lst:=[[(a+a*sin(d*x+c))*tan(d*x+c)^5,x,3,-23/16*a*ln(1-sin(d*x+c))/d+7/16*a*ln(1+sin(d*x+c))/d-a*sin(d*x+c)/d+1/8*a^3/d/(a-a*sin(d*x+c))^2-a^2/d/(a-a*sin(d*x+c))+1/8*a^2/d/(a+a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))*tan(d*x+c)^3,x,3,5/4*a*ln(1-sin(d*x+c))/d-1/4*a*ln(1+sin(d*x+c))/d+a*sin(d*x+c)/d+1/2*a^2/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))*tan(d*x+c),x,3,-a*ln(1-sin(d*x+c))/d-a*sin(d*x+c)/d,1],
[cot(d*x+c)*(a+a*sin(d*x+c)),x,3,a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d,1],
[cot(d*x+c)^3*(a+a*sin(d*x+c)),x,3,-a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d,1],
[cot(d*x+c)^5*(a+a*sin(d*x+c)),x,3,2*a*csc(d*x+c)/d+a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d+a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d,1],
[cot(d*x+c)^7*(a+a*sin(d*x+c)),x,3,-3*a*csc(d*x+c)/d-3/2*a*csc(d*x+c)^2/d+a*csc(d*x+c)^3/d+3/4*a*csc(d*x+c)^4/d-1/5*a*csc(d*x+c)^5/d-1/6*a*csc(d*x+c)^6/d-a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))*tan(d*x+c)^6,x,9,-a*x+a*cos(d*x+c)/d+3*a*sec(d*x+c)/d-a*sec(d*x+c)^3/d+1/5*a*sec(d*x+c)^5/d+a*tan(d*x+c)/d-1/3*a*tan(d*x+c)^3/d+1/5*a*tan(d*x+c)^5/d,1],
[(a+a*sin(d*x+c))*tan(d*x+c)^4,x,8,a*x-a*cos(d*x+c)/d-2*a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d-a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))*tan(d*x+c)^2,x,5,-a*x+a*cos(d*x+c)/d+a*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[cot(d*x+c)^2*(a+a*sin(d*x+c)),x,7,-a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d-a*cot(d*x+c)/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c)),x,10,a*x+3/2*a*arctanh(cos(d*x+c))/d-a*cos(d*x+c)/d+a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^6*(a+a*sin(d*x+c)),x,12,-a*x-15/8*a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d-a*cot(d*x+c)/d+1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d+9/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^5,x,3,-31/8*a^2*ln(1-sin(d*x+c))/d-1/8*a^2*ln(1+sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d+1/4*a^4/d/(a-a*sin(d*x+c))^2-9/4*a^3/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^3,x,3,3*a^2*ln(1-sin(d*x+c))/d+2*a^2*sin(d*x+c)/d+1/2*a^2*sin(d*x+c)^2/d+a^3/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^2*tan(d*x+c),x,3,-2*a^2*ln(1-sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x,2,-1/2*csc(d*x+c)^2*(a+a*sin(d*x+c))^4/a^2/d,1],
[cot(d*x+c)^7*(a+a*sin(d*x+c))^2,x,3,-6*a^2*csc(d*x+c)/d+2*a^2*csc(d*x+c)^3/d+1/2*a^2*csc(d*x+c)^4/d-2/5*a^2*csc(d*x+c)^5/d-1/6*a^2*csc(d*x+c)^6/d+2*a^2*ln(sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^6,x,14,-9/2*a^2*x+2*a^2*cos(d*x+c)/d+6*a^2*sec(d*x+c)/d-2*a^2*sec(d*x+c)^3/d+2/5*a^2*sec(d*x+c)^5/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d+4*a^2*tan(d*x+c)/d-a^2*tan(d*x+c)^3/d+2/5*a^2*tan(d*x+c)^5/d,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^4,x,4,7/2*a^2*x-16/3*a^2*cos(d*x+c)/d-7/2*a^2*cos(d*x+c)*sin(d*x+c)/d-8/3*a^2*cos(d*x+c)*sin(d*x+c)^2/d/(1-sin(d*x+c))+1/3*a^4*cos(d*x+c)*sin(d*x+c)^3/d/(a-a*sin(d*x+c))^2,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^2,x,6,-5/2*a^2*x+2*a^2*cos(d*x+c)/d+2*a^2*cos(d*x+c)/d/(1-sin(d*x+c))+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))^2,x,1,3/2*a^2*x-2*a^2*cos(d*x+c)/d-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x,8,-1/2*a^2*x-2*a^2*arctanh(cos(d*x+c))/d+2*a^2*cos(d*x+c)/d-a^2*cot(d*x+c)/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x,12,-1/2*a^2*x+3*a^2*arctanh(cos(d*x+c))/d-2*a^2*cos(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)*csc(d*x+c)/d-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^7,x,3,209/16*a^3*ln(1-sin(d*x+c))/d-1/16*a^3*ln(1+sin(d*x+c))/d+7*a^3*sin(d*x+c)/d+3/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d+1/6*a^6/d/(a-a*sin(d*x+c))^3-13/8*a^5/d/(a-a*sin(d*x+c))^2+71/8*a^4/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^3,x,3,7*a^3*ln(1-sin(d*x+c))/d+5*a^3*sin(d*x+c)/d+3/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d+2*a^4/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^3*tan(d*x+c),x,3,-4*a^3*ln(1-sin(d*x+c))/d-4*a^3*sin(d*x+c)/d-3/2*a^3*sin(d*x+c)^2/d-1/3*a^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x,3,-3*a^3*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d+2*a^3*ln(sin(d*x+c))/d-2*a^3*sin(d*x+c)/d-3/2*a^3*sin(d*x+c)^2/d-1/3*a^3*sin(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^6,x,9,-23/2*a^3*x+136/5*a^3*cos(d*x+c)/d-136/15*a^3*cos(d*x+c)^3/d+23/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/5*a^6*cos(d*x+c)*sin(d*x+c)^5/d/(a-a*sin(d*x+c))^3-13/15*a^5*cos(d*x+c)*sin(d*x+c)^4/d/(a-a*sin(d*x+c))^2+23/3*a^6*cos(d*x+c)*sin(d*x+c)^3/d/(a^3-a^3*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^4,x,10,17/2*a^3*x-6*a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2-25/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^2,x,8,-11/2*a^3*x+5*a^3*cos(d*x+c)/d-1/3*a^3*cos(d*x+c)^3/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c))+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))^3,x,7,5/2*a^3*x-4*a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x,10,1/2*a^3*x-3*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d-1/3*a^3*cos(d*x+c)^3/d-a^3*cot(d*x+c)/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*sin(d*x+c))^4*tan(d*x+c)^5,x,3,-25*a^4*ln(1-sin(d*x+c))/d-16*a^4*sin(d*x+c)/d-9/2*a^4*sin(d*x+c)^2/d-4/3*a^4*sin(d*x+c)^3/d-1/4*a^4*sin(d*x+c)^4/d+a^6/d/(a-a*sin(d*x+c))^2-11*a^5/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4*tan(d*x+c)^3,x,3,16*a^4*ln(1-sin(d*x+c))/d+12*a^4*sin(d*x+c)/d+4*a^4*sin(d*x+c)^2/d+4/3*a^4*sin(d*x+c)^3/d+1/4*a^4*sin(d*x+c)^4/d+4*a^5/d/(a-a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4*tan(d*x+c),x,3,-8*a^4*ln(1-sin(d*x+c))/d-8*a^4*sin(d*x+c)/d-7/2*a^4*sin(d*x+c)^2/d-4/3*a^4*sin(d*x+c)^3/d-1/4*a^4*sin(d*x+c)^4/d,1],
[cot(d*x+c)^3*(a+a*sin(d*x+c))^4,x,3,-4*a^4*csc(d*x+c)/d-1/2*a^4*csc(d*x+c)^2/d+5*a^4*ln(sin(d*x+c))/d-5/2*a^4*sin(d*x+c)^2/d-4/3*a^4*sin(d*x+c)^3/d-1/4*a^4*sin(d*x+c)^4/d,1],
[(a+a*sin(d*x+c))^4*tan(d*x+c)^4,x,13,163/8*a^4*x-16*a^4*cos(d*x+c)/d+4/3*a^4*cos(d*x+c)^3/d+4/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))^2-56/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))-35/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^4*tan(d*x+c)^2,x,11,-95/8*a^4*x+12*a^4*cos(d*x+c)/d-4/3*a^4*cos(d*x+c)^3/d+8*a^4*cos(d*x+c)/d/(1-sin(d*x+c))+31/8*a^4*cos(d*x+c)*sin(d*x+c)/d+1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^4,x,10,35/8*a^4*x-8*a^4*cos(d*x+c)/d+4/3*a^4*cos(d*x+c)^3/d-27/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^4,x,12,17/8*a^4*x-4*a^4*arctanh(cos(d*x+c))/d+4*a^4*cos(d*x+c)/d-4/3*a^4*cos(d*x+c)^3/d-a^4*cot(d*x+c)/d+23/8*a^4*cos(d*x+c)*sin(d*x+c)/d+1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x,17,-61/8*a^4*x+2*a^4*arctanh(cos(d*x+c))/d+4/3*a^4*cos(d*x+c)^3/d-5*a^4*cot(d*x+c)/d-1/3*a^4*cot(d*x+c)^3/d-2*a^4*cot(d*x+c)*csc(d*x+c)/d-19/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cot(d*x+c)^6*(a+a*sin(d*x+c))^4,x,21,97/8*a^4*x+5/2*a^4*arctanh(cos(d*x+c))/d-4*a^4*cos(d*x+c)/d-4/3*a^4*cos(d*x+c)^3/d+10*a^4*cot(d*x+c)/d-5/3*a^4*cot(d*x+c)^3/d-1/5*a^4*cot(d*x+c)^5/d+5/2*a^4*cot(d*x+c)*csc(d*x+c)/d-a^4*cot(d*x+c)*csc(d*x+c)^3/d+15/8*a^4*cos(d*x+c)*sin(d*x+c)/d+1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[tan(d*x+c)^7/(a+a*sin(d*x+c)),x,8,-35/128*arctanh(sin(d*x+c))/a/d+35/128*sec(d*x+c)*tan(d*x+c)/a/d-35/192*sec(d*x+c)*tan(d*x+c)^3/a/d+7/48*sec(d*x+c)*tan(d*x+c)^5/a/d-1/8*sec(d*x+c)*tan(d*x+c)^7/a/d+1/8*tan(d*x+c)^8/a/d,1],
[tan(d*x+c)^5/(a+a*sin(d*x+c)),x,7,5/16*arctanh(sin(d*x+c))/a/d-5/16*sec(d*x+c)*tan(d*x+c)/a/d+5/24*sec(d*x+c)*tan(d*x+c)^3/a/d-1/6*sec(d*x+c)*tan(d*x+c)^5/a/d+1/6*tan(d*x+c)^6/a/d,1],
[tan(d*x+c)^3/(a+a*sin(d*x+c)),x,6,-3/8*arctanh(sin(d*x+c))/a/d+3/8*sec(d*x+c)*tan(d*x+c)/a/d-1/4*sec(d*x+c)*tan(d*x+c)^3/a/d+1/4*tan(d*x+c)^4/a/d,1],
[tan(d*x+c)/(a+a*sin(d*x+c)),x,5,1/2*arctanh(sin(d*x+c))/a/d+1/2/d/(a+a*sin(d*x+c)),1],
[cot(d*x+c)/(a+a*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-ln(1+sin(d*x+c))/a/d,1],
[cot(d*x+c)^3/(a+a*sin(d*x+c)),x,5,csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c)),x,5,-1/4*cot(d*x+c)^4/a/d-csc(d*x+c)/a/d+1/3*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^7/(a+a*sin(d*x+c)),x,6,-1/6*cot(d*x+c)^6/a/d+csc(d*x+c)/a/d-2/3*csc(d*x+c)^3/a/d+1/5*csc(d*x+c)^5/a/d,1],
[cot(d*x+c)^9/(a+a*sin(d*x+c)),x,6,-1/8*cot(d*x+c)^8/a/d-csc(d*x+c)/a/d+csc(d*x+c)^3/a/d-3/5*csc(d*x+c)^5/a/d+1/7*csc(d*x+c)^7/a/d,1],
[tan(d*x+c)^6/(a+a*sin(d*x+c)),x,6,sec(d*x+c)/a/d-sec(d*x+c)^3/a/d+3/5*sec(d*x+c)^5/a/d-1/7*sec(d*x+c)^7/a/d+1/7*tan(d*x+c)^7/a/d,1],
[tan(d*x+c)^4/(a+a*sin(d*x+c)),x,6,-sec(d*x+c)/a/d+2/3*sec(d*x+c)^3/a/d-1/5*sec(d*x+c)^5/a/d+1/5*tan(d*x+c)^5/a/d,1],
[tan(d*x+c)^2/(a+a*sin(d*x+c)),x,5,sec(d*x+c)/a/d-1/3*sec(d*x+c)^3/a/d+1/3*tan(d*x+c)^3/a/d,1],
[1/(a+a*sin(d*x+c)),x,1,-cos(d*x+c)/d/(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2/(a+a*sin(d*x+c)),x,4,arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d,1],
[cot(d*x+c)^4/(a+a*sin(d*x+c)),x,5,-1/2*arctanh(cos(d*x+c))/a/d-1/3*cot(d*x+c)^3/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^6/(a+a*sin(d*x+c)),x,6,3/8*arctanh(cos(d*x+c))/a/d-1/5*cot(d*x+c)^5/a/d-3/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)^3*csc(d*x+c)/a/d,1],
[cot(d*x+c)^8/(a+a*sin(d*x+c)),x,7,-5/16*arctanh(cos(d*x+c))/a/d-1/7*cot(d*x+c)^7/a/d+5/16*cot(d*x+c)*csc(d*x+c)/a/d-5/24*cot(d*x+c)^3*csc(d*x+c)/a/d+1/6*cot(d*x+c)^5*csc(d*x+c)/a/d,1],
[tan(d*x+c)^7/(a+a*sin(d*x+c))^2,x,4,-7/128*arctanh(sin(d*x+c))/a^2/d+1/192*a/d/(a-a*sin(d*x+c))^3-1/32/d/(a-a*sin(d*x+c))^2+1/80*a^3/d/(a+a*sin(d*x+c))^5-5/64*a^2/d/(a+a*sin(d*x+c))^4+19/96*a/d/(a+a*sin(d*x+c))^3-1/4/d/(a+a*sin(d*x+c))^2+21/256/d/(a^2-a^2*sin(d*x+c))+35/256/d/(a^2+a^2*sin(d*x+c)),1],
[tan(d*x+c)^5/(a+a*sin(d*x+c))^2,x,4,5/64*arctanh(sin(d*x+c))/a^2/d+1/64/d/(a-a*sin(d*x+c))^2+1/32*a^2/d/(a+a*sin(d*x+c))^4-7/48*a/d/(a+a*sin(d*x+c))^3+1/4/d/(a+a*sin(d*x+c))^2-5/64/d/(a^2-a^2*sin(d*x+c))-5/32/d/(a^2+a^2*sin(d*x+c)),1],
[tan(d*x+c)^3/(a+a*sin(d*x+c))^2,x,4,-1/8*arctanh(sin(d*x+c))/a^2/d+1/12*a/d/(a+a*sin(d*x+c))^3-1/4/d/(a+a*sin(d*x+c))^2+1/16/d/(a^2-a^2*sin(d*x+c))+3/16/d/(a^2+a^2*sin(d*x+c)),1],
[tan(d*x+c)/(a+a*sin(d*x+c))^2,x,4,1/4*arctanh(sin(d*x+c))/a^2/d+1/4/d/(a+a*sin(d*x+c))^2-1/4/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)/(a+a*sin(d*x+c))^2,x,3,ln(sin(d*x+c))/a^2/d-ln(1+sin(d*x+c))/a^2/d+1/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x,3,2*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a^2/d+2*ln(sin(d*x+c))/a^2/d-2*ln(1+sin(d*x+c))/a^2/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x,3,-1/2*csc(d*x+c)^2/a^2/d+2/3*csc(d*x+c)^3/a^2/d-1/4*csc(d*x+c)^4/a^2/d,1],
[cot(d*x+c)^7/(a+a*sin(d*x+c))^2,x,3,1/2*csc(d*x+c)^2/a^2/d-2/3*csc(d*x+c)^3/a^2/d+2/5*csc(d*x+c)^5/a^2/d-1/6*csc(d*x+c)^6/a^2/d,1],
[cot(d*x+c)^9/(a+a*sin(d*x+c))^2,x,3,-1/2*csc(d*x+c)^2/a^2/d+2/3*csc(d*x+c)^3/a^2/d+1/4*csc(d*x+c)^4/a^2/d-4/5*csc(d*x+c)^5/a^2/d+1/6*csc(d*x+c)^6/a^2/d+2/7*csc(d*x+c)^7/a^2/d-1/8*csc(d*x+c)^8/a^2/d,1],
[cot(d*x+c)^11/(a+a*sin(d*x+c))^2,x,3,1/2*csc(d*x+c)^2/a^2/d-2/3*csc(d*x+c)^3/a^2/d-1/2*csc(d*x+c)^4/a^2/d+6/5*csc(d*x+c)^5/a^2/d-6/7*csc(d*x+c)^7/a^2/d+1/4*csc(d*x+c)^8/a^2/d+2/9*csc(d*x+c)^9/a^2/d-1/10*csc(d*x+c)^10/a^2/d,1],
[cot(d*x+c)^13/(a+a*sin(d*x+c))^2,x,3,-1/2*csc(d*x+c)^2/a^2/d+2/3*csc(d*x+c)^3/a^2/d+3/4*csc(d*x+c)^4/a^2/d-8/5*csc(d*x+c)^5/a^2/d-1/3*csc(d*x+c)^6/a^2/d+12/7*csc(d*x+c)^7/a^2/d-1/4*csc(d*x+c)^8/a^2/d-8/9*csc(d*x+c)^9/a^2/d+3/10*csc(d*x+c)^10/a^2/d+2/11*csc(d*x+c)^11/a^2/d-1/12*csc(d*x+c)^12/a^2/d,1],
[tan(d*x+c)^5/(a+a*sin(d*x+c))^3,x,4,1/128*arctanh(sin(d*x+c))/a^3/d+1/128/a/d/(a-a*sin(d*x+c))^2+1/40*a^2/d/(a+a*sin(d*x+c))^5-7/64*a/d/(a+a*sin(d*x+c))^4+1/6/d/(a+a*sin(d*x+c))^3-5/64/a/d/(a+a*sin(d*x+c))^2-1/32/d/(a^3-a^3*sin(d*x+c))-5/128/d/(a^3+a^3*sin(d*x+c)),1],
[tan(d*x+c)^3/(a+a*sin(d*x+c))^3,x,4,-1/32*arctanh(sin(d*x+c))/a^3/d+1/16*a/d/(a+a*sin(d*x+c))^4-1/6/d/(a+a*sin(d*x+c))^3+3/32/a/d/(a+a*sin(d*x+c))^2+1/32/d/(a^3-a^3*sin(d*x+c))+1/16/d/(a^3+a^3*sin(d*x+c)),1],
[tan(d*x+c)/(a+a*sin(d*x+c))^3,x,4,1/8*arctanh(sin(d*x+c))/a^3/d+1/6/d/(a+a*sin(d*x+c))^3-1/8/a/d/(a+a*sin(d*x+c))^2-1/8/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)/(a+a*sin(d*x+c))^3,x,3,ln(sin(d*x+c))/a^3/d-ln(1+sin(d*x+c))/a^3/d+1/2/a/d/(a+a*sin(d*x+c))^2+1/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x,3,3*csc(d*x+c)/a^3/d-1/2*csc(d*x+c)^2/a^3/d+5*ln(sin(d*x+c))/a^3/d-5*ln(1+sin(d*x+c))/a^3/d+2/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x,3,4*csc(d*x+c)/a^3/d-2*csc(d*x+c)^2/a^3/d+csc(d*x+c)^3/a^3/d-1/4*csc(d*x+c)^4/a^3/d+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d,1],
[cot(d*x+c)^7/(a+a*sin(d*x+c))^3,x,3,1/3*csc(d*x+c)^3/a^3/d-3/4*csc(d*x+c)^4/a^3/d+3/5*csc(d*x+c)^5/a^3/d-1/6*csc(d*x+c)^6/a^3/d,1],
[cot(d*x+c)^9/(a+a*sin(d*x+c))^3,x,3,-1/3*csc(d*x+c)^3/a^3/d+3/4*csc(d*x+c)^4/a^3/d-2/5*csc(d*x+c)^5/a^3/d-1/3*csc(d*x+c)^6/a^3/d+3/7*csc(d*x+c)^7/a^3/d-1/8*csc(d*x+c)^8/a^3/d,1],
[cot(d*x+c)^11/(a+a*sin(d*x+c))^3,x,3,1/3*csc(d*x+c)^3/a^3/d-3/4*csc(d*x+c)^4/a^3/d+1/5*csc(d*x+c)^5/a^3/d+5/6*csc(d*x+c)^6/a^3/d-5/7*csc(d*x+c)^7/a^3/d-1/8*csc(d*x+c)^8/a^3/d+1/3*csc(d*x+c)^9/a^3/d-1/10*csc(d*x+c)^10/a^3/d,1],
[cot(d*x+c)^13/(a+a*sin(d*x+c))^3,x,3,-1/3*csc(d*x+c)^3/a^3/d+3/4*csc(d*x+c)^4/a^3/d-4/3*csc(d*x+c)^6/a^3/d+6/7*csc(d*x+c)^7/a^3/d+3/4*csc(d*x+c)^8/a^3/d-8/9*csc(d*x+c)^9/a^3/d+3/11*csc(d*x+c)^11/a^3/d-1/12*csc(d*x+c)^12/a^3/d,1],
[tan(d*x+c)^5/(a+a*sin(d*x+c))^4,x,4,-1/128*arctanh(sin(d*x+c))/a^4/d+1/48*a^2/d/(a+a*sin(d*x+c))^6-7/80*a/d/(a+a*sin(d*x+c))^5+1/8/d/(a+a*sin(d*x+c))^4-5/96/a/d/(a+a*sin(d*x+c))^3+1/256/d/(a^2-a^2*sin(d*x+c))^2-5/256/d/(a^2+a^2*sin(d*x+c))^2-3/256/d/(a^4-a^4*sin(d*x+c))-1/256/d/(a^4+a^4*sin(d*x+c)),1],
[tan(d*x+c)^3/(a+a*sin(d*x+c))^4,x,3,1/20*a/d/(a+a*sin(d*x+c))^5-1/8/d/(a+a*sin(d*x+c))^4+1/16/a/d/(a+a*sin(d*x+c))^3+1/32/d/(a^2+a^2*sin(d*x+c))^2+1/64/d/(a^4-a^4*sin(d*x+c))+1/64/d/(a^4+a^4*sin(d*x+c)),1],
[tan(d*x+c)/(a+a*sin(d*x+c))^4,x,4,1/16*arctanh(sin(d*x+c))/a^4/d+1/8/d/(a+a*sin(d*x+c))^4-1/12/a/d/(a+a*sin(d*x+c))^3-1/16/d/(a^2+a^2*sin(d*x+c))^2-1/16/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)^3/(a+a*sin(d*x+c))^4,x,3,4*csc(d*x+c)/a^4/d-1/2*csc(d*x+c)^2/a^4/d+9*ln(sin(d*x+c))/a^4/d-9*ln(1+sin(d*x+c))/a^4/d+1/d/(a^2+a^2*sin(d*x+c))^2+5/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)^7/(a+a*sin(d*x+c))^4,x,3,8*csc(d*x+c)/a^4/d-4*csc(d*x+c)^2/a^4/d+8/3*csc(d*x+c)^3/a^4/d-7/4*csc(d*x+c)^4/a^4/d+4/5*csc(d*x+c)^5/a^4/d-1/6*csc(d*x+c)^6/a^4/d+8*ln(sin(d*x+c))/a^4/d-8*ln(1+sin(d*x+c))/a^4/d,1],
[tan(d*x+c)^2/(a+a*sin(d*x+c))^4,x,17,-4/5*sec(d*x+c)^5/a^4/d+12/7*sec(d*x+c)^7/a^4/d-8/9*sec(d*x+c)^9/a^4/d+1/3*tan(d*x+c)^3/a^4/d+9/5*tan(d*x+c)^5/a^4/d+16/7*tan(d*x+c)^7/a^4/d+8/9*tan(d*x+c)^9/a^4/d,1],
[cot(d*x+c)^2/(a+a*sin(d*x+c))^4,x,14,4*arctanh(cos(d*x+c))/a^4/d-cot(d*x+c)/a^4/d-2/5*cot(d*x+c)/a^4/d/(1+csc(d*x+c))^3+31/15*cot(d*x+c)/a^4/d/(1+csc(d*x+c))^2-104/15*cot(d*x+c)/a^4/d/(1+csc(d*x+c)),1],
[cot(d*x+c)^4/(a+a*sin(d*x+c))^4,x,14,14*arctanh(cos(d*x+c))/a^4/d-9*cot(d*x+c)/a^4/d-1/3*cot(d*x+c)^3/a^4/d+2*cot(d*x+c)*csc(d*x+c)/a^4/d+4/3*cot(d*x+c)/a^4/d/(1+csc(d*x+c))^2-44/3*cot(d*x+c)/a^4/d/(1+csc(d*x+c)),1],
[cot(d*x+c)^6/(a+a*sin(d*x+c))^4,x,16,27/2*arctanh(cos(d*x+c))/a^4/d-16*cot(d*x+c)/a^4/d-3*cot(d*x+c)^3/a^4/d-1/5*cot(d*x+c)^5/a^4/d+11/2*cot(d*x+c)*csc(d*x+c)/a^4/d+cot(d*x+c)*csc(d*x+c)^3/a^4/d-8*cot(d*x+c)/a^4/d/(1+csc(d*x+c)),1],
[sqrt(a+a*sin(f*x+e))*tan(f*x+e)^4,x,15,11/8*sqrt(a)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/f-27/8*sec(f*x+e)*sqrt(a*(1+sin(f*x+e)))/f-1/12*sec(f*x+e)^3*sqrt(a*(1+sin(f*x+e)))/f+29/12*sqrt(a+a*sin(f*x+e))*tan(f*x+e)/f+5/12*sqrt(a*(1+sin(f*x+e)))*tan(f*x+e)^3/f,1],
[sqrt(a+a*sin(f*x+e))*tan(f*x+e)^2,x,4,-sqrt(a)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/f+5*sec(f*x+e)*sqrt(a+a*sin(f*x+e))/f-2*sec(f*x+e)*(a+a*sin(f*x+e))^(3/2)/a/f,1],
[cot(f*x+e)^2*sqrt(a+a*sin(f*x+e)),x,4,-sqrt(a)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f+3*a*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))-cot(f*x+e)*sqrt(a+a*sin(f*x+e))/f,1],
[cot(f*x+e)^4*sqrt(a+a*sin(f*x+e)),x,7,11/8*sqrt(a)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f-2*a*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+11/8*a*cot(f*x+e)/f/sqrt(a+a*sin(f*x+e))-1/12*a*cot(f*x+e)*csc(f*x+e)/f/sqrt(a+a*sin(f*x+e))-1/3*cot(f*x+e)*csc(f*x+e)^2*sqrt(a+a*sin(f*x+e))/f,1],
[(a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^4,x,14,-1/2*a^(3/2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/f+2/3*a^3*cos(f*x+e)^3/f/(a+a*sin(f*x+e))^(3/2)-4*a^2*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))-7/2*a*sec(f*x+e)*sqrt(a+a*sin(f*x+e))/f+1/3*sec(f*x+e)^3*(a+a*sin(f*x+e))^(3/2)/f,1],
[(a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^2,x,3,11/3*a^2*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+7/3*sec(f*x+e)*(a+a*sin(f*x+e))^(3/2)/f-2/3*sec(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/f,1],
[cot(f*x+e)^2*(a+a*sin(f*x+e))^(3/2),x,5,-3*a^(3/2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f+11/3*a^2*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+5/3*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/f-cot(f*x+e)*(a+a*sin(f*x+e))^(3/2)/f,1],
[cot(f*x+e)^4*(a+a*sin(f*x+e))^(3/2),x,8,37/8*a^(3/2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f-8/3*a^2*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+29/24*a^2*cot(f*x+e)/f/sqrt(a+a*sin(f*x+e))-2/3*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/f-1/4*a*cot(f*x+e)*csc(f*x+e)*sqrt(a+a*sin(f*x+e))/f-1/3*cot(f*x+e)*csc(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/f,1],
[(a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^4,x,10,-2/5*a^5*cos(f*x+e)^5/f/(a+a*sin(f*x+e))^(5/2)+8/3*a^4*cos(f*x+e)^3/f/(a+a*sin(f*x+e))^(3/2)-12*a^3*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))-8*a^2*sec(f*x+e)*sqrt(a+a*sin(f*x+e))/f+2/3*a*sec(f*x+e)^3*(a+a*sin(f*x+e))^(3/2)/f,1],
[(a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^2,x,4,124/15*a^3*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+31/15*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/f+9/5*sec(f*x+e)*(a+a*sin(f*x+e))^(5/2)/f-2/5*sec(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/f,1],
[cot(f*x+e)^2*(a+a*sin(f*x+e))^(5/2),x,6,-5*a^(5/2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f+49/15*a^3*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))+31/15*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/f+7/5*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/f-cot(f*x+e)*(a+a*sin(f*x+e))^(5/2)/f,1],
[cot(f*x+e)^4*(a+a*sin(f*x+e))^(5/2),x,10,55/8*a^(5/2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/f-9/40*a^3*cos(f*x+e)/f/sqrt(a+a*sin(f*x+e))-16/15*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/f+17/24*a^2*cot(f*x+e)*sqrt(a+a*sin(f*x+e))/f-2/5*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/f-5/12*a*cot(f*x+e)*csc(f*x+e)*(a+a*sin(f*x+e))^(3/2)/f-1/3*cot(f*x+e)*csc(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/f,1],
[tan(f*x+e)^4/sqrt(a+a*sin(f*x+e)),x,17,-67/64*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/sqrt(a)/f-1/192*sec(f*x+e)*(53+127*sin(f*x+e))/f/sqrt(a+a*sin(f*x+e))+1/24*a*sin(f*x+e)*tan(f*x+e)/f/(a+a*sin(f*x+e))^(3/2)+1/3*tan(f*x+e)^3/f/sqrt(a+a*sin(f*x+e)),1],
[tan(f*x+e)^2/sqrt(a+a*sin(f*x+e)),x,4,5/4*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/sqrt(a)/f-1/2*sec(f*x+e)/f/sqrt(a+a*sin(f*x+e))+3/4*sec(f*x+e)*sqrt(a+a*sin(f*x+e))/a/f,1],
[cot(f*x+e)^2/sqrt(a+a*sin(f*x+e)),x,4,arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/sqrt(a)/f-cot(f*x+e)/f/sqrt(a+a*sin(f*x+e)),1],
[cot(f*x+e)^4/sqrt(a+a*sin(f*x+e)),x,11,-7/8*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/sqrt(a)/f+9/8*cot(f*x+e)/f/sqrt(a+a*sin(f*x+e))+1/12*cot(f*x+e)*csc(f*x+e)/f/sqrt(a+a*sin(f*x+e))-1/3*cot(f*x+e)*csc(f*x+e)^2/f/sqrt(a+a*sin(f*x+e)),1],
[tan(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x,20,7/256*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/a^(3/2)/f+7/256*cos(f*x+e)/f/(a+a*sin(f*x+e))^(3/2)-1/192*sec(f*x+e)*(65+87*sin(f*x+e))/f/(a+a*sin(f*x+e))^(3/2)+1/12*a*sin(f*x+e)*tan(f*x+e)/f/(a+a*sin(f*x+e))^(5/2)+1/3*tan(f*x+e)^3/f/(a+a*sin(f*x+e))^(3/2),1],
[tan(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x,5,1/32*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/a^(3/2)/f+1/32*cos(f*x+e)/f/(a+a*sin(f*x+e))^(3/2)-1/4*sec(f*x+e)/f/(a+a*sin(f*x+e))^(3/2)+5/8*sec(f*x+e)/a/f/sqrt(a+a*sin(f*x+e)),1],
[cot(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x,6,3*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/a^(3/2)/f-2*sqrt(2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/a^(3/2)/f-cot(f*x+e)/a/f/sqrt(a+a*sin(f*x+e)),1],
[cot(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x,10,-1/8*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/a^(3/2)/f-1/8*cot(f*x+e)/a/f/sqrt(a+a*sin(f*x+e))+11/12*cot(f*x+e)*csc(f*x+e)/a/f/sqrt(a+a*sin(f*x+e))-1/3*cot(f*x+e)*csc(f*x+e)^2*sqrt(a+a*sin(f*x+e))/a^2/f,1],
[tan(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x,23,317/4096*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/a^(5/2)/f+317/3072*cos(f*x+e)/f/(a+a*sin(f*x+e))^(5/2)-1/384*sec(f*x+e)*(115+129*sin(f*x+e))/f/(a+a*sin(f*x+e))^(5/2)+317/4096*cos(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2)+5/48*a*sin(f*x+e)*tan(f*x+e)/f/(a+a*sin(f*x+e))^(7/2)+1/3*tan(f*x+e)^3/f/(a+a*sin(f*x+e))^(5/2),1],
[tan(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x,6,-11/128*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/a^(5/2)/f-1/6*sec(f*x+e)/f/(a+a*sin(f*x+e))^(5/2)-11/128*cos(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2)+17/48*sec(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2)+11/96*sec(f*x+e)/a^2/f/sqrt(a+a*sin(f*x+e)),1],
[cot(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x,7,5*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/a^(5/2)/f-7*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/sqrt(2)/a^(5/2)/f-2*cos(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2)-cot(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cot(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x,16,45/8*arctanh(sqrt(a)*cos(f*x+e)/sqrt(a+a*sin(f*x+e)))/a^(5/2)/f-4*sqrt(2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/a^(5/2)/f-19/8*cot(f*x+e)/a^2/f/sqrt(a+a*sin(f*x+e))+13/12*cot(f*x+e)*csc(f*x+e)/a^2/f/sqrt(a+a*sin(f*x+e))-1/3*cot(f*x+e)*csc(f*x+e)^2/a^2/f/sqrt(a+a*sin(f*x+e)),1],
[(a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^4,x,10,-49/9*a*sec(f*x+e)/f/(a+a*sin(f*x+e))^(2/3)+65/63*sec(f*x+e)*(a-a*sin(f*x+e))/f/(a+a*sin(f*x+e))^(2/3)+361/63*sec(f*x+e)*(1-sin(f*x+e))*(a+a*sin(f*x+e))^(1/3)/f+361/63*(1+sqrt(3))*sec(f*x+e)*(1-sin(f*x+e))*(a+a*sin(f*x+e))^(2/3)/f/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))-361/63*2^(1/3)*EllipticE(sin(arccos((2^(1/3)*a^(1/3)-(1-sqrt(3))*(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3)))),sqrt(1/2+1/4*sqrt(3)))*sec(f*x+e)*(a+a*sin(f*x+e))^(2/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))*sqrt((2^(2/3)*a^(2/3)+2^(1/3)*a^(1/3)*(a+a*sin(f*x+e))^(1/3)+(a+a*sin(f*x+e))^(2/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)*3^(1/4)/a^(2/3)/f/sqrt(-(a+a*sin(f*x+e))^(1/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)-361/378*(1-sqrt(3))*InverseJacobiAM(arccos((2^(1/3)*a^(1/3)-(1-sqrt(3))*(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))),sqrt(1/2+1/4*sqrt(3)))*sec(f*x+e)*(a+a*sin(f*x+e))^(2/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))*sqrt((2^(2/3)*a^(2/3)+2^(1/3)*a^(1/3)*(a+a*sin(f*x+e))^(1/3)+(a+a*sin(f*x+e))^(2/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)*2^(1/3)*3^(3/4)/a^(2/3)/f/sqrt(-(a+a*sin(f*x+e))^(1/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)+10/3*a^2*sin(f*x+e)*tan(f*x+e)/f/(a-a*sin(f*x+e))/(a+a*sin(f*x+e))^(2/3)-3*a^2*sin(f*x+e)^2*tan(f*x+e)/f/(a-a*sin(f*x+e))/(a+a*sin(f*x+e))^(2/3),1],
[(a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^2,x,4,-5/6*a*cos(f*x+e)*hypergeom([1/2, 7/6],[3/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(1/6)*2^(5/6)/f/(a+a*sin(f*x+e))^(2/3)+7*sec(f*x+e)*(a+a*sin(f*x+e))^(1/3)/f-3*sec(f*x+e)*(a+a*sin(f*x+e))^(4/3)/a/f,1],
[cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/3),x,3,6/11*sqrt(2)*AppellF1(11/6,-1/2,2,17/6,1/2+1/2*sin(f*x+e),1+sin(f*x+e))*sec(f*x+e)*sqrt(1-sin(f*x+e))*(a+a*sin(f*x+e))^(7/3)/a^2/f,1],
[cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/3),x,3,12/17*sqrt(2)*AppellF1(17/6,4,-3/2,23/6,1+sin(f*x+e),1/2+1/2*sin(f*x+e))*sec(f*x+e)*sqrt(1-sin(f*x+e))*(a+a*sin(f*x+e))^(10/3)/a^3/f,1],
[tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x,8,7/9*a*sec(f*x+e)/f/(a+a*sin(f*x+e))^(4/3)+95/99*sec(f*x+e)*(a-a*sin(f*x+e))/f/(a+a*sin(f*x+e))^(4/3)-973/495*sec(f*x+e)*(1-sin(f*x+e))/f/(a+a*sin(f*x+e))^(1/3)+973/2970*InverseJacobiAM(arccos((2^(1/3)*a^(1/3)-(1-sqrt(3))*(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))),sqrt(1/2+1/4*sqrt(3)))*sec(f*x+e)*(a+a*sin(f*x+e))^(2/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))*sqrt((2^(2/3)*a^(2/3)+2^(1/3)*a^(1/3)*(a+a*sin(f*x+e))^(1/3)+(a+a*sin(f*x+e))^(2/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)*2^(2/3)*3^(3/4)/a^(4/3)/f/sqrt(-(a+a*sin(f*x+e))^(1/3)*(2^(1/3)*a^(1/3)-(a+a*sin(f*x+e))^(1/3))/(2^(1/3)*a^(1/3)-(1+sqrt(3))*(a+a*sin(f*x+e))^(1/3))^2)-8/3*a^2*sin(f*x+e)*tan(f*x+e)/f/(a-a*sin(f*x+e))/(a+a*sin(f*x+e))^(4/3)+3*a^2*sin(f*x+e)^2*tan(f*x+e)/f/(a-a*sin(f*x+e))/(a+a*sin(f*x+e))^(4/3),1],
[tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x,4,-3/5*sec(f*x+e)/f/(a+a*sin(f*x+e))^(1/3)+11/15*2^(1/6)*cos(f*x+e)*hypergeom([1/2, 5/6],[3/2],1/2-1/2*sin(f*x+e))/f/(1+sin(f*x+e))^(1/6)/(a+a*sin(f*x+e))^(1/3)+4/5*sec(f*x+e)*(a+a*sin(f*x+e))^(2/3)/a/f,1],
[cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x,3,6/7*sqrt(2)*AppellF1(7/6,-1/2,2,13/6,1/2+1/2*sin(f*x+e),1+sin(f*x+e))*sec(f*x+e)*sqrt(1-sin(f*x+e))*(a+a*sin(f*x+e))^(5/3)/a^2/f,1],
[cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x,3,12/13*sqrt(2)*AppellF1(13/6,4,-3/2,19/6,1+sin(f*x+e),1/2+1/2*sin(f*x+e))*sec(f*x+e)*sqrt(1-sin(f*x+e))*(a+a*sin(f*x+e))^(8/3)/a^3/f,1],
[(a+a*sin(f*x+e))^3*(g*tan(f*x+e))^p,x,10,a^3*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+3*a^3*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p)+a^3*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 2+1/2*p],[3+1/2*p],sin(f*x+e)^2)*sin(f*x+e)^3*(g*tan(f*x+e))^(p+1)/f/g/(4+p)+3*a^3*hypergeom([2, 3/2+1/2*p],[5/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(3+p)/f/g^3/(3+p),1],
[(a+a*sin(f*x+e))^2*(g*tan(f*x+e))^p,x,8,a^2*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+2*a^2*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p)+a^2*hypergeom([2, 3/2+1/2*p],[5/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(3+p)/f/g^3/(3+p),1],
[(a+a*sin(f*x+e))*(g*tan(f*x+e))^p,x,6,a*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+a*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p),1],
[(g*tan(f*x+e))^p/(a+a*sin(f*x+e)),x,4,(g*tan(f*x+e))^(p+1)/a/f/g/(p+1)-(cos(f*x+e)^2)^(3/2+1/2*p)*hypergeom([1+1/2*p, 3/2+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sec(f*x+e)*(g*tan(f*x+e))^(2+p)/a/f/g^2/(2+p),1],
[(g*tan(f*x+e))^p/(a+a*sin(f*x+e))^2,x,11,(g*tan(f*x+e))^(p+1)/a^2/f/g/(p+1)-2*(cos(f*x+e)^2)^(5/2+1/2*p)*hypergeom([1+1/2*p, 5/2+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sec(f*x+e)^3*(g*tan(f*x+e))^(2+p)/a^2/f/g^2/(2+p)+2*(g*tan(f*x+e))^(3+p)/a^2/f/g^3/(3+p),1],
[(g*tan(f*x+e))^p/(a+a*sin(f*x+e))^3,x,15,(g*tan(f*x+e))^(p+1)/a^3/f/g/(p+1)-3*(cos(f*x+e)^2)^(7/2+1/2*p)*hypergeom([1+1/2*p, 7/2+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sec(f*x+e)^5*(g*tan(f*x+e))^(2+p)/a^3/f/g^2/(2+p)+5*(g*tan(f*x+e))^(3+p)/a^3/f/g^3/(3+p)-(cos(f*x+e)^2)^(7/2+1/2*p)*hypergeom([2+1/2*p, 7/2+1/2*p],[3+1/2*p],sin(f*x+e)^2)*sec(f*x+e)^3*(g*tan(f*x+e))^(4+p)/a^3/f/g^4/(4+p)+4*(g*tan(f*x+e))^(5+p)/a^3/f/g^5/(5+p),1],
[(a+a*sin(f*x+e))^m*(g*tan(f*x+e))^p,x,4,AppellF1(p+1,1/2*p+1/2,1/2-m+1/2*p,2+p,sin(f*x+e),-sin(f*x+e))*(1-sin(f*x+e))^(1/2*p+1/2)*(1+sin(f*x+e))^(1/2-m+1/2*p)*(a+a*sin(f*x+e))^m*(g*tan(f*x+e))^(p+1)/f/g/(p+1),1],
[(a+a*sin(f*x+e))^m*tan(f*x+e)^3,x,5,1/4*a*m*(a+a*sin(f*x+e))^(-1+m)/f/(1-m)+1/2*a^2*(2+m)*(a+a*sin(f*x+e))^(-1+m)/f/m/(a-a*sin(f*x+e))-a^2*sin(f*x+e)^2*(a+a*sin(f*x+e))^(-1+m)/f/m/(a-a*sin(f*x+e))-1/8*(4+m)*hypergeom([1, m],[1+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^m/f/m,1],
[(a+a*sin(f*x+e))^m*tan(f*x+e),x,3,-1/2*(a+a*sin(f*x+e))^m/f/m+1/4*hypergeom([1, 1+m],[2+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m),1],
[cot(f*x+e)*(a+a*sin(f*x+e))^m,x,2,-hypergeom([1, 1+m],[2+m],1+sin(f*x+e))*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m),1],
[cot(f*x+e)^3*(a+a*sin(f*x+e))^m,x,3,-1/2*csc(f*x+e)^2*(a+a*sin(f*x+e))^(2+m)/a^2/f-1/2*(2-m)*hypergeom([2, 2+m],[3+m],1+sin(f*x+e))*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m),1],
[cot(f*x+e)^5*(a+a*sin(f*x+e))^m,x,4,1/12*(9-m)*csc(f*x+e)^3*(a+a*sin(f*x+e))^(3+m)/a^3/f-1/4*csc(f*x+e)^4*(a+a*sin(f*x+e))^(3+m)/a^3/f-1/12*(m^2-9*m+12)*hypergeom([3, 3+m],[4+m],1+sin(f*x+e))*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m),1],
[(a+a*sin(f*x+e))^m*tan(f*x+e)^4,x,7,-1/3*a*(m^2+7*m+3)*sec(f*x+e)*(a+a*sin(f*x+e))^(-1+m)/f/m+1/3*(-m^2-5*m+9)*sec(f*x+e)*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^(-1+m)/f/(3-2*m)+1/3*2^(-1/2+m)*(m^4+6*m^3-7*m^2-12*m+9)*hypergeom([1/2, 3/2-m],[3/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(3/2-m)*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^(-1+m)/f/(3-2*m)/m+1/3*a^2*(3+m)*sin(f*x+e)*(a+a*sin(f*x+e))^(-1+m)*tan(f*x+e)/f/m/(a-a*sin(f*x+e))-a^2*sin(f*x+e)^2*(a+a*sin(f*x+e))^(-1+m)*tan(f*x+e)/f/m/(a-a*sin(f*x+e)),1],
[(a+a*sin(f*x+e))^m*tan(f*x+e)^2,x,4,sec(f*x+e)*(a+a*sin(f*x+e))^m/f/(1-m)/m+2^(-1/2+m)*(-m^2-m+1)*hypergeom([-1/2, 3/2-m],[1/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(1/2-m)*(a+a*sin(f*x+e))^m/f/(1-m)/m-sec(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/m,1],
[(a+a*sin(f*x+e))^m,x,2,-2^(1/2+m)*cos(f*x+e)*hypergeom([1/2, 1/2-m],[3/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-1/2-m)*(a+a*sin(f*x+e))^m/f,1],
[cot(f*x+e)^2*(a+a*sin(f*x+e))^m,x,3,-1/3*2^(3/2+m)*AppellF1(3/2,2,-1/2-m,5/2,1-sin(f*x+e),1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-1/2-m)*(a-a*sin(f*x+e))^2*(a+a*sin(f*x+e))^(1+m)/a^3/f,1],
[cot(f*x+e)^4*(a+a*sin(f*x+e))^m,x,3,-1/5*2^(5/2+m)*AppellF1(5/2,4,-3/2-m,7/2,1-sin(f*x+e),1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-3/2-m)*(a-a*sin(f*x+e))^3*(a+a*sin(f*x+e))^(2+m)/a^5/f,1],
[(a+b*sin(d*x+c))*tan(d*x+c)^3,x,7,1/4*(2*a+3*b)*ln(1-sin(d*x+c))/d+1/4*(2*a-3*b)*ln(1+sin(d*x+c))/d+b*sin(d*x+c)/d+1/2*sec(d*x+c)^2*(a+b*sin(d*x+c))/d,1],
[(a+b*sin(d*x+c))*tan(d*x+c),x,6,-1/2*(a+b)*ln(1-sin(d*x+c))/d-1/2*(a-b)*ln(1+sin(d*x+c))/d-b*sin(d*x+c)/d,1],
[cot(d*x+c)*(a+b*sin(d*x+c)),x,3,a*ln(sin(d*x+c))/d+b*sin(d*x+c)/d,1],
[cot(d*x+c)^3*(a+b*sin(d*x+c)),x,3,-b*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-a*ln(sin(d*x+c))/d-b*sin(d*x+c)/d,1],
[cot(d*x+c)^5*(a+b*sin(d*x+c)),x,3,2*b*csc(d*x+c)/d+a*csc(d*x+c)^2/d-1/3*b*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d+a*ln(sin(d*x+c))/d+b*sin(d*x+c)/d,1],
[(a+b*sin(d*x+c))*tan(d*x+c)^4,x,8,a*x-b*cos(d*x+c)/d-2*b*sec(d*x+c)/d+1/3*b*sec(d*x+c)^3/d-a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[(a+b*sin(d*x+c))*tan(d*x+c)^2,x,7,-a*x+b*cos(d*x+c)/d+b*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c)),x,7,-a*x-b*arctanh(cos(d*x+c))/d+b*cos(d*x+c)/d-a*cot(d*x+c)/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c)),x,10,a*x+3/2*b*arctanh(cos(d*x+c))/d-b*cos(d*x+c)/d+a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*b*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^6*(a+b*sin(d*x+c)),x,12,-a*x-15/8*b*arctanh(cos(d*x+c))/d+b*cos(d*x+c)/d-a*cot(d*x+c)/d+1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d+9/8*b*cot(d*x+c)*csc(d*x+c)/d-1/4*b*cot(d*x+c)*csc(d*x+c)^3/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c)^3,x,7,1/2*(a+b)*(a+2*b)*ln(1-sin(d*x+c))/d+1/2*(a-2*b)*(a-b)*ln(1+sin(d*x+c))/d+2*a*b*sin(d*x+c)/d+1/2*b^2*sin(d*x+c)^2/d+1/2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c),x,6,-1/2*(a+b)^2*ln(1-sin(d*x+c))/d-1/2*(a-b)^2*ln(1+sin(d*x+c))/d-2*a*b*sin(d*x+c)/d-1/2*b^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)*(a+b*sin(d*x+c))^2,x,3,a^2*ln(sin(d*x+c))/d+2*a*b*sin(d*x+c)/d+1/2*b^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x,3,-2*a*b*csc(d*x+c)/d-1/2*a^2*csc(d*x+c)^2/d-(a^2-b^2)*ln(sin(d*x+c))/d-2*a*b*sin(d*x+c)/d-1/2*b^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x,3,4*a*b*csc(d*x+c)/d+1/2*(2*a^2-b^2)*csc(d*x+c)^2/d-2/3*a*b*csc(d*x+c)^3/d-1/4*a^2*csc(d*x+c)^4/d+(a^2-2*b^2)*ln(sin(d*x+c))/d+2*a*b*sin(d*x+c)/d+1/2*b^2*sin(d*x+c)^2/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c)^4,x,13,a^2*x+5/2*b^2*x-2*a*b*cos(d*x+c)/d-4*a*b*sec(d*x+c)/d+2/3*a*b*sec(d*x+c)^3/d-1/2*b^2*cos(d*x+c)*sin(d*x+c)/d-a^2*tan(d*x+c)/d-2*b^2*tan(d*x+c)/d+1/3*a^2*tan(d*x+c)^3/d+1/3*b^2*tan(d*x+c)^3/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c)^2,x,12,-a^2*x-3/2*b^2*x+2*a*b*cos(d*x+c)/d+2*a*b*sec(d*x+c)/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d+a^2*tan(d*x+c)/d+b^2*tan(d*x+c)/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x,9,-a^2*x+1/2*b^2*x-2*a*b*arctanh(cos(d*x+c))/d+2*a*b*cos(d*x+c)/d-a^2*cot(d*x+c)/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x,15,a^2*x-3/2*b^2*x+3*a*b*arctanh(cos(d*x+c))/d-2*a*b*cos(d*x+c)/d+a^2*cot(d*x+c)/d-b^2*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a*b*cot(d*x+c)*csc(d*x+c)/d-1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*(a+b*sin(d*x+c))^2,x,17,-a^2*x+5/2*b^2*x-15/4*a*b*arctanh(cos(d*x+c))/d+2*a*b*cos(d*x+c)/d-a^2*cot(d*x+c)/d+2*b^2*cot(d*x+c)/d+1/3*a^2*cot(d*x+c)^3/d-1/3*b^2*cot(d*x+c)^3/d-1/5*a^2*cot(d*x+c)^5/d+9/4*a*b*cot(d*x+c)*csc(d*x+c)/d-1/2*a*b*cot(d*x+c)*csc(d*x+c)^3/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c)^3,x,7,1/4*(a+b)^2*(2*a+5*b)*ln(1-sin(d*x+c))/d+1/4*(2*a-5*b)*(a-b)^2*ln(1+sin(d*x+c))/d+1/2*b*(6*a^2+5*b^2)*sin(d*x+c)/d+3/2*a*b^2*sin(d*x+c)^2/d+1/3*b^3*sin(d*x+c)^3/d+1/2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c),x,6,-1/2*(a+b)^3*ln(1-sin(d*x+c))/d-1/2*(a-b)^3*ln(1+sin(d*x+c))/d-b*(3*a^2+b^2)*sin(d*x+c)/d-3/2*a*b^2*sin(d*x+c)^2/d-1/3*b^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)*(a+b*sin(d*x+c))^3,x,3,a^3*ln(sin(d*x+c))/d+3*a^2*b*sin(d*x+c)/d+3/2*a*b^2*sin(d*x+c)^2/d+1/3*b^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)^3*(a+b*sin(d*x+c))^3,x,3,-3*a^2*b*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d-a*(a^2-3*b^2)*ln(sin(d*x+c))/d-b*(3*a^2-b^2)*sin(d*x+c)/d-3/2*a*b^2*sin(d*x+c)^2/d-1/3*b^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)^5*(a+b*sin(d*x+c))^3,x,3,b*(6*a^2-b^2)*csc(d*x+c)/d+1/2*a*(2*a^2-3*b^2)*csc(d*x+c)^2/d-a^2*b*csc(d*x+c)^3/d-1/4*a^3*csc(d*x+c)^4/d+a*(a^2-6*b^2)*ln(sin(d*x+c))/d+b*(3*a^2-2*b^2)*sin(d*x+c)/d+3/2*a*b^2*sin(d*x+c)^2/d+1/3*b^3*sin(d*x+c)^3/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c)^4,x,16,a^3*x+15/2*a*b^2*x-3*a^2*b*cos(d*x+c)/d-3*b^3*cos(d*x+c)/d+1/3*b^3*cos(d*x+c)^3/d-6*a^2*b*sec(d*x+c)/d-3*b^3*sec(d*x+c)/d+a^2*b*sec(d*x+c)^3/d+1/3*b^3*sec(d*x+c)^3/d-3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d-a^3*tan(d*x+c)/d-6*a*b^2*tan(d*x+c)/d+1/3*a^3*tan(d*x+c)^3/d+a*b^2*tan(d*x+c)^3/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c)^2,x,15,-a^3*x-9/2*a*b^2*x+3*a^2*b*cos(d*x+c)/d+2*b^3*cos(d*x+c)/d-1/3*b^3*cos(d*x+c)^3/d+3*a^2*b*sec(d*x+c)/d+b^3*sec(d*x+c)/d+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+a^3*tan(d*x+c)/d+3*a*b^2*tan(d*x+c)/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x,11,-a^3*x+3/2*a*b^2*x-3*a^2*b*arctanh(cos(d*x+c))/d+3*a^2*b*cos(d*x+c)/d-1/3*b^3*cos(d*x+c)^3/d-a^3*cot(d*x+c)/d+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^3,x,19,a^3*x-9/2*a*b^2*x+9/2*a^2*b*arctanh(cos(d*x+c))/d-b^3*arctanh(cos(d*x+c))/d-3*a^2*b*cos(d*x+c)/d+b^3*cos(d*x+c)/d+1/3*b^3*cos(d*x+c)^3/d+a^3*cot(d*x+c)/d-3*a*b^2*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^2*b*cot(d*x+c)*csc(d*x+c)/d-3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*(a+b*sin(d*x+c))^3,x,22,-a^3*x+15/2*a*b^2*x-45/8*a^2*b*arctanh(cos(d*x+c))/d+5/2*b^3*arctanh(cos(d*x+c))/d+3*a^2*b*cos(d*x+c)/d-2*b^3*cos(d*x+c)/d-1/3*b^3*cos(d*x+c)^3/d-a^3*cot(d*x+c)/d+6*a*b^2*cot(d*x+c)/d+1/3*a^3*cot(d*x+c)^3/d-a*b^2*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d+27/8*a^2*b*cot(d*x+c)*csc(d*x+c)/d-1/2*b^3*cot(d*x+c)*csc(d*x+c)/d-3/4*a^2*b*cot(d*x+c)*csc(d*x+c)^3/d+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[tan(d*x+c)^5/(a+b*sin(d*x+c)),x,4,-1/16*(8*a^2+9*a*b+3*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d-1/16*(8*a^2-9*a*b+3*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d+a^5*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/16*(8*a^2-a*b-5*b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))-1/16*(8*a^2+a*b-5*b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a/(a^2-b^2)-b*sin(d*x+c)/(a^2-b^2))/d,1],
[tan(d*x+c)^3/(a+b*sin(d*x+c)),x,4,1/4*(2*a+b)*ln(1-sin(d*x+c))/(a+b)^2/d+1/4*(2*a-b)*ln(1+sin(d*x+c))/(a-b)^2/d-a^3*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+1/2*sec(d*x+c)^2*(a/(a^2-b^2)-b*sin(d*x+c)/(a^2-b^2))/d,1],
[tan(d*x+c)/(a+b*sin(d*x+c)),x,3,-1/2*ln(1-sin(d*x+c))/(a+b)/d-1/2*ln(1+sin(d*x+c))/(a-b)/d+a*ln(a+b*sin(d*x+c))/(a^2-b^2)/d,1],
[cot(d*x+c)/(a+b*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-ln(a+b*sin(d*x+c))/a/d,1],
[cot(d*x+c)^3/(a+b*sin(d*x+c)),x,3,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-(a^2-b^2)*ln(sin(d*x+c))/a^3/d+(a^2-b^2)*ln(a+b*sin(d*x+c))/a^3/d,1],
[cot(d*x+c)^5/(a+b*sin(d*x+c)),x,3,-b*(2*a^2-b^2)*csc(d*x+c)/a^4/d+1/2*(2*a^2-b^2)*csc(d*x+c)^2/a^3/d+1/3*b*csc(d*x+c)^3/a^2/d-1/4*csc(d*x+c)^4/a/d+(a^2-b^2)^2*ln(sin(d*x+c))/a^5/d-(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^5/d,1],
[tan(d*x+c)^4/(a+b*sin(d*x+c)),x,13,2*a^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+a^2*b*sec(d*x+c)/(a^2-b^2)^2/d+b*sec(d*x+c)/(a^2-b^2)/d-1/3*b*sec(d*x+c)^3/(a^2-b^2)/d-a^3*tan(d*x+c)/(a^2-b^2)^2/d+1/3*a*tan(d*x+c)^3/(a^2-b^2)/d,1],
[tan(d*x+c)^2/(a+b*sin(d*x+c)),x,8,-2*a^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)/d-b*sec(d*x+c)/(a^2-b^2)/d+a*tan(d*x+c)/(a^2-b^2)/d,1],
[cot(d*x+c)^2/(a+b*sin(d*x+c)),x,7,-2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/d+b*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a/d,1],
[cot(d*x+c)^4/(a+b*sin(d*x+c)),x,7,2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/d-1/2*b*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/a^4/d+1/3*(4*a^2-3*b^2)*cot(d*x+c)/a^3/d+1/2*b*cot(d*x+c)*csc(d*x+c)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d,1],
[cot(d*x+c)^6/(a+b*sin(d*x+c)),x,9,-2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d+1/8*b*(15*a^4-20*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^6/d-1/15*(23*a^4-35*a^2*b^2+15*b^4)*cot(d*x+c)/a^5/d-cot(d*x+c)*csc(d*x+c)/b/d+1/8*(8*a^4-9*a^2*b^2+4*b^4)*cot(d*x+c)*csc(d*x+c)/a^4/b/d+1/2*a*cot(d*x+c)*csc(d*x+c)^2/b^2/d-1/30*(15*a^4-22*a^2*b^2+10*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^3/b^2/d+1/4*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d,1],
[tan(d*x+c)^5/(a+b*sin(d*x+c))^2,x,4,-1/8*a*(4*a+b)*ln(1-sin(d*x+c))/(a+b)^4/d-1/8*a*(4*a-b)*ln(1+sin(d*x+c))/(a-b)^4/d+a^4*(a^2+5*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d-1/8*(4*a^3-5*a^2*b+a*b^2+2*b^3)/(a-b)^2/(a+b)^3/d/(1-sin(d*x+c))-1/8*(4*a^3+5*a^2*b+a*b^2-2*b^3)/(a-b)^3/(a+b)^2/d/(1+sin(d*x+c))-a^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c))+1/4*sec(d*x+c)^4*(a^2+b^2-2*a*b*sin(d*x+c))/(a^2-b^2)^2/d,1],
[tan(d*x+c)^3/(a+b*sin(d*x+c))^2,x,4,1/2*a*ln(1-sin(d*x+c))/(a+b)^3/d+1/2*a*ln(1+sin(d*x+c))/(a-b)^3/d-a^2*(a^2+3*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+a^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))+1/2*sec(d*x+c)^2*(a^2+b^2-2*a*b*sin(d*x+c))/(a^2-b^2)^2/d,1],
[tan(d*x+c)/(a+b*sin(d*x+c))^2,x,3,-1/2*ln(1-sin(d*x+c))/(a+b)^2/d-1/2*ln(1+sin(d*x+c))/(a-b)^2/d+(a^2+b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d-a/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)/(a+b*sin(d*x+c))^2,x,3,ln(sin(d*x+c))/a^2/d-ln(a+b*sin(d*x+c))/a^2/d+1/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x,3,2*b*csc(d*x+c)/a^3/d-1/2*csc(d*x+c)^2/a^2/d-(a^2-3*b^2)*ln(sin(d*x+c))/a^4/d+(a^2-3*b^2)*ln(a+b*sin(d*x+c))/a^4/d-(a^2-b^2)/a^3/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x,3,-4*b*(a^2-b^2)*csc(d*x+c)/a^5/d+1/2*(2*a^2-3*b^2)*csc(d*x+c)^2/a^4/d+2/3*b*csc(d*x+c)^3/a^3/d-1/4*csc(d*x+c)^4/a^2/d+(a^4-6*a^2*b^2+5*b^4)*ln(sin(d*x+c))/a^6/d-(a^4-6*a^2*b^2+5*b^4)*ln(a+b*sin(d*x+c))/a^6/d+(a^2-b^2)^2/a^5/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^4/(a+b*sin(d*x+c))^2,x,16,2*a^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+8*a^3*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+1/12*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))^2+1/12*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))-1/4*(3*a+b)*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/12*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))^2-1/12*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))+1/4*(3*a-b)*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))+a^4*b*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x,12,-2*a^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d-4*a*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))-a^2*b*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x,8,-2*(a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/sqrt(a^2-b^2)/d+2*b*arctanh(cos(d*x+c))/a^3/d-2*cot(d*x+c)/a^2/d+cot(d*x+c)/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x,8,2*(a^4-5*a^2*b^2+4*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/sqrt(a^2-b^2)/d-b*(3*a^2-4*b^2)*arctanh(cos(d*x+c))/a^5/d+1/3*(7*a^2-12*b^2)*cot(d*x+c)/a^4/d-(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/b/d+1/3*(3*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6/(a+b*sin(d*x+c))^2,x,10,-2*(a^2-6*b^2)*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^7/d+1/4*b*(15*a^4-40*a^2*b^2+24*b^4)*arctanh(cos(d*x+c))/a^7/d-1/15*(38*a^4-135*a^2*b^2+90*b^4)*cot(d*x+c)/a^6/d+1/4*(4*a^4-17*a^2*b^2+12*b^4)*cot(d*x+c)*csc(d*x+c)/a^5/b/d-1/30*(15*a^4-82*a^2*b^2+60*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^4/b^2/d-1/2*cot(d*x+c)*csc(d*x+c)/b/d/(a+b*sin(d*x+c))+1/6*a*cot(d*x+c)*csc(d*x+c)^2/b^2/d/(a+b*sin(d*x+c))+1/6*(2*a^4-12*a^2*b^2+9*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^3/b^2/d/(a+b*sin(d*x+c))+3/10*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d/(a+b*sin(d*x+c))-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^5/(a+b*sin(d*x+c))^3,x,4,-1/16*(8*a^2-5*a*b-b^2)*ln(1-sin(d*x+c))/(a+b)^5/d-1/16*(8*a^2+5*a*b-b^2)*ln(1+sin(d*x+c))/(a-b)^5/d+a^3*(a^4+13*a^2*b^2+10*b^4)*ln(a+b*sin(d*x+c))/(a^2-b^2)^5/d-1/16*(8*a^4-19*a^3*b+21*a^2*b^2-a*b^3-b^4)/(a-b)^3/(a+b)^4/d/(1-sin(d*x+c))-1/16*(8*a^4+19*a^3*b+21*a^2*b^2+a*b^3-b^4)/(a-b)^4/(a+b)^3/d/(1+sin(d*x+c))-1/2*a^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^2-a^4*(a^2+5*b^2)/(a^2-b^2)^4/d/(a+b*sin(d*x+c))+1/4*sec(d*x+c)^4*(a*(a^2+3*b^2)-b*(3*a^2+b^2)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[tan(d*x+c)^3/(a+b*sin(d*x+c))^3,x,4,1/4*(2*a-b)*ln(1-sin(d*x+c))/(a+b)^4/d+1/4*(2*a+b)*ln(1+sin(d*x+c))/(a-b)^4/d-a*(a^4+8*a^2*b^2+3*b^4)*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d+1/2*a^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2+a^2*(a^2+3*b^2)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))+1/2*sec(d*x+c)^2*(a*(a^2+3*b^2)-b*(3*a^2+b^2)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[tan(d*x+c)/(a+b*sin(d*x+c))^3,x,3,-1/2*ln(1-sin(d*x+c))/(a+b)^3/d-1/2*ln(1+sin(d*x+c))/(a-b)^3/d+a*(a^2+3*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/2*a/(a^2-b^2)/d/(a+b*sin(d*x+c))^2-(a^2+b^2)/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)/(a+b*sin(d*x+c))^3,x,3,ln(sin(d*x+c))/a^3/d-ln(a+b*sin(d*x+c))/a^3/d+1/2/a/d/(a+b*sin(d*x+c))^2+1/a^2/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x,3,3*b*csc(d*x+c)/a^4/d-1/2*csc(d*x+c)^2/a^3/d-(a^2-6*b^2)*ln(sin(d*x+c))/a^5/d+(a^2-6*b^2)*ln(a+b*sin(d*x+c))/a^5/d-1/2*(a^2-b^2)/a^3/d/(a+b*sin(d*x+c))^2-(a^2-3*b^2)/a^4/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^5/(a+b*sin(d*x+c))^3,x,3,-2*b*(3*a^2-5*b^2)*csc(d*x+c)/a^6/d+(a^2-3*b^2)*csc(d*x+c)^2/a^5/d+b*csc(d*x+c)^3/a^4/d-1/4*csc(d*x+c)^4/a^3/d+(a^4-12*a^2*b^2+15*b^4)*ln(sin(d*x+c))/a^7/d-(a^4-12*a^2*b^2+15*b^4)*ln(a+b*sin(d*x+c))/a^7/d+1/2*(a^2-b^2)^2/a^5/d/(a+b*sin(d*x+c))^2+(a^4-6*a^2*b^2+5*b^4)/a^6/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^4/(a+b*sin(d*x+c))^3,x,22,8*a^4*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(9/2)/d+12*a^2*b^2*(a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(9/2)/d+a^4*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(9/2)/d+1/12*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))^2-3/4*a*cos(d*x+c)/(a+b)^4/d/(1-sin(d*x+c))+1/12*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/12*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))^2+3/4*a*cos(d*x+c)/(a-b)^4/d/(1+sin(d*x+c))-1/12*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))+1/2*a^4*b*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^2+3/2*a^5*b*cos(d*x+c)/(a^2-b^2)^4/d/(a+b*sin(d*x+c))+4*a^3*b^3*cos(d*x+c)/(a^2-b^2)^4/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x,18,-4*a^2*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-a^2*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-2*b^2*(3*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))-1/2*a^2*b*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2-3/2*a^3*b*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))-2*a*b^3*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x,9,-(2*a^4-9*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/(a^2-b^2)^(3/2)/d+3*b*arctanh(cos(d*x+c))/a^4/d-1/2*(5*a^2-6*b^2)*cot(d*x+c)/a^3/(a^2-b^2)/d+1/2*cot(d*x+c)/a/d/(a+b*sin(d*x+c))^2+1/2*(2*a^2-3*b^2)*cot(d*x+c)/a^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x,9,(2*a^4-19*a^2*b^2+20*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/sqrt(a^2-b^2)/d-1/2*b*(9*a^2-20*b^2)*arctanh(cos(d*x+c))/a^6/d+1/6*(17*a^2-60*b^2)*cot(d*x+c)/a^5/d-(a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/b/d+1/6*(3*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^2-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c))^2+1/6*(3*a^2-20*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/b/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6/(a+b*sin(d*x+c))^3,x,11,-sqrt(a^2-b^2)*(2*a^4-29*a^2*b^2+42*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^8/d+1/8*b*(45*a^4-200*a^2*b^2+168*b^4)*arctanh(cos(d*x+c))/a^8/d-1/30*(91*a^4-645*a^2*b^2+630*b^4)*cot(d*x+c)/a^7/d+1/8*(8*a^4-79*a^2*b^2+84*b^4)*cot(d*x+c)*csc(d*x+c)/a^6/b/d-1/30*(15*a^4-187*a^2*b^2+210*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^5/b^2/d-1/3*cot(d*x+c)*csc(d*x+c)/b/d/(a+b*sin(d*x+c))^2+1/12*a*cot(d*x+c)*csc(d*x+c)^2/b^2/d/(a+b*sin(d*x+c))^2+1/60*(5*a^4-60*a^2*b^2+63*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^3/b^2/d/(a+b*sin(d*x+c))^2+7/20*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d/(a+b*sin(d*x+c))^2-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d/(a+b*sin(d*x+c))^2+1/12*(4*a^4-54*a^2*b^2+63*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^4/b^2/d/(a+b*sin(d*x+c)),1],
[(a+b*sin(f*x+e))^3*(g*tan(f*x+e))^p,x,10,a^3*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+3*a^2*b*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p)+b^3*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 2+1/2*p],[3+1/2*p],sin(f*x+e)^2)*sin(f*x+e)^3*(g*tan(f*x+e))^(p+1)/f/g/(4+p)+3*a*b^2*hypergeom([2, 3/2+1/2*p],[5/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(3+p)/f/g^3/(3+p),1],
[(a+b*sin(f*x+e))^2*(g*tan(f*x+e))^p,x,8,a^2*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+2*a*b*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p)+b^2*hypergeom([2, 3/2+1/2*p],[5/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(3+p)/f/g^3/(3+p),1],
[(a+b*sin(f*x+e))*(g*tan(f*x+e))^p,x,6,a*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],-tan(f*x+e)^2)*(g*tan(f*x+e))^(p+1)/f/g/(p+1)+b*(cos(f*x+e)^2)^(1/2*p+1/2)*hypergeom([1/2*p+1/2, 1+1/2*p],[2+1/2*p],sin(f*x+e)^2)*sin(f*x+e)*(g*tan(f*x+e))^(p+1)/f/g/(2+p),1],
[(g*tan(f*x+e))^p/(a+b*sin(f*x+e)),x,0,a*g*(1-b^2*cos(f*x+e)^2/(-a^2+b^2))^(-1/2+1/2*p)*hypergeom([1/2-1/2*p, 1/2-1/2*p],[3/2-1/2*p],(cos(f*x+e)^2-b^2*cos(f*x+e)^2/(-a^2+b^2))/(1-b^2*cos(f*x+e)^2/(-a^2+b^2)))*(sin(f*x+e)^2)^(1/2-1/2*p)*(g*tan(f*x+e))^(-1+p)/(a^2-b^2)/f/(-1+p)+b*AppellF1(1/2-1/2*p,-1/2*p,1,3/2-1/2*p,cos(f*x+e)^2,b^2*cos(f*x+e)^2/(-a^2+b^2))*cos(f*x+e)*(g*tan(f*x+e))^p/(-a^2+b^2)/f/(-1+p)/((sin(f*x+e)^2)^(1/2*p)),1],
[(g*tan(f*x+e))^p/(a+b*sin(f*x+e))^2,x,0,1/2*a^2*cos(f*x+e)*(1-cos(f*x+e)^2)^(-1/2+1/2*q)/(1-b^2*cos(f*x+e)^2/(-a^2+b^2))*((2*a^2-2*b^2+b^2*(1+q)*cos(f*x+e)^2)*HurwitzLerchPhi(-a^2*cot(f*x+e)^2/(a^2-b^2),1,1/2-1/2*q)-b^2*(-1+q)*cos(f*x+e)^2*HurwitzLerchPhi(-a^2*cot(f*x+e)^2/(a^2-b^2),1,3/2-1/2*q))*sin(f*x+e)*(sin(f*x+e)^2)^(-1/2-1/2*q)*(g*tan(f*x+e))^q/(a^2-b^2)^2/(-a^2+b^2)/f-a^2*cos(f*x+e)*(1-b^2*cos(f*x+e)^2/(-a^2+b^2))^(-1/2+1/2*q)*hypergeom([1/2-1/2*q, 1/2-1/2*q],[3/2-1/2*q],(cos(f*x+e)^2-b^2*cos(f*x+e)^2/(-a^2+b^2))/(1-b^2*cos(f*x+e)^2/(-a^2+b^2)))*sin(f*x+e)*(sin(f*x+e)^2)^(-1/2-1/2*q)*(g*tan(f*x+e))^q/(a^2-b^2)^2/f/(-1+q)+b^2*cos(f*x+e)*(1-b^2*cos(f*x+e)^2/(-a^2+b^2))^(-1/2+1/2*q)*hypergeom([1/2-1/2*q, 1/2-1/2*q],[3/2-1/2*q],(cos(f*x+e)^2-b^2*cos(f*x+e)^2/(-a^2+b^2))/(1-b^2*cos(f*x+e)^2/(-a^2+b^2)))*sin(f*x+e)*(sin(f*x+e)^2)^(-1/2-1/2*q)*(g*tan(f*x+e))^q/(a^2-b^2)^2/f/(-1+q)-2*a*b*AppellF1(1/2-1/2*q,-1/2*q,2,3/2-1/2*q,cos(f*x+e)^2,b^2*cos(f*x+e)^2/(-a^2+b^2))*cos(f*x+e)*(g*tan(f*x+e))^q/(a^2-b^2)^2/f/(-1+q)/((sin(f*x+e)^2)^(1/2*q)),1],
[(a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x,0,Defer(Int)((a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x),0]]: