tan(f*x+e))/f+1/420*b^2*(390*a^2-84*a*b-61*b^2)*(3+4*tan(f*x+e))^(3/2)/f+3/70*(6*a-b)*b^3*tan(f*x+e)*(3+4*tan(f*x+e))^(3/2)/f+1/14*b^2*(3+4*tan(f*x+e))^(3/2)*(a+b*tan(f*x+e))^2/f,1],
[sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e))^3,x,8,-(2*a^3-3*a^2*b-6*a*b^2+b^3)*arctan((2*a^3-3*a^2*b-6*a*b^2+b^3-2*(2*a^3-3*a^2*b-6*a*b^2+b^3)*tan(f*x+e))/(2*a^3-3*a^2*b-6*a*b^2+b^3)/sqrt(3+4*tan(f*x+e)))/f-(a^3+6*a^2*b-3*a*b^2-2*b^3)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+2*b*(3*a^2-b^2)*sqrt(3+4*tan(f*x+e))/f+1/20*(8*a-b)*b^2*(3+4*tan(f*x+e))^(3/2)/f+1/10*b^2*(3+4*tan(f*x+e))^(3/2)*(a+b*tan(f*x+e))/f,1],
[sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e))^2,x,7,-2*(a^2-a*b-b^2)*arctan((a^2-a*b-b^2-2*(a^2-a*b-b^2)*tan(f*x+e))/(a^2-a*b-b^2)/sqrt(3+4*tan(f*x+e)))/f-(a^2+4*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+4*a*b*sqrt(3+4*tan(f*x+e))/f+1/6*b^2*(3+4*tan(f*x+e))^(3/2)/f,1],
[sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e)),x,6,-(2*a-b)*arctan((2*a-b-2*(2*a-b)*tan(f*x+e))/(2*a-b)/sqrt(3+4*tan(f*x+e)))/f-(a+2*b)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+2*b*sqrt(3+4*tan(f*x+e))/f,1],
[sqrt(3+4*tan(f*x+e)),x,10,-2*arctan(2-sqrt(3+4*tan(f*x+e)))/f+2*arctan(2+sqrt(3+4*tan(f*x+e)))/f-arctanh(sqrt(3+4*tan(f*x+e))/(2+tan(f*x+e)))/f,1],
[sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e)),x,9,-2*sqrt(4*a-3*b)*sqrt(b)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(a^2+b^2)/f-(2*a+b)*arctan((2*a+b-2*(2*a+b)*tan(f*x+e))/(2*a+b)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f-(a-2*b)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f,1],
[sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e))^2,x,10,-4*sqrt(b)*(3*a^2-3*a*b-b^2)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/sqrt(4*a-3*b)/(a^2+b^2)^2/f-2*(a^2+a*b-b^2)*arctan((a^2+a*b-b^2-2*(a^2+a*b-b^2)*tan(f*x+e))/(a^2+a*b-b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f-(a^2-4*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f-b*sqrt(3+4*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e))^3,x,11,-2*sqrt(b)*(30*a^4-60*a^3*b-9*a^2*b^2+36*a*b^3-11*b^4)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(4*a-3*b)^(3/2)/(a^2+b^2)^3/f-(2*a^3+3*a^2*b-6*a*b^2-b^3)*arctan(((4*a-3*b)*(2*a^3+3*a^2*b-6*a*b^2-b^3)-2*(4*a-3*b)*(2*a^3+3*a^2*b-6*a*b^2-b^3)*tan(f*x+e))/(8*a^4+6*a^3*b-33*a^2*b^2+14*a*b^3+3*b^4)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^3/f-(a^3-6*a^2*b-3*a*b^2+2*b^3)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^3/f-1/2*b*sqrt(3+4*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^2-(a-b)*b*(7*a+b)*sqrt(3+4*tan(f*x+e))/(4*a-3*b)/(a^2+b^2)^2/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/sqrt(c+d*tan(f*x+e)),x,10,-I*(a-I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f+I*(a+I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/sqrt(c+I*d)/f-2/15*b^2*(40*a*b*c*d-87*a^2*d^2-b^2*(8*c^2-15*d^2))*sqrt(c+d*tan(f*x+e))/d^3/f-4/15*b^3*(-7*a*d+2*b*c)*tan(f*x+e)*sqrt(c+d*tan(f*x+e))/d^2/f+2/5*b^2*(a+b*tan(f*x+e))^2*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+b*tan(f*x+e))^3/sqrt(c+d*tan(f*x+e)),x,9,(I*a+b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f-(I*a-b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/sqrt(c+I*d)/f-4/3*b^2*(-4*a*d+b*c)*sqrt(c+d*tan(f*x+e))/d^2/f+2/3*b^2*(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+b*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e)),x,8,-I*(a-I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f+I*(a+I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/sqrt(c+I*d)/f+2*b^2*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,7,-(I*a+b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/sqrt(c-I*d)/f+(I*a-b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/sqrt(c+I*d)/f,1],
[1/(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,11,arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)/sqrt(c-I*d)/f-arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)/sqrt(c+I*d)/f-2*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)/sqrt(-a*d+b*c)/f,1],
[1/(a+b*tan(f*x+e))^2/sqrt(c+d*tan(f*x+e)),x,12,-I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(a-I*b)^2/sqrt(c-I*d)/f+I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(a+I*b)^2/sqrt(c+I*d)/f-b^(3/2)*(-5*a^2*d+4*a*b*c-b^2*d)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)^2/(-a*d+b*c)^(3/2)/f-b^2*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(3/2),x,10,-I*(a-I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f+I*(a+I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(3/2)/f-2*(-a*d+b*c)^2*(a+b*tan(f*x+e))^2/d/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e))-2/3*b*(15*a^2*b*c*d^2-6*a^3*d^3-12*a*b^2*d*(2*c^2+d^2)+b^3*(8*c^3+5*c*d^2))*sqrt(c+d*tan(f*x+e))/d^3/(c^2+d^2)/f-2/3*b^2*(3*a*d*(-a*d+2*b*c)-b^2*(4*c^2+d^2))*tan(f*x+e)*sqrt(c+d*tan(f*x+e))/d^2/(c^2+d^2)/f,1],
[(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x,9,(I*a+b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f-(I*a-b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(3/2)/f-2*(-a*d+b*c)^2*(a+b*tan(f*x+e))/d/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e))-2*b*(a*d*(-a*d+2*b*c)-b^2*(2*c^2+d^2))*sqrt(c+d*tan(f*x+e))/d^2/(c^2+d^2)/f,1],
[(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x,8,-I*(a-I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f+I*(a+I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(3/2)/f-2*(-a*d+b*c)^2/d/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,8,-(I*a+b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(3/2)/f+(I*a-b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(3/2)/f+2*(-a*d+b*c)/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,12,arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)/(c-I*d)^(3/2)/f-arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)/(c+I*d)^(3/2)/f-2*b^(5/2)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)/(-a*d+b*c)^(3/2)/f+2*d^2/(-a*d+b*c)/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x,13,-I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(a-I*b)^2/(c-I*d)^(3/2)/f+I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(a+I*b)^2/(c+I*d)^(3/2)/f-b^(5/2)*(-7*a^2*d+4*a*b*c-3*b^2*d)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)^2/(-a*d+b*c)^(5/2)/f-d*(2*a^2*d^2+b^2*(c^2+3*d^2))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e))-b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(5/2),x,10,-I*(a-I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f+I*(a+I*b)^4*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(5/2)/f-2/3*(-a*d+b*c)^2*(a+b*tan(f*x+e))^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+4/3*(-a*d+b*c)^3*(3*a*c*d+2*b*c^2+5*b*d^2)/d^3/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e))-2/3*b^2*(a*d*(-a*d+2*b*c)-b^2*(4*c^2+3*d^2))*sqrt(c+d*tan(f*x+e))/d^3/(c^2+d^2)/f,1],
[(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x,9,(I*a+b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f-(I*a-b)^3*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(5/2)/f-2/3*(-a*d+b*c)^2*(a+b*tan(f*x+e))/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-4/3*(-a*d+b*c)^2*(3*a*c*d+b*(c^2+4*d^2))/d^2/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x,9,-I*(a-I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f+I*(a+I*b)^2*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(5/2)/f-2/3*(-a*d+b*c)^2/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+4*(-a*d+b*c)*(a*c+b*d)/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,9,-(I*a+b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(c-I*d)^(5/2)/f+(I*a-b)*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(c+I*d)^(5/2)/f+2/3*(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-2*(2*a*c*d-b*(c^2-d^2))/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,13,arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(I*a+b)/(c-I*d)^(5/2)/f-arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(I*a-b)/(c+I*d)^(5/2)/f-2*b^(7/2)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)/(-a*d+b*c)^(5/2)/f+2/3*d^2/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-2*d^2*(2*a*c*d-b*(3*c^2+d^2))/(-a*d+b*c)^2/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x,14,-I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c-I*d))/(a-I*b)^2/(c-I*d)^(5/2)/f+I*arctanh(sqrt(c+d*tan(f*x+e))/sqrt(c+I*d))/(a+I*b)^2/(c+I*d)^(5/2)/f-b^(7/2)*(-9*a^2*d+4*a*b*c-5*b^2*d)*arctanh(sqrt(b)*sqrt(c+d*tan(f*x+e))/sqrt(-a*d+b*c))/(a^2+b^2)^2/(-a*d+b*c)^(7/2)/f-1/3*d*(2*a^2*d^2+b^2*(3*c^2+5*d^2))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+d*(4*a^3*c*d^3+4*a*b^2*c*d^3-4*a^2*b*d^2*(2*c^2+d^2)-b^3*(c^4+10*c^2*d^2+5*d^4))/(a^2+b^2)/(-a*d+b*c)^3/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^4/sqrt(3+4*tan(f*x+e)),x,8,-2/5*(a^4+2*a^3*b-6*a^2*b^2-2*a*b^3+b^4)*arctan((a^4+2*a^3*b-6*a^2*b^2-2*a*b^3+b^4-2*(a^4+2*a^3*b-6*a^2*b^2-2*a*b^3+b^4)*tan(f*x+e))/(a^4+2*a^3*b-6*a^2*b^2-2*a*b^3+b^4)/sqrt(3+4*tan(f*x+e)))/f+1/5*(a^4-8*a^3*b-6*a^2*b^2+8*a*b^3+b^4)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+1/20*b^2*(58*a^2-20*a*b-7*b^2)*sqrt(3+4*tan(f*x+e))/f+1/30*(14*a-3*b)*b^3*tan(f*x+e)*sqrt(3+4*tan(f*x+e))/f+1/10*b^2*sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e))^2/f,1],
[(a+b*tan(f*x+e))^3/sqrt(3+4*tan(f*x+e)),x,7,-1/5*(2*a^3+3*a^2*b-6*a*b^2-b^3)*arctan((2*a^3+3*a^2*b-6*a*b^2-b^3-2*(2*a^3+3*a^2*b-6*a*b^2-b^3)*tan(f*x+e))/(2*a^3+3*a^2*b-6*a*b^2-b^3)/sqrt(3+4*tan(f*x+e)))/f+1/5*(a^3-6*a^2*b-3*a*b^2+2*b^3)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+1/12*(16*a-3*b)*b^2*sqrt(3+4*tan(f*x+e))/f+1/6*b^2*sqrt(3+4*tan(f*x+e))*(a+b*tan(f*x+e))/f,1],
[(a+b*tan(f*x+e))^2/sqrt(3+4*tan(f*x+e)),x,6,-2/5*(a^2+a*b-b^2)*arctan((a^2+a*b-b^2-2*(a^2+a*b-b^2)*tan(f*x+e))/(a^2+a*b-b^2)/sqrt(3+4*tan(f*x+e)))/f+1/5*(a^2-4*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+1/2*b^2*sqrt(3+4*tan(f*x+e))/f,1],
[(a+b*tan(f*x+e))/sqrt(3+4*tan(f*x+e)),x,5,-1/5*(2*a+b)*arctan((2*a+b-2*(2*a+b)*tan(f*x+e))/(2*a+b)/sqrt(3+4*tan(f*x+e)))/f+1/5*(a-2*b)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f,1],
[1/sqrt(3+4*tan(f*x+e)),x,10,-2/5*arctan(2-sqrt(3+4*tan(f*x+e)))/f+2/5*arctan(2+sqrt(3+4*tan(f*x+e)))/f+1/5*arctanh(sqrt(3+4*tan(f*x+e))/(2+tan(f*x+e)))/f,1],
[1/sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e)),x,9,2*b^(3/2)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/sqrt(4*a-3*b)/(a^2+b^2)/f-1/5*(2*a-b)*arctan((2*a-b-2*(2*a-b)*tan(f*x+e))/(2*a-b)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f+1/5*(a+2*b)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f,1],
[1/sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e))^2,x,10,4*b^(3/2)*(5*a^2-3*a*b+b^2)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(4*a-3*b)^(3/2)/(a^2+b^2)^2/f-2/5*(a^2-a*b-b^2)*arctan((a^2-a*b-b^2-2*(a^2-a*b-b^2)*tan(f*x+e))/(a^2-a*b-b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f+1/5*(a^2+4*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f+b^2*sqrt(3+4*tan(f*x+e))/(4*a-3*b)/(a^2+b^2)/f/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^3/(3+4*tan(f*x+e))^(3/2),x,7,-1/125*(2*a+b)*(a^2+16*a*b-11*b^2)*arctan((a^2+16*a*b-11*b^2-2*(a^2+16*a*b-11*b^2)*tan(f*x+e))/(a^2+16*a*b-11*b^2)/sqrt(3+4*tan(f*x+e)))/f+1/125*(a-2*b)*(11*a^2+16*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+1/100*b*(8*a^2-12*a*b+17*b^2)*sqrt(3+4*tan(f*x+e))/f-1/50*(4*a-3*b)^2*(a+b*tan(f*x+e))/f/sqrt(3+4*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^2/(3+4*tan(f*x+e))^(3/2),x,6,-2/125*(a^2+11*a*b-b^2)*arctan((a^2+11*a*b-b^2-2*(a^2+11*a*b-b^2)*tan(f*x+e))/(a^2+11*a*b-b^2)/sqrt(3+4*tan(f*x+e)))/f+1/125*(11*a^2-4*a*b-11*b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f-1/50*(4*a-3*b)^2/f/sqrt(3+4*tan(f*x+e)),1],
[(a+b*tan(f*x+e))/(3+4*tan(f*x+e))^(3/2),x,6,-1/125*(2*a+11*b)*arctan((2*a+11*b-2*(2*a+11*b)*tan(f*x+e))/(2*a+11*b)/sqrt(3+4*tan(f*x+e)))/f+1/125*(11*a-2*b)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f-2/25*(4*a-3*b)/f/sqrt(3+4*tan(f*x+e)),1],
[1/(3+4*tan(f*x+e))^(3/2),x,6,-2/125*arctan((1-2*tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f+11/125*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/f-8/25/f/sqrt(3+4*tan(f*x+e)),1],
[1/(3+4*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x,10,-2*b^(5/2)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(4*a-3*b)^(3/2)/(a^2+b^2)/f-1/125*(2*a-11*b)*arctan(((2*a-11*b)*(4*a-3*b)-2*(2*a-11*b)*(4*a-3*b)*tan(f*x+e))/(8*a^2-50*a*b+33*b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f+1/125*(11*a+2*b)*arctanh((2*(4*a-3*b)*(11*a+2*b)+(4*a-3*b)*(11*a+2*b)*tan(f*x+e))/(44*a^2-25*a*b-6*b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)/f-32/25/(4*a-3*b)/f/sqrt(3+4*tan(f*x+e)),1],
[1/(3+4*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x,11,-4*b^(5/2)*(7*a^2-3*a*b+3*b^2)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(4*a-3*b)^(5/2)/(a^2+b^2)^2/f-2/125*(a^2-11*a*b-b^2)*arctan((a^2-11*a*b-b^2-2*(a^2-11*a*b-b^2)*tan(f*x+e))/(a^2-11*a*b-b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f+1/125*(11*a^2+4*a*b-11*b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^2/f-4/25*(32*a^2+57*b^2)/(4*a-3*b)^2/(a^2+b^2)/f/sqrt(3+4*tan(f*x+e))+b^2/(4*a-3*b)/(a^2+b^2)/f/sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e)),1],
[1/(3+4*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x,12,-2*b^(5/2)*(126*a^4-108*a^3*b+119*a^2*b^2-12*a*b^3+21*b^4)*arctan(sqrt(b)*sqrt(3+4*tan(f*x+e))/sqrt(4*a-3*b))/(4*a-3*b)^(7/2)/(a^2+b^2)^3/f-1/125*(2*a-b)*(a^2-16*a*b-11*b^2)*arctan((a^2-16*a*b-11*b^2-2*(a^2-16*a*b-11*b^2)*tan(f*x+e))/(a^2-16*a*b-11*b^2)/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^3/f+1/125*(a+2*b)*(11*a^2-16*a*b-b^2)*arctanh((2+tan(f*x+e))/sqrt(3+4*tan(f*x+e)))/(a^2+b^2)^3/f-4/25*(128*a^4+631*a^2*b^2-150*a*b^3+303*b^4)/(4*a-3*b)^3/(a^2+b^2)^2/f/sqrt(3+4*tan(f*x+e))+1/2*b^2/(4*a-3*b)/(a^2+b^2)/f/sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e))^2+b^2*(13*a^2-6*a*b+5*b^2)/(4*a-3*b)^2/(a^2+b^2)^2/f/sqrt(3+4*tan(f*x+e))/(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(5/2)*sqrt(c+d*tan(f*x+e)),x,11,-I*(a-I*b)^(5/2)*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*(a+I*b)^(5/2)*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+1/4*sqrt(b)*(10*a*b*c*d+15*a^2*d^2-b^2*(c^2+8*d^2))*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-1/4*b*(-9*a*d+b*c)*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f+1/2*b^2*sqrt(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/d/f,1],
[(a+b*tan(f*x+e))^(3/2)*sqrt(c+d*tan(f*x+e)),x,10,-I*(a-I*b)^(3/2)*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*(a+I*b)^(3/2)*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+sqrt(b)*(3*a*d+b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f+b*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f,1],
[sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e)),x,10,-I*sqrt(a-I*b)*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*sqrt(a+I*b)*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+2*sqrt(b)*sqrt(d)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/f,1],
[sqrt(c+d*tan(f*x+e))/sqrt(a+b*tan(f*x+e)),x,7,-I*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/f+I*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/f,1],
[sqrt(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^(3/2),x,8,-I*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/f+I*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/f-2*b*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/sqrt(a+b*tan(f*x+e)),1],
[sqrt(c+d*tan(f*x+e))/(a+b*tan(f*x+e))^(5/2),x,9,-I*sqrt(c-I*d)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/f+I*sqrt(c+I*d)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/f-2/3*b*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^(3/2)-2/3*b*(-5*a^2*d+6*a*b*c+b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)/f/sqrt(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x,11,-I*(a-I*b)^(3/2)*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*(a+I*b)^(3/2)*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+1/4*(18*a*b*c*d+3*a^2*d^2+b^2*(3*c^2-8*d^2))*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/sqrt(b)/sqrt(d)/f+1/4*(5*a*d+3*b*c)*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f+1/2*b*sqrt(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2)/f,1],
[sqrt(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x,10,-I*sqrt(a-I*b)*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*sqrt(a+I*b)*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+sqrt(d)*(a*d+3*b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/sqrt(b)/f+d*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/f,1],
[(c+d*tan(f*x+e))^(3/2)/sqrt(a+b*tan(f*x+e)),x,11,-I*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/f+I*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/f+2*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/sqrt(b)/f,1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x,8,-I*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/f+I*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/f-2*(-a*d+b*c)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/sqrt(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x,9,-I*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/f+I*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/f-2/3*(-a*d+b*c)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^(3/2)-4/3*(-a^2*d+3*a*b*c+2*b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/f/sqrt(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x,10,-I*(c-I*d)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(7/2)/f+I*(c+I*d)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(7/2)/f-2/5*(-a*d+b*c)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/f/(a+b*tan(f*x+e))^(5/2)-4/15*(-2*a^2*d+5*a*b*c+3*b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/f/(a+b*tan(f*x+e))^(3/2)+2/15*(50*a^3*b*c*d-70*a*b^3*c*d-8*a^4*d^2-a^2*b^2*(45*c^2-49*d^2)+3*b^4*(5*c^2-d^2))*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^3/(-a*d+b*c)/f/sqrt(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x,12,-I*(a-I*b)^(3/2)*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*(a+I*b)^(3/2)*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+1/8*(15*a^2*b*c*d^2-a^3*d^3+3*a*b^2*d*(15*c^2-8*d^2)+5*b^3*(c^3-8*c*d^2))*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/b^(3/2)/sqrt(d)/f+1/8*(14*a*b*c*d-a^2*d^2+b^2*(11*c^2-8*d^2))*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/b/f+1/12*d*(-a*d+13*b*c)*(a+b*tan(f*x+e))^(3/2)*sqrt(c+d*tan(f*x+e))/b/f+1/3*d^2*(a+b*tan(f*x+e))^(5/2)*sqrt(c+d*tan(f*x+e))/b/f,1],
[sqrt(a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x,11,-I*sqrt(a-I*b)*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/f+I*sqrt(a+I*b)*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/f+1/4*sqrt(d)*(10*a*b*c*d-a^2*d^2+b^2*(15*c^2-8*d^2))*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/b^(3/2)/f+1/4*d*(-a*d+9*b*c)*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/b/f+1/2*d^2*(a+b*tan(f*x+e))^(3/2)*sqrt(c+d*tan(f*x+e))/b/f,1],
[(c+d*tan(f*x+e))^(5/2)/sqrt(a+b*tan(f*x+e)),x,10,-I*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/f+I*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/f+d^(3/2)*(-a*d+5*b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/b^(3/2)/f+d^2*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/b/f,1],
[(c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x,10,-I*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/f+I*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/f+2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/b^(3/2)/f-2*(-a*d+b*c)^2*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)/f/sqrt(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x,9,-I*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/f+I*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/f-2/3*(-a*d+b*c)^2*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)/f/(a+b*tan(f*x+e))^(3/2)-2/3*(-a*d+b*c)*(a^2*d+6*a*b*c+7*b^2*d)*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)^2/f/sqrt(a+b*tan(f*x+e)),1],
[(c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x,10,-I*(c-I*d)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(7/2)/f+I*(c+I*d)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(7/2)/f-2/5*(-a*d+b*c)^2*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)/f/(a+b*tan(f*x+e))^(5/2)-2/15*(-a*d+b*c)*(a^2*d+10*a*b*c+11*b^2*d)*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)^2/f/(a+b*tan(f*x+e))^(3/2)+2/15*(20*a^3*b*c*d-100*a*b^3*c*d+2*a^4*d^2+b^4*(15*c^2-23*d^2)-3*a^2*b^2*(15*c^2-13*d^2))*sqrt(c+d*tan(f*x+e))/b/(a^2+b^2)^3/f/sqrt(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(5/2)/sqrt(c+d*tan(f*x+e)),x,10,-I*(a-I*b)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c-I*d)/f+I*(a+I*b)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c+I*d)/f-b^(3/2)*(-5*a*d+b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f+b^2*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d/f,1],
[(a+b*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e)),x,11,-I*(a-I*b)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c-I*d)/f+I*(a+I*b)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c+I*d)/f+2*b^(3/2)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/sqrt(d)/f,1],
[sqrt(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,7,-I*sqrt(a-I*b)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c-I*d)/f+I*sqrt(a+I*b)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(c+I*d)/f,1],
[1/sqrt(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e)),x,7,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/sqrt(c-I*d)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/sqrt(c+I*d)/f,1],
[1/(a+b*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e)),x,8,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/sqrt(c-I*d)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/sqrt(c+I*d)/f-2*b^2*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)/f/sqrt(a+b*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^(5/2)/sqrt(c+d*tan(f*x+e)),x,9,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/sqrt(c-I*d)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/sqrt(c+I*d)/f-2/3*b^2*sqrt(c+d*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^(3/2)-4/3*b^2*(-4*a^2*d+3*a*b*c-b^2*d)*sqrt(c+d*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^2/f/sqrt(a+b*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x,11,-I*(a-I*b)^(7/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(3/2)/f+I*(a+I*b)^(7/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(3/2)/f-b^(5/2)*(-7*a*d+3*b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(5/2)/f-2*(-a*d+b*c)^2*(a+b*tan(f*x+e))^(3/2)/d/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e))-b*(2*a*d*(-a*d+2*b*c)-b^2*(3*c^2+d^2))*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d^2/(c^2+d^2)/f,1],
[(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x,10,-I*(a-I*b)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(3/2)/f+I*(a+I*b)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(3/2)/f+2*b^(5/2)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(3/2)/f-2*(-a*d+b*c)^2*sqrt(a+b*tan(f*x+e))/d/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x,8,-I*(a-I*b)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(3/2)/f+I*(a+I*b)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(3/2)/f+2*(-a*d+b*c)*sqrt(a+b*tan(f*x+e))/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,8,-I*sqrt(a-I*b)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(3/2)/f+I*sqrt(a+I*b)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(3/2)/f-2*d*sqrt(a+b*tan(f*x+e))/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x,8,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/(c-I*d)^(3/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/(c+I*d)^(3/2)/f+2*d^2*sqrt(a+b*tan(f*x+e))/(-a*d+b*c)/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x,9,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/(c-I*d)^(3/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/(c+I*d)^(3/2)/f-2*b^2/(a^2+b^2)/(-a*d+b*c)/f/sqrt(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e))-2*d*(a^2*d^2+b^2*(c^2+2*d^2))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x,10,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/(c-I*d)^(3/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/(c+I*d)^(3/2)/f-2/3*b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^(3/2)/sqrt(c+d*tan(f*x+e))-4/3*b^2*(-5*a^2*d+3*a*b*c-2*b^2*d)/(a^2+b^2)^2/(-a*d+b*c)^2/f/sqrt(a+b*tan(f*x+e))/sqrt(c+d*tan(f*x+e))+2/3*d*(3*a^4*d^3-6*a*b^3*c*(c^2+d^2)+b^4*d*(5*c^2+8*d^2)+a^2*b^2*d*(11*c^2+17*d^2))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^3/(c^2+d^2)/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x,12,-I*(a-I*b)^(9/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(5/2)/f+I*(a+I*b)^(9/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(5/2)/f-b^(7/2)*(-9*a*d+5*b*c)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(7/2)/f-2/3*(-a*d+b*c)^2*(a+b*tan(f*x+e))^(5/2)/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-2/3*(-a*d+b*c)^2*(6*a*c*d+5*b*c^2+11*b*d^2)*(a+b*tan(f*x+e))^(3/2)/d^2/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e))+b*(4*a^3*c*d^3-4*a^2*b*d^2*(c^2-2*d^2)-4*a*b^2*c*d*(c^2+4*d^2)+b^3*(5*c^4+10*c^2*d^2+d^4))*sqrt(a+b*tan(f*x+e))*sqrt(c+d*tan(f*x+e))/d^3/(c^2+d^2)^2/f,1],
[(a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x,11,-I*(a-I*b)^(7/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(5/2)/f+I*(a+I*b)^(7/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(5/2)/f+2*b^(7/2)*arctanh(sqrt(d)*sqrt(a+b*tan(f*x+e))/sqrt(b)/sqrt(c+d*tan(f*x+e)))/d^(5/2)/f-2/3*(-a*d+b*c)^2*(a+b*tan(f*x+e))^(3/2)/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-2*(-a*d+b*c)^2*(2*a*c*d+b*(c^2+3*d^2))*sqrt(a+b*tan(f*x+e))/d^2/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x,9,-I*(a-I*b)^(5/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(5/2)/f+I*(a+I*b)^(5/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(5/2)/f-2/3*(-a*d+b*c)^2*sqrt(a+b*tan(f*x+e))/d/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+2/3*(-a*d+b*c)*(6*a*c*d+b*(c^2+7*d^2))*sqrt(a+b*tan(f*x+e))/d/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x,9,-I*(a-I*b)^(3/2)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(5/2)/f+I*(a+I*b)^(3/2)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(5/2)/f+2/3*(-a*d+b*c)*sqrt(a+b*tan(f*x+e))/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+4/3*(-3*a*c*d+b*c^2-2*b*d^2)*sqrt(a+b*tan(f*x+e))/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,9,-I*sqrt(a-I*b)*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(c-I*d)^(5/2)/f+I*sqrt(a+I*b)*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(c+I*d)^(5/2)/f-2/3*d*sqrt(a+b*tan(f*x+e))/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+2/3*d*(6*a*c*d-b*(5*c^2-d^2))*sqrt(a+b*tan(f*x+e))/(-a*d+b*c)/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x,9,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a-I*b)/(c-I*d)^(5/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/sqrt(a+I*b)/(c+I*d)^(5/2)/f+2/3*d^2*sqrt(a+b*tan(f*x+e))/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-4/3*d^2*(3*a*c*d-b*(4*c^2+d^2))*sqrt(a+b*tan(f*x+e))/(-a*d+b*c)^2/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x,10,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(3/2)/(c-I*d)^(5/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(3/2)/(c+I*d)^(5/2)/f-2*b^2/(a^2+b^2)/(-a*d+b*c)/f/sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)-2/3*d*(a^2*d^2+b^2*(3*c^2+4*d^2))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)^2/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)+2/3*(6*a^3*c*d^4+6*a*b^2*c*d^4-a^2*b*d^3*(11*c^2+5*d^2)-b^3*(3*c^4*d+17*c^2*d^3+8*d^5))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)/(-a*d+b*c)^3/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x,11,-I*arctanh(sqrt(c-I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a-I*b)/sqrt(c+d*tan(f*x+e)))/(a-I*b)^(5/2)/(c-I*d)^(5/2)/f+I*arctanh(sqrt(c+I*d)*sqrt(a+b*tan(f*x+e))/sqrt(a+I*b)/sqrt(c+d*tan(f*x+e)))/(a+I*b)^(5/2)/(c+I*d)^(5/2)/f-2/3*b^2/(a^2+b^2)/(-a*d+b*c)/f/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2)-4*b^2*(-2*a^2*d+a*b*c-b^2*d)/(a^2+b^2)^2/(-a*d+b*c)^2/f/sqrt(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2)+2/3*d*(a^4*d^3-6*a*b^3*c*(c^2+d^2)+b^4*d*(7*c^2+8*d^2)+a^2*b^2*d*(13*c^2+15*d^2))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^3/(c^2+d^2)/f/(c+d*tan(f*x+e))^(3/2)-4/3*d*(3*a^5*c*d^4+6*a^3*b^2*c*d^4-a^4*b*d^3*(7*c^2+4*d^2)+3*a*b^4*c*(c^4+2*c^2*d^2+2*d^4)-b^5*d*(4*c^4+15*c^2*d^2+8*d^4)-a^2*b^3*d*(7*c^4+28*c^2*d^2+15*d^4))*sqrt(a+b*tan(f*x+e))/(a^2+b^2)^2/(-a*d+b*c)^4/(c^2+d^2)^2/f/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x,7,1/2*AppellF1(1+m,-n,1,2+m,-d*(a+b*tan(f*x+e))/(-a*d+b*c),(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)*(c+d*tan(f*x+e))^n/(I*a+b)/f/(1+m)/((b*(c+d*tan(f*x+e))/(-a*d+b*c))^n)-1/2*AppellF1(1+m,-n,1,2+m,-d*(a+b*tan(f*x+e))/(-a*d+b*c),(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)*(c+d*tan(f*x+e))^n/(I*a-b)/f/(1+m)/((b*(c+d*tan(f*x+e))/(-a*d+b*c))^n),1],
[(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x,7,d^2*(-a*d+3*b*c)*(a+b*tan(f*x+e))^(1+m)/b^2/f/(1+m)+1/2*(I*c+d)^3*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(a-I*b)/f/(1+m)-1/2*(I*c-d)^3*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(a+I*b)/f/(1+m)+d^3*(a+b*tan(f*x+e))^(2+m)/b^2/f/(2+m),1],
[(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x,6,d^2*(a+b*tan(f*x+e))^(1+m)/b/f/(1+m)+1/2*(c-I*d)^2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a+b)/f/(1+m)-1/2*(c+I*d)^2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a-b)/f/(1+m),1],
[(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e)),x,5,1/2*(c-I*d)*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a+b)/f/(1+m)+1/2*(I*c-d)*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(a+I*b)/f/(1+m),1],
[(a+b*tan(f*x+e))^m,x,5,1/2*b*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-sqrt(-b^2)))*(a+b*tan(f*x+e))^(1+m)/sqrt(-b^2)/(a-sqrt(-b^2))/f/(1+m)-1/2*b*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+sqrt(-b^2)))*(a+b*tan(f*x+e))^(1+m)/sqrt(-b^2)/(a+sqrt(-b^2))/f/(1+m),1],
[(a+b*tan(f*x+e))^m/(c+d*tan(f*x+e)),x,8,1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a+b)/(c-I*d)/f/(1+m)-1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(a+I*b)/(I*c-d)/f/(1+m)+d^2*hypergeom([1, 1+m],[2+m],-d*(a+b*tan(f*x+e))/(-a*d+b*c))*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)/(c^2+d^2)/f/(1+m),1],
[(a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x,9,1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a+b)/(c-I*d)^2/f/(1+m)-1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a-b)/(c+I*d)^2/f/(1+m)-d^2*(2*a*c*d-b*(c^2*(2-m)-d^2*m))*hypergeom([1, 1+m],[2+m],-d*(a+b*tan(f*x+e))/(-a*d+b*c))*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)^2/(c^2+d^2)^2/f/(1+m)+d^2*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x,10,1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a-I*b))*(a+b*tan(f*x+e))^(1+m)/(I*a+b)/(c-I*d)^3/f/(1+m)+1/2*hypergeom([1, 1+m],[2+m],(a+b*tan(f*x+e))/(a+I*b))*(a+b*tan(f*x+e))^(1+m)/(a+I*b)/(I*c-d)^3/f/(1+m)+1/2*d^2*(2*a^2*d^2*(3*c^2-d^2)-4*a*b*c*d*(c^2*(3-m)-d^2*(1+m))-b^2*(d^4*(1-m)*m+2*c^2*d^2*(-m^2+3*m+1)-c^4*(m^2-5*m+6)))*hypergeom([1, 1+m],[2+m],-d*(a+b*tan(f*x+e))/(-a*d+b*c))*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)^3/(c^2+d^2)^3/f/(1+m)+1/2*d^2*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)/(c^2+d^2)/f/(c+d*tan(f*x+e))^2-1/2*d^2*(4*a*c*d-b*(d^2*(1-m)+c^2*(5-m)))*(a+b*tan(f*x+e))^(1+m)/(-a*d+b*c)^2/(c^2+d^2)^2/f/(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x,7,1/5*AppellF1(5/2,-m,1,7/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c-I*d))*(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(5/2)/(I*c+d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)-1/5*AppellF1(5/2,-m,1,7/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c+I*d))*(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(5/2)/(I*c-d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m),1],
[(a+b*tan(f*x+e))^m*sqrt(c+d*tan(f*x+e)),x,7,1/3*AppellF1(3/2,-m,1,5/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c-I*d))*(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2)/(I*c+d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)-1/3*AppellF1(3/2,-m,1,5/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c+I*d))*(a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2)/(I*c-d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m),1],
[(a+b*tan(f*x+e))^m/sqrt(c+d*tan(f*x+e)),x,7,AppellF1(1/2,-m,1,3/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c-I*d))*(a+b*tan(f*x+e))^m*sqrt(c+d*tan(f*x+e))/(I*c+d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)-AppellF1(1/2,-m,1,3/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c+I*d))*(a+b*tan(f*x+e))^m*sqrt(c+d*tan(f*x+e))/(I*c-d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m),1],
[(a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x,7,-AppellF1(-1/2,-m,1,1/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c-I*d))*(a+b*tan(f*x+e))^m/(I*c+d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)/sqrt(c+d*tan(f*x+e))+AppellF1(-1/2,-m,1,1/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c+I*d))*(a+b*tan(f*x+e))^m/(I*c-d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)/sqrt(c+d*tan(f*x+e)),1],
[(a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x,7,-1/3*AppellF1(-3/2,-m,1,-1/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c-I*d))*(a+b*tan(f*x+e))^m/(I*c+d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)/(c+d*tan(f*x+e))^(3/2)+1/3*AppellF1(-3/2,-m,1,-1/2,b*(c+d*tan(f*x+e))/(-a*d+b*c),(c+d*tan(f*x+e))/(c+I*d))*(a+b*tan(f*x+e))^m/(I*c-d)/f/((-d*(a+b*tan(f*x+e))/(-a*d+b*c))^m)/(c+d*tan(f*x+e))^(3/2),1],
[(c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m,x,4,AppellF1(n*p+1,1-m,1,n*p+2,-I*tan(f*x+e),I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m/f/(n*p+1)/((1+I*tan(f*x+e))^m),1],
[(c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^3,x,8,-3*a^3*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+4*a^3*hypergeom([1, n*p+1],[n*p+2],I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)-I*a^3*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^2,x,5,-a^2*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+2*a^2*hypergeom([1, n*p+1],[n*p+2],I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1),1],
[(c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e)),x,4,a*hypergeom([1, n*p+1],[n*p+2],I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1),1],
[(c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x,8,hypergeom([2, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a/f/(n*p+1)-I*hypergeom([2, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/a/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x,9,1/4*(-n*p+1)^2*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a^2/f/(n*p+1)+1/4*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a^2/f/(1+I*tan(f*x+e))^2+1/4*(-n*p+2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a^2/f/(1+I*tan(f*x+e))+1/4*I*n*p*(-n*p+2)*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/a^2/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m,x,8,1/2*AppellF1(n*p+1,-m,1,n*p+2,-b*tan(f*x+e)/a,-I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m/f/(n*p+1)/(((a+b*tan(f*x+e))/a)^m)+1/2*AppellF1(n*p+1,-m,1,n*p+2,-b*tan(f*x+e)/a,I*tan(f*x+e))*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m/f/(n*p+1)/(((a+b*tan(f*x+e))/a)^m),1],
[(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x,7,3*a*b^2*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+a*(a^2-3*b^2)*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+b^3*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/f/(n*p+2)+b*(3*a^2-b^2)*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^2,x,7,b^2*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+(a^2-b^2)*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+2*a*b*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e)),x,5,a*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/f/(n*p+1)+b*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e)),x,8,a*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/(a^2+b^2)/f/(n*p+1)+b^2*hypergeom([1, n*p+1],[n*p+2],-b*tan(f*x+e)/a)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a/(a^2+b^2)/f/(n*p+1)-b*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/(a^2+b^2)/f/(n*p+2),1],
[(c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e))^2,x,9,(a^2-b^2)*hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/(a^2+b^2)^2/f/(n*p+1)+2*b^2*hypergeom([1, n*p+1],[n*p+2],-b*tan(f*x+e)/a)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/(a^2+b^2)^2/f/(n*p+1)+b^2*hypergeom([2, n*p+1],[n*p+2],-b*tan(f*x+e)/a)*tan(f*x+e)*(c*(d*tan(f*x+e))^p)^n/a^2/(a^2+b^2)/f/(n*p+1)-2*a*b*hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(c*(d*tan(f*x+e))^p)^n/(a^2+b^2)^2/f/(n*p+2),1]]: