lst:=[[(a+a*sec(d*x+c))*sin(d*x+c)^9,x,5,-a*cos(d*x+c)/d+2*a*cos(d*x+c)^2/d+4/3*a*cos(d*x+c)^3/d-3/2*a*cos(d*x+c)^4/d-6/5*a*cos(d*x+c)^5/d+2/3*a*cos(d*x+c)^6/d+4/7*a*cos(d*x+c)^7/d-1/8*a*cos(d*x+c)^8/d-1/9*a*cos(d*x+c)^9/d-a*ln(cos(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^7,x,5,-a*cos(d*x+c)/d+3/2*a*cos(d*x+c)^2/d+a*cos(d*x+c)^3/d-3/4*a*cos(d*x+c)^4/d-3/5*a*cos(d*x+c)^5/d+1/6*a*cos(d*x+c)^6/d+1/7*a*cos(d*x+c)^7/d-a*ln(cos(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^5,x,5,-a*cos(d*x+c)/d+a*cos(d*x+c)^2/d+2/3*a*cos(d*x+c)^3/d-1/4*a*cos(d*x+c)^4/d-1/5*a*cos(d*x+c)^5/d-a*ln(cos(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^3,x,5,-a*cos(d*x+c)/d+1/2*a*cos(d*x+c)^2/d+1/3*a*cos(d*x+c)^3/d-a*ln(cos(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c),x,4,-a*cos(d*x+c)/d-a*ln(cos(d*x+c))/d,1],
[csc(d*x+c)*(a+a*sec(d*x+c)),x,6,a*ln(1-cos(d*x+c))/d-a*ln(cos(d*x+c))/d,1],
[csc(d*x+c)^3*(a+a*sec(d*x+c)),x,5,-1/2*a^3/d/(a^2-a^2*cos(d*x+c))+3/4*a*ln(1-cos(d*x+c))/d-a*ln(cos(d*x+c))/d+1/4*a*ln(1+cos(d*x+c))/d,1],
[csc(d*x+c)^5*(a+a*sec(d*x+c)),x,5,-1/8*a^5/d/(a^2-a^2*cos(d*x+c))^2-1/2*a^5/d/(a^4-a^4*cos(d*x+c))-1/8*a^5/d/(a^4+a^4*cos(d*x+c))+11/16*a*ln(1-cos(d*x+c))/d-a*ln(cos(d*x+c))/d+5/16*a*ln(1+cos(d*x+c))/d,1],
[csc(d*x+c)^7*(a+a*sec(d*x+c)),x,5,-1/24*a^7/d/(a^2-a^2*cos(d*x+c))^3-5/32*a^7/d/(a^3-a^3*cos(d*x+c))^2-1/32*a^7/d/(a^3+a^3*cos(d*x+c))^2-1/2*a^7/d/(a^6-a^6*cos(d*x+c))-3/16*a^7/d/(a^6+a^6*cos(d*x+c))+21/32*a*ln(1-cos(d*x+c))/d-a*ln(cos(d*x+c))/d+11/32*a*ln(1+cos(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^8,x,11,35/128*a*x+a*arctanh(sin(d*x+c))/d-a*sin(d*x+c)/d-35/128*a*cos(d*x+c)*sin(d*x+c)/d-1/3*a*sin(d*x+c)^3/d-35/192*a*cos(d*x+c)*sin(d*x+c)^3/d-1/5*a*sin(d*x+c)^5/d-7/48*a*cos(d*x+c)*sin(d*x+c)^5/d-1/7*a*sin(d*x+c)^7/d-1/8*a*cos(d*x+c)*sin(d*x+c)^7/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^6,x,10,5/16*a*x+a*arctanh(sin(d*x+c))/d-a*sin(d*x+c)/d-5/16*a*cos(d*x+c)*sin(d*x+c)/d-1/3*a*sin(d*x+c)^3/d-5/24*a*cos(d*x+c)*sin(d*x+c)^3/d-1/5*a*sin(d*x+c)^5/d-1/6*a*cos(d*x+c)*sin(d*x+c)^5/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^4,x,9,3/8*a*x+a*arctanh(sin(d*x+c))/d-a*sin(d*x+c)/d-3/8*a*cos(d*x+c)*sin(d*x+c)/d-1/3*a*sin(d*x+c)^3/d-1/4*a*cos(d*x+c)*sin(d*x+c)^3/d,1],
[(a+a*sec(d*x+c))*sin(d*x+c)^2,x,7,1/2*a*x+a*arctanh(sin(d*x+c))/d-a*sin(d*x+c)/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[csc(d*x+c)^2*(a+a*sec(d*x+c)),x,7,a*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-a*csc(d*x+c)/d,1],
[csc(d*x+c)^4*(a+a*sec(d*x+c)),x,8,a*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-a*csc(d*x+c)/d-1/3*a*csc(d*x+c)^3/d,1],
[csc(d*x+c)^6*(a+a*sec(d*x+c)),x,8,a*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-2/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d-a*csc(d*x+c)/d-1/3*a*csc(d*x+c)^3/d-1/5*a*csc(d*x+c)^5/d,1],
[csc(d*x+c)^8*(a+a*sec(d*x+c)),x,8,a*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-a*cot(d*x+c)^3/d-3/5*a*cot(d*x+c)^5/d-1/7*a*cot(d*x+c)^7/d-a*csc(d*x+c)/d-1/3*a*csc(d*x+c)^3/d-1/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d,1],
[csc(d*x+c)^10*(a+a*sec(d*x+c)),x,8,a*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-4/3*a*cot(d*x+c)^3/d-6/5*a*cot(d*x+c)^5/d-4/7*a*cot(d*x+c)^7/d-1/9*a*cot(d*x+c)^9/d-a*csc(d*x+c)/d-1/3*a*csc(d*x+c)^3/d-1/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d-1/9*a*csc(d*x+c)^9/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^9,x,5,3*a^2*cos(d*x+c)/d+4*a^2*cos(d*x+c)^2/d-2/3*a^2*cos(d*x+c)^3/d-3*a^2*cos(d*x+c)^4/d-2/5*a^2*cos(d*x+c)^5/d+4/3*a^2*cos(d*x+c)^6/d+3/7*a^2*cos(d*x+c)^7/d-1/4*a^2*cos(d*x+c)^8/d-1/9*a^2*cos(d*x+c)^9/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^7,x,5,2*a^2*cos(d*x+c)/d+3*a^2*cos(d*x+c)^2/d-3/2*a^2*cos(d*x+c)^4/d-2/5*a^2*cos(d*x+c)^5/d+1/3*a^2*cos(d*x+c)^6/d+1/7*a^2*cos(d*x+c)^7/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^5,x,5,a^2*cos(d*x+c)/d+2*a^2*cos(d*x+c)^2/d+1/3*a^2*cos(d*x+c)^3/d-1/2*a^2*cos(d*x+c)^4/d-1/5*a^2*cos(d*x+c)^5/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^3,x,5,a^2*cos(d*x+c)^2/d+1/3*a^2*cos(d*x+c)^3/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c),x,5,-a^2*cos(d*x+c)/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[csc(d*x+c)*(a+a*sec(d*x+c))^2,x,5,2*a^2*ln(1-cos(d*x+c))/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[csc(d*x+c)^3*(a+a*sec(d*x+c))^2,x,5,-a^3/d/(a-a*cos(d*x+c))+2*a^2*ln(1-cos(d*x+c))/d-2*a^2*ln(cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[csc(d*x+c)^5*(a+a*sec(d*x+c))^2,x,5,-1/4*a^4/d/(a-a*cos(d*x+c))^2-5/4*a^5/d/(a^3-a^3*cos(d*x+c))+17/8*a^2*ln(1-cos(d*x+c))/d-2*a^2*ln(cos(d*x+c))/d-1/8*a^2*ln(1+cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[csc(d*x+c)^7*(a+a*sec(d*x+c))^2,x,5,-1/12*a^5/d/(a-a*cos(d*x+c))^3-3/8*a^4/d/(a-a*cos(d*x+c))^2-23/16*a^7/d/(a^5-a^5*cos(d*x+c))+1/16*a^7/d/(a^5+a^5*cos(d*x+c))+9/4*a^2*ln(1-cos(d*x+c))/d-2*a^2*ln(cos(d*x+c))/d-1/4*a^2*ln(1+cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[csc(d*x+c)^9*(a+a*sec(d*x+c))^2,x,5,-1/32*a^6/d/(a-a*cos(d*x+c))^4-7/48*a^5/d/(a-a*cos(d*x+c))^3-15/32*a^4/d/(a-a*cos(d*x+c))^2+1/64*a^4/d/(a+a*cos(d*x+c))^2-51/32*a^9/d/(a^7-a^7*cos(d*x+c))+9/64*a^9/d/(a^7+a^7*cos(d*x+c))+303/128*a^2*ln(1-cos(d*x+c))/d-2*a^2*ln(cos(d*x+c))/d-47/128*a^2*ln(1+cos(d*x+c))/d+a^2*sec(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^8,x,27,-245/128*a^2*x+2*a^2*arctanh(sin(d*x+c))/d-2*a^2*sin(d*x+c)/d+139/128*a^2*cos(d*x+c)*sin(d*x+c)/d+11/192*a^2*cos(d*x+c)^3*sin(d*x+c)/d-17/48*a^2*cos(d*x+c)^5*sin(d*x+c)/d+1/8*a^2*cos(d*x+c)^7*sin(d*x+c)/d-2/3*a^2*sin(d*x+c)^3/d-2/5*a^2*sin(d*x+c)^5/d-2/7*a^2*sin(d*x+c)^7/d+a^2*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^6,x,18,-25/16*a^2*x+2*a^2*arctanh(sin(d*x+c))/d-2*a^2*sin(d*x+c)/d+7/16*a^2*cos(d*x+c)*sin(d*x+c)/d+7/24*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a^2*cos(d*x+c)^5*sin(d*x+c)/d-2/3*a^2*sin(d*x+c)^3/d-2/5*a^2*sin(d*x+c)^5/d+a^2*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^4,x,14,-9/8*a^2*x+2*a^2*arctanh(sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/8*a^2*cos(d*x+c)*sin(d*x+c)/d+1/4*a^2*cos(d*x+c)^3*sin(d*x+c)/d-2/3*a^2*sin(d*x+c)^3/d+a^2*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2*sin(d*x+c)^2,x,9,-1/2*a^2*x+2*a^2*arctanh(sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d+a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+a*sec(d*x+c))^2,x,11,2*a^2*arctanh(sin(d*x+c))/d-2*a^2*cot(d*x+c)/d-2*a^2*csc(d*x+c)/d+a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+a*sec(d*x+c))^2,x,8,2*a^2*arctanh(sin(d*x+c))/d+10/3*a^2*tan(d*x+c)/d-2*a^2*tan(d*x+c)/d/(1-cos(d*x+c))-1/3*a^4*tan(d*x+c)/d/(a-a*cos(d*x+c))^2,1],
[csc(d*x+c)^6*(a+a*sec(d*x+c))^2,x,12,2*a^2*arctanh(sin(d*x+c))/d-4*a^2*cot(d*x+c)/d-5/3*a^2*cot(d*x+c)^3/d-2/5*a^2*cot(d*x+c)^5/d-2*a^2*csc(d*x+c)/d-2/3*a^2*csc(d*x+c)^3/d-2/5*a^2*csc(d*x+c)^5/d+a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^8*(a+a*sec(d*x+c))^2,x,12,2*a^2*arctanh(sin(d*x+c))/d-5*a^2*cot(d*x+c)/d-3*a^2*cot(d*x+c)^3/d-7/5*a^2*cot(d*x+c)^5/d-2/7*a^2*cot(d*x+c)^7/d-2*a^2*csc(d*x+c)/d-2/3*a^2*csc(d*x+c)^3/d-2/5*a^2*csc(d*x+c)^5/d-2/7*a^2*csc(d*x+c)^7/d+a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^10*(a+a*sec(d*x+c))^2,x,12,2*a^2*arctanh(sin(d*x+c))/d-6*a^2*cot(d*x+c)/d-14/3*a^2*cot(d*x+c)^3/d-16/5*a^2*cot(d*x+c)^5/d-9/7*a^2*cot(d*x+c)^7/d-2/9*a^2*cot(d*x+c)^9/d-2*a^2*csc(d*x+c)/d-2/3*a^2*csc(d*x+c)^3/d-2/5*a^2*csc(d*x+c)^5/d-2/7*a^2*csc(d*x+c)^7/d-2/9*a^2*csc(d*x+c)^9/d+a^2*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^9,x,5,11*a^3*cos(d*x+c)/d+3*a^3*cos(d*x+c)^2/d-14/3*a^3*cos(d*x+c)^3/d-7/2*a^3*cos(d*x+c)^4/d+6/5*a^3*cos(d*x+c)^5/d+11/6*a^3*cos(d*x+c)^6/d+1/7*a^3*cos(d*x+c)^7/d-3/8*a^3*cos(d*x+c)^8/d-1/9*a^3*cos(d*x+c)^9/d+a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^7,x,5,8*a^3*cos(d*x+c)/d+3*a^3*cos(d*x+c)^2/d-2*a^3*cos(d*x+c)^3/d-2*a^3*cos(d*x+c)^4/d+1/2*a^3*cos(d*x+c)^6/d+1/7*a^3*cos(d*x+c)^7/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^5,x,5,5*a^3*cos(d*x+c)/d+5/2*a^3*cos(d*x+c)^2/d-1/3*a^3*cos(d*x+c)^3/d-3/4*a^3*cos(d*x+c)^4/d-1/5*a^3*cos(d*x+c)^5/d-a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^3,x,4,2*a^3*cos(d*x+c)/d+3/2*a^3*cos(d*x+c)^2/d+1/3*a^3*cos(d*x+c)^3/d-2*a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c),x,5,-a^3*cos(d*x+c)/d-3*a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)*(a+a*sec(d*x+c))^3,x,5,4*a^3*ln(1-cos(d*x+c))/d-4*a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)^3*(a+a*sec(d*x+c))^3,x,5,-2*a^3/d/(1-cos(d*x+c))+5*a^3*ln(1-cos(d*x+c))/d-5*a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)^5*(a+a*sec(d*x+c))^3,x,5,-1/2*a^5/d/(a-a*cos(d*x+c))^2-3*a^5/d/(a^2-a^2*cos(d*x+c))+6*a^3*ln(1-cos(d*x+c))/d-6*a^3*ln(cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)^7*(a+a*sec(d*x+c))^3,x,5,-1/6*a^6/d/(a-a*cos(d*x+c))^3-7/8*a^7/d/(a^2-a^2*cos(d*x+c))^2-31/8*a^7/d/(a^4-a^4*cos(d*x+c))+111/16*a^3*ln(1-cos(d*x+c))/d-7*a^3*ln(cos(d*x+c))/d+1/16*a^3*ln(1+cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)^9*(a+a*sec(d*x+c))^3,x,5,-1/16*a^7/d/(a-a*cos(d*x+c))^4-1/3*a^9/d/(a^2-a^2*cos(d*x+c))^3-39/32*a^9/d/(a^3-a^3*cos(d*x+c))^2-75/16*a^9/d/(a^6-a^6*cos(d*x+c))-1/32*a^9/d/(a^6+a^6*cos(d*x+c))+501/64*a^3*ln(1-cos(d*x+c))/d-8*a^3*ln(cos(d*x+c))/d+11/64*a^3*ln(1+cos(d*x+c))/d+3*a^3*sec(d*x+c)/d+1/2*a^3*sec(d*x+c)^2/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^8,x,29,-805/128*a^3*x-1/2*a^3*arctanh(sin(d*x+c))/d+603/128*a^3*cos(d*x+c)*sin(d*x+c)/d-293/192*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/48*a^3*cos(d*x+c)^5*sin(d*x+c)/d+1/8*a^3*cos(d*x+c)^7*sin(d*x+c)/d-1/3*a^3*sin(d*x+c)^3/d-2/5*a^3*sin(d*x+c)^5/d-3/7*a^3*sin(d*x+c)^7/d+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^6,x,18,-85/16*a^3*x+1/2*a^3*arctanh(sin(d*x+c))/d-a^3*sin(d*x+c)/d+43/16*a^3*cos(d*x+c)*sin(d*x+c)/d-5/24*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a^3*cos(d*x+c)^5*sin(d*x+c)/d-2/3*a^3*sin(d*x+c)^3/d-3/5*a^3*sin(d*x+c)^5/d+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^4,x,16,-33/8*a^3*x+3/2*a^3*arctanh(sin(d*x+c))/d-2*a^3*sin(d*x+c)/d+7/8*a^3*cos(d*x+c)*sin(d*x+c)/d+1/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d-a^3*sin(d*x+c)^3/d+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^3*sin(d*x+c)^2,x,11,-5/2*a^3*x+5/2*a^3*arctanh(sin(d*x+c))/d-3*a^3*sin(d*x+c)/d-1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+a*sec(d*x+c))^3,x,9,9/2*a^3*arctanh(sin(d*x+c))/d-4*a^3*sin(d*x+c)/d/(1-cos(d*x+c))+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+a*sec(d*x+c))^3,x,11,11/2*a^3*arctanh(sin(d*x+c))/d-2/3*a^3*sin(d*x+c)/d/(1-cos(d*x+c))^2-17/3*a^3*sin(d*x+c)/d/(1-cos(d*x+c))+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^6*(a+a*sec(d*x+c))^3,x,10,13/2*a^3*arctanh(sin(d*x+c))/d+152/15*a^3*tan(d*x+c)/d+13/2*a^3*sec(d*x+c)*tan(d*x+c)/d-1/5*a^6*sec(d*x+c)*tan(d*x+c)/d/(a-a*cos(d*x+c))^3-11/15*a^5*sec(d*x+c)*tan(d*x+c)/d/(a-a*cos(d*x+c))^2-76/15*a^6*sec(d*x+c)*tan(d*x+c)/d/(a^3-a^3*cos(d*x+c)),1],
[csc(d*x+c)^8*(a+a*sec(d*x+c))^3,x,17,15/2*a^3*arctanh(sin(d*x+c))/d-13*a^3*cot(d*x+c)/d-7*a^3*cot(d*x+c)^3/d-3*a^3*cot(d*x+c)^5/d-4/7*a^3*cot(d*x+c)^7/d-15/2*a^3*csc(d*x+c)/d-5/2*a^3*csc(d*x+c)^3/d-3/2*a^3*csc(d*x+c)^5/d-15/14*a^3*csc(d*x+c)^7/d+1/2*a^3*csc(d*x+c)^7*sec(d*x+c)^2/d+3*a^3*tan(d*x+c)/d,1],
[csc(d*x+c)^10*(a+a*sec(d*x+c))^3,x,17,17/2*a^3*arctanh(sin(d*x+c))/d-16*a^3*cot(d*x+c)/d-34/3*a^3*cot(d*x+c)^3/d-36/5*a^3*cot(d*x+c)^5/d-19/7*a^3*cot(d*x+c)^7/d-4/9*a^3*cot(d*x+c)^9/d-17/2*a^3*csc(d*x+c)/d-17/6*a^3*csc(d*x+c)^3/d-17/10*a^3*csc(d*x+c)^5/d-17/14*a^3*csc(d*x+c)^7/d-17/18*a^3*csc(d*x+c)^9/d+1/2*a^3*csc(d*x+c)^9*sec(d*x+c)^2/d+3*a^3*tan(d*x+c)/d,1],
[sin(d*x+c)^9/(a+a*sec(d*x+c)),x,7,1/3*cos(d*x+c)^3/a/d-3/5*cos(d*x+c)^5/a/d+3/7*cos(d*x+c)^7/a/d-1/9*cos(d*x+c)^9/a/d+1/8*sin(d*x+c)^8/a/d,1],
[sin(d*x+c)^7/(a+a*sec(d*x+c)),x,7,1/3*cos(d*x+c)^3/a/d-2/5*cos(d*x+c)^5/a/d+1/7*cos(d*x+c)^7/a/d+1/6*sin(d*x+c)^6/a/d,1],
[sin(d*x+c)^5/(a+a*sec(d*x+c)),x,7,1/3*cos(d*x+c)^3/a/d-1/5*cos(d*x+c)^5/a/d+1/4*sin(d*x+c)^4/a/d,1],
[sin(d*x+c)^3/(a+a*sec(d*x+c)),x,6,1/3*cos(d*x+c)^3/a/d+1/2*sin(d*x+c)^2/a/d,1],
[sin(d*x+c)/(a+a*sec(d*x+c)),x,5,-cos(d*x+c)/a/d+ln(1+cos(d*x+c))/a/d,1],
[csc(d*x+c)/(a+a*sec(d*x+c)),x,6,-1/2*arctanh(cos(d*x+c))/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d,1],
[csc(d*x+c)^3/(a+a*sec(d*x+c)),x,7,-1/8*arctanh(cos(d*x+c))/a/d-1/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)*csc(d*x+c)^3/a/d-1/4*csc(d*x+c)^4/a/d,1],
[csc(d*x+c)^5/(a+a*sec(d*x+c)),x,8,-1/16*arctanh(cos(d*x+c))/a/d-1/16*cot(d*x+c)*csc(d*x+c)/a/d-1/24*cot(d*x+c)*csc(d*x+c)^3/a/d+1/6*cot(d*x+c)*csc(d*x+c)^5/a/d-1/6*csc(d*x+c)^6/a/d,1],
[sin(d*x+c)^8/(a+a*sec(d*x+c)),x,9,-5/128*x/a-5/128*cos(d*x+c)*sin(d*x+c)/a/d+5/64*cos(d*x+c)^3*sin(d*x+c)/a/d+5/48*cos(d*x+c)^3*sin(d*x+c)^3/a/d+1/8*cos(d*x+c)^3*sin(d*x+c)^5/a/d+1/7*sin(d*x+c)^7/a/d,1],
[sin(d*x+c)^6/(a+a*sec(d*x+c)),x,8,-1/16*x/a-1/16*cos(d*x+c)*sin(d*x+c)/a/d+1/8*cos(d*x+c)^3*sin(d*x+c)/a/d+1/6*cos(d*x+c)^3*sin(d*x+c)^3/a/d+1/5*sin(d*x+c)^5/a/d,1],
[sin(d*x+c)^4/(a+a*sec(d*x+c)),x,7,-1/8*x/a-1/8*cos(d*x+c)*sin(d*x+c)/a/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a/d+1/3*sin(d*x+c)^3/a/d,1],
[sin(d*x+c)^2/(a+a*sec(d*x+c)),x,5,-1/2*x/a+sin(d*x+c)/a/d-1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[csc(d*x+c)^2/(a+a*sec(d*x+c)),x,6,1/3*cot(d*x+c)^3/a/d-1/3*csc(d*x+c)^3/a/d,1],
[csc(d*x+c)^4/(a+a*sec(d*x+c)),x,7,1/3*cot(d*x+c)^3/a/d+1/5*cot(d*x+c)^5/a/d-1/5*csc(d*x+c)^5/a/d,1],
[csc(d*x+c)^6/(a+a*sec(d*x+c)),x,7,1/3*cot(d*x+c)^3/a/d+2/5*cot(d*x+c)^5/a/d+1/7*cot(d*x+c)^7/a/d-1/7*csc(d*x+c)^7/a/d,1],
[csc(d*x+c)^8/(a+a*sec(d*x+c)),x,7,1/3*cot(d*x+c)^3/a/d+3/5*cot(d*x+c)^5/a/d+3/7*cot(d*x+c)^7/a/d+1/9*cot(d*x+c)^9/a/d-1/9*csc(d*x+c)^9/a/d,1],
[csc(d*x+c)^10/(a+a*sec(d*x+c)),x,7,1/3*cot(d*x+c)^3/a/d+4/5*cot(d*x+c)^5/a/d+6/7*cot(d*x+c)^7/a/d+4/9*cot(d*x+c)^9/a/d+1/11*cot(d*x+c)^11/a/d-1/11*csc(d*x+c)^11/a/d,1],
[sin(d*x+c)^11/(a+a*sec(d*x+c))^2,x,5,4/3*(a-a*cos(d*x+c))^6/a^8/d-4*(a-a*cos(d*x+c))^7/a^9/d+19/4*(a-a*cos(d*x+c))^8/a^10/d-25/9*(a-a*cos(d*x+c))^9/a^11/d+4/5*(a-a*cos(d*x+c))^10/a^12/d-1/11*(a-a*cos(d*x+c))^11/a^13/d,1],
[sin(d*x+c)^9/(a+a*sec(d*x+c))^2,x,5,4/5*(a-a*cos(d*x+c))^5/a^7/d-2*(a-a*cos(d*x+c))^6/a^8/d+13/7*(a-a*cos(d*x+c))^7/a^9/d-3/4*(a-a*cos(d*x+c))^8/a^10/d+1/9*(a-a*cos(d*x+c))^9/a^11/d,1],
[sin(d*x+c)^7/(a+a*sec(d*x+c))^2,x,5,-1/3*cos(d*x+c)^3/a^2/d+1/2*cos(d*x+c)^4/a^2/d-1/3*cos(d*x+c)^6/a^2/d+1/7*cos(d*x+c)^7/a^2/d,1],
[sin(d*x+c)^5/(a+a*sec(d*x+c))^2,x,5,-1/3*cos(d*x+c)^3/a^2/d+1/2*cos(d*x+c)^4/a^2/d-1/5*cos(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^3/(a+a*sec(d*x+c))^2,x,5,2*cos(d*x+c)/a^2/d-cos(d*x+c)^2/a^2/d+1/3*cos(d*x+c)^3/a^2/d-2*ln(1+cos(d*x+c))/a^2/d,1],
[sin(d*x+c)/(a+a*sec(d*x+c))^2,x,5,-cos(d*x+c)/a^2/d+1/d/(a^2+a^2*cos(d*x+c))+2*ln(1+cos(d*x+c))/a^2/d,1],
[csc(d*x+c)/(a+a*sec(d*x+c))^2,x,6,-1/4*arctanh(cos(d*x+c))/a^2/d+1/4/d/(a+a*cos(d*x+c))^2-3/4/d/(a^2+a^2*cos(d*x+c)),1],
[csc(d*x+c)^3/(a+a*sec(d*x+c))^2,x,4,-1/6*(a+2*a*cos(d*x+c))/d/(1+cos(d*x+c))^3/(a^3-a^3*cos(d*x+c)),1],
[csc(d*x+c)^5/(a+a*sec(d*x+c))^2,x,6,1/64*arctanh(cos(d*x+c))/a^2/d-1/64/d/(a-a*cos(d*x+c))^2+1/32*a^2/d/(a+a*cos(d*x+c))^4-1/48*a/d/(a+a*cos(d*x+c))^3-1/32/d/(a+a*cos(d*x+c))^2-1/64/d/(a^2-a^2*cos(d*x+c))-1/32/d/(a^2+a^2*cos(d*x+c)),1],
[sin(d*x+c)^8/(a+a*sec(d*x+c))^2,x,16,11/128*x/a^2+11/128*cos(d*x+c)*sin(d*x+c)/a^2/d-7/64*cos(d*x+c)^3*sin(d*x+c)/a^2/d-1/16*cos(d*x+c)^5*sin(d*x+c)/a^2/d-1/6*cos(d*x+c)^3*sin(d*x+c)^3/a^2/d-1/8*cos(d*x+c)^5*sin(d*x+c)^3/a^2/d-2/5*sin(d*x+c)^5/a^2/d+2/7*sin(d*x+c)^7/a^2/d,1],
[sin(d*x+c)^6/(a+a*sec(d*x+c))^2,x,7,3/16*x/a^2-3/16*cos(d*x+c)*sin(d*x+c)/a^2/d-1/8*cos(d*x+c)*sin(d*x+c)^3/a^2/d-1/6*(a-a*cos(d*x+c))^3*sin(d*x+c)^3/a^5/d-1/10*sin(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^4/(a+a*sec(d*x+c))^2,x,11,7/8*x/a^2-2*sin(d*x+c)/a^2/d+7/8*cos(d*x+c)*sin(d*x+c)/a^2/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a^2/d+2/3*sin(d*x+c)^3/a^2/d,1],
[sin(d*x+c)^2/(a+a*sec(d*x+c))^2,x,9,-5/2*x/a^2+2*sin(d*x+c)/a^2/d-1/2*cos(d*x+c)*sin(d*x+c)/a^2/d+2*sin(d*x+c)/a^2/d/(1+cos(d*x+c)),1],
[csc(d*x+c)^2/(a+a*sec(d*x+c))^2,x,11,-1/3*cot(d*x+c)^3/a^2/d-2/5*cot(d*x+c)^5/a^2/d-2/3*csc(d*x+c)^3/a^2/d+2/5*csc(d*x+c)^5/a^2/d,1],
[csc(d*x+c)^4/(a+a*sec(d*x+c))^2,x,13,-1/3*cot(d*x+c)^3/a^2/d-3/5*cot(d*x+c)^5/a^2/d-2/7*cot(d*x+c)^7/a^2/d-2/5*csc(d*x+c)^5/a^2/d+2/7*csc(d*x+c)^7/a^2/d,1],
[csc(d*x+c)^6/(a+a*sec(d*x+c))^2,x,13,-1/3*cot(d*x+c)^3/a^2/d-4/5*cot(d*x+c)^5/a^2/d-5/7*cot(d*x+c)^7/a^2/d-2/9*cot(d*x+c)^9/a^2/d-2/7*csc(d*x+c)^7/a^2/d+2/9*csc(d*x+c)^9/a^2/d,1],
[csc(d*x+c)^8/(a+a*sec(d*x+c))^2,x,13,-1/3*cot(d*x+c)^3/a^2/d-cot(d*x+c)^5/a^2/d-9/7*cot(d*x+c)^7/a^2/d-7/9*cot(d*x+c)^9/a^2/d-2/11*cot(d*x+c)^11/a^2/d-2/9*csc(d*x+c)^9/a^2/d+2/11*csc(d*x+c)^11/a^2/d,1],
[sin(d*x+c)^11/(a+a*sec(d*x+c))^3,x,5,2/3*(a-a*cos(d*x+c))^6/a^9/d-16/7*(a-a*cos(d*x+c))^7/a^10/d+25/8*(a-a*cos(d*x+c))^8/a^11/d-19/9*(a-a*cos(d*x+c))^9/a^12/d+7/10*(a-a*cos(d*x+c))^10/a^13/d-1/11*(a-a*cos(d*x+c))^11/a^14/d,1],
[sin(d*x+c)^9/(a+a*sec(d*x+c))^3,x,5,-1/4*cos(d*x+c)^4/a^3/d+3/5*cos(d*x+c)^5/a^3/d-1/3*cos(d*x+c)^6/a^3/d-2/7*cos(d*x+c)^7/a^3/d+3/8*cos(d*x+c)^8/a^3/d-1/9*cos(d*x+c)^9/a^3/d,1],
[sin(d*x+c)^7/(a+a*sec(d*x+c))^3,x,5,-1/4*cos(d*x+c)^4/a^3/d+3/5*cos(d*x+c)^5/a^3/d-1/2*cos(d*x+c)^6/a^3/d+1/7*cos(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^5/(a+a*sec(d*x+c))^3,x,5,-4*cos(d*x+c)/a^3/d+2*cos(d*x+c)^2/a^3/d-4/3*cos(d*x+c)^3/a^3/d+3/4*cos(d*x+c)^4/a^3/d-1/5*cos(d*x+c)^5/a^3/d+4*ln(1+cos(d*x+c))/a^3/d,1],
[sin(d*x+c)^3/(a+a*sec(d*x+c))^3,x,5,5*cos(d*x+c)/a^3/d-3/2*cos(d*x+c)^2/a^3/d+1/3*cos(d*x+c)^3/a^3/d-2/a^3/d/(1+cos(d*x+c))-7*ln(1+cos(d*x+c))/a^3/d,1],
[sin(d*x+c)/(a+a*sec(d*x+c))^3,x,5,-cos(d*x+c)/a^3/d-1/2/a/d/(a+a*cos(d*x+c))^2+3/d/(a^3+a^3*cos(d*x+c))+3*ln(1+cos(d*x+c))/a^3/d,1],
[csc(d*x+c)/(a+a*sec(d*x+c))^3,x,6,-1/8*arctanh(cos(d*x+c))/a^3/d-1/6/d/(a+a*cos(d*x+c))^3+5/8*a/d/(a^2+a^2*cos(d*x+c))^2-7/8/d/(a^3+a^3*cos(d*x+c)),1],
[csc(d*x+c)^3/(a+a*sec(d*x+c))^3,x,5,1/32*arctanh(cos(d*x+c))/a^3/d-1/16*a/d/(a+a*cos(d*x+c))^4+1/6/d/(a+a*cos(d*x+c))^3-3/32/a/d/(a+a*cos(d*x+c))^2-1/32/d/(a^3-a^3*cos(d*x+c))-1/16/d/(a^3+a^3*cos(d*x+c)),1],
[csc(d*x+c)^5/(a+a*sec(d*x+c))^3,x,6,3/128*arctanh(cos(d*x+c))/a^3/d-1/40*a^2/d/(a+a*cos(d*x+c))^5+3/64*a^5/d/(a^2+a^2*cos(d*x+c))^4-3/128/d/(a^3+a^3*cos(d*x+c))-1/128*a^5/d/(a^4-a^4*cos(d*x+c))^2-1/64*a^5/d/(a^4+a^4*cos(d*x+c))^2,1],
[sin(d*x+c)^8/(a+a*sec(d*x+c))^3,x,19,-29/128*x/a^3-29/128*cos(d*x+c)*sin(d*x+c)/a^3/d-29/192*cos(d*x+c)^3*sin(d*x+c)/a^3/d+23/48*cos(d*x+c)^5*sin(d*x+c)/a^3/d+1/8*cos(d*x+c)^7*sin(d*x+c)/a^3/d+4/3*sin(d*x+c)^3/a^3/d-7/5*sin(d*x+c)^5/a^3/d+3/7*sin(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^6/(a+a*sec(d*x+c))^3,x,15,-23/16*x/a^3+4*sin(d*x+c)/a^3/d-23/16*cos(d*x+c)*sin(d*x+c)/a^3/d-23/24*cos(d*x+c)^3*sin(d*x+c)/a^3/d-1/6*cos(d*x+c)^5*sin(d*x+c)/a^3/d-7/3*sin(d*x+c)^3/a^3/d+3/5*sin(d*x+c)^5/a^3/d,1],
[sin(d*x+c)^4/(a+a*sec(d*x+c))^3,x,13,51/8*x/a^3-7*sin(d*x+c)/a^3/d+19/8*cos(d*x+c)*sin(d*x+c)/a^3/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a^3/d-4*sin(d*x+c)/a^3/d/(1+cos(d*x+c))+sin(d*x+c)^3/a^3/d,1],
[sin(d*x+c)^2/(a+a*sec(d*x+c))^3,x,10,-11/2*x/a^3+3*sin(d*x+c)/a^3/d-1/2*cos(d*x+c)*sin(d*x+c)/a^3/d-2/3*sin(d*x+c)/a^3/d/(1+cos(d*x+c))^2+19/3*sin(d*x+c)/a^3/d/(1+cos(d*x+c)),1],
[csc(d*x+c)^2/(a+a*sec(d*x+c))^3,x,15,3/5*cot(d*x+c)^5/a^3/d+4/7*cot(d*x+c)^7/a^3/d-csc(d*x+c)^3/a^3/d+7/5*csc(d*x+c)^5/a^3/d-4/7*csc(d*x+c)^7/a^3/d,1],
[csc(d*x+c)^4/(a+a*sec(d*x+c))^3,x,16,3/5*cot(d*x+c)^5/a^3/d+cot(d*x+c)^7/a^3/d+4/9*cot(d*x+c)^9/a^3/d-3/5*csc(d*x+c)^5/a^3/d+csc(d*x+c)^7/a^3/d-4/9*csc(d*x+c)^9/a^3/d,1],
[csc(d*x+c)^6/(a+a*sec(d*x+c))^3,x,16,3/5*cot(d*x+c)^5/a^3/d+10/7*cot(d*x+c)^7/a^3/d+11/9*cot(d*x+c)^9/a^3/d+4/11*cot(d*x+c)^11/a^3/d-3/7*csc(d*x+c)^7/a^3/d+7/9*csc(d*x+c)^9/a^3/d-4/11*csc(d*x+c)^11/a^3/d,1],
[csc(d*x+c)^8/(a+a*sec(d*x+c))^3,x,16,3/5*cot(d*x+c)^5/a^3/d+13/7*cot(d*x+c)^7/a^3/d+7/3*cot(d*x+c)^9/a^3/d+15/11*cot(d*x+c)^11/a^3/d+4/13*cot(d*x+c)^13/a^3/d-1/3*csc(d*x+c)^9/a^3/d+7/11*csc(d*x+c)^11/a^3/d-4/13*csc(d*x+c)^13/a^3/d,1],
[(a+a*sec(d*x+c))*(e*sin(d*x+c))^(5/2),x,11,-a*e^(5/2)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+a*e^(5/2)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d+6/5*a*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))-2/3*a*e*(e*sin(d*x+c))^(3/2)/d-2/5*a*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/d,1],
[(a+a*sec(d*x+c))*(e*sin(d*x+c))^(3/2),x,11,a*e^(3/2)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+a*e^(3/2)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d+2/3*a*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-2*a*e*sqrt(e*sin(d*x+c))/d-2/3*a*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/d,1],
[(a+a*sec(d*x+c))*sqrt(e*sin(d*x+c)),x,9,-a*sqrt(e)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+a*sqrt(e)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d+2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))/sqrt(e*sin(d*x+c)),x,9,a*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/sqrt(e)+a*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/sqrt(e)+2*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c)),1],
[(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x,11,-a*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(3/2)+a*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(3/2)-2*a/d/e/sqrt(e*sin(d*x+c))-2*a*cos(d*x+c)/d/e/sqrt(e*sin(d*x+c))-2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^2/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x,11,a*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(5/2)+a*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(5/2)-2/3*a/d/e/(e*sin(d*x+c))^(3/2)-2/3*a*cos(d*x+c)/d/e/(e*sin(d*x+c))^(3/2)+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^2/sqrt(e*sin(d*x+c)),1],
[(a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(5/2),x,15,-2*a^2*e^(5/2)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+2*a^2*e^(5/2)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d-9/5*a^2*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))-4/3*a^2*e*(e*sin(d*x+c))^(3/2)/d-2/5*a^2*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/d+a^2*e*sec(d*x+c)*(e*sin(d*x+c))^(3/2)/d,1],
[(a+a*sec(d*x+c))^2*(e*sin(d*x+c))^(3/2),x,15,2*a^2*e^(3/2)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+2*a^2*e^(3/2)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d-1/3*a^2*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-4*a^2*e*sqrt(e*sin(d*x+c))/d-2/3*a^2*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/d+a^2*e*sec(d*x+c)*sqrt(e*sin(d*x+c))/d,1],
[(a+a*sec(d*x+c))^2*sqrt(e*sin(d*x+c)),x,13,-2*a^2*sqrt(e)*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d+2*a^2*sqrt(e)*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d+a^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))+a^2*sec(d*x+c)*(e*sin(d*x+c))^(3/2)/d/e,1],
[(a+a*sec(d*x+c))^2/sqrt(e*sin(d*x+c)),x,13,2*a^2*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/sqrt(e)+2*a^2*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/sqrt(e)+3*a^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))+a^2*sec(d*x+c)*sqrt(e*sin(d*x+c))/d/e,1],
[(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x,16,-2*a^2*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(3/2)+2*a^2*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(3/2)-4*a^2/d/e/sqrt(e*sin(d*x+c))-2*a^2*cos(d*x+c)/d/e/sqrt(e*sin(d*x+c))-2*a^2*sec(d*x+c)/d/e/sqrt(e*sin(d*x+c))-5*a^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^2/sqrt(sin(d*x+c))+3*a^2*sec(d*x+c)*(e*sin(d*x+c))^(3/2)/d/e^3,1],
[(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x,16,2*a^2*arctan(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(5/2)+2*a^2*arctanh(sqrt(e*sin(d*x+c))/sqrt(e))/d/e^(5/2)-4/3*a^2/d/e/(e*sin(d*x+c))^(3/2)-2/3*a^2*cos(d*x+c)/d/e/(e*sin(d*x+c))^(3/2)-2/3*a^2*sec(d*x+c)/d/e/(e*sin(d*x+c))^(3/2)+7/3*a^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^2/sqrt(e*sin(d*x+c))+5/3*a^2*sec(d*x+c)*sqrt(e*sin(d*x+c))/d/e^3,1],
[(e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x,8,-4/21*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d/sqrt(e*sin(d*x+c))-2/21*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/a/d+2/7*e^3*cos(d*x+c)^3*sqrt(e*sin(d*x+c))/a/d+2/5*e*(e*sin(d*x+c))^(5/2)/a/d,1],
[(e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x,7,-4/5*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a/d/sqrt(sin(d*x+c))+2/3*e*(e*sin(d*x+c))^(3/2)/a/d-2/5*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/a/d,1],
[(e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x,7,-4/3*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d/sqrt(e*sin(d*x+c))+2*e*sqrt(e*sin(d*x+c))/a/d-2/3*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/a/d,1],
[sqrt(e*sin(d*x+c))/(a+a*sec(d*x+c)),x,7,-2*e/a/d/sqrt(e*sin(d*x+c))+2*e*cos(d*x+c)/a/d/sqrt(e*sin(d*x+c))+4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a/d/sqrt(sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))/sqrt(e*sin(d*x+c)),x,7,-2/3*e/a/d/(e*sin(d*x+c))^(3/2)+2/3*e*cos(d*x+c)/a/d/(e*sin(d*x+c))^(3/2)+4/3*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d/sqrt(e*sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x,8,-2/5*e/a/d/(e*sin(d*x+c))^(5/2)+2/5*e*cos(d*x+c)/a/d/(e*sin(d*x+c))^(5/2)-4/5*cos(d*x+c)/a/d/e/sqrt(e*sin(d*x+c))-4/5*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x,8,-2/7*e/a/d/(e*sin(d*x+c))^(7/2)+2/7*e*cos(d*x+c)/a/d/(e*sin(d*x+c))^(7/2)-4/21*cos(d*x+c)/a/d/e/(e*sin(d*x+c))^(3/2)+4/21*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d/e^2/sqrt(e*sin(d*x+c)),1],
[(e*sin(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x,14,52/21*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c))-4*e^3*sqrt(e*sin(d*x+c))/a^2/d+26/21*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/a^2/d+2/7*e^3*cos(d*x+c)^3*sqrt(e*sin(d*x+c))/a^2/d+4/5*e*(e*sin(d*x+c))^(5/2)/a^2/d,1],
[(e*sin(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x,14,4*e^3/a^2/d/sqrt(e*sin(d*x+c))-2*e^3*cos(d*x+c)/a^2/d/sqrt(e*sin(d*x+c))-2*e^3*cos(d*x+c)^3/a^2/d/sqrt(e*sin(d*x+c))-44/5*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/sqrt(sin(d*x+c))+4/3*e*(e*sin(d*x+c))^(3/2)/a^2/d-12/5*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/a^2/d,1],
[(e*sin(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x,14,4/3*e^3/a^2/d/(e*sin(d*x+c))^(3/2)-2/3*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(3/2)-2/3*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(3/2)-4*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c))+4*e*sqrt(e*sin(d*x+c))/a^2/d-4/3*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/a^2/d,1],
[sqrt(e*sin(d*x+c))/(a+a*sec(d*x+c))^2,x,15,4/5*e^3/a^2/d/(e*sin(d*x+c))^(5/2)-2/5*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(5/2)-2/5*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(5/2)-4*e/a^2/d/sqrt(e*sin(d*x+c))+16/5*e*cos(d*x+c)/a^2/d/sqrt(e*sin(d*x+c))+28/5*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/sqrt(sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))^2/sqrt(e*sin(d*x+c)),x,15,4/7*e^3/a^2/d/(e*sin(d*x+c))^(7/2)-2/7*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(7/2)-2/7*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(7/2)-4/3*e/a^2/d/(e*sin(d*x+c))^(3/2)+16/21*e*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(3/2)+20/21*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x,17,4/9*e^3/a^2/d/(e*sin(d*x+c))^(9/2)-2/9*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(9/2)-2/9*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(9/2)-4/5*e/a^2/d/(e*sin(d*x+c))^(5/2)+16/45*e*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(5/2)-4/15*cos(d*x+c)/a^2/d/e/sqrt(e*sin(d*x+c))-4/15*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+a*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x,17,4/11*e^3/a^2/d/(e*sin(d*x+c))^(11/2)-2/11*e^3*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(11/2)-2/11*e^3*cos(d*x+c)^3/a^2/d/(e*sin(d*x+c))^(11/2)-4/7*e/a^2/d/(e*sin(d*x+c))^(7/2)+16/77*e*cos(d*x+c)/a^2/d/(e*sin(d*x+c))^(7/2)-4/231*cos(d*x+c)/a^2/d/e/(e*sin(d*x+c))^(3/2)+4/231*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/e^2/sqrt(e*sin(d*x+c)),1],
[(a+a*sec(d*x+c))^3*(e*sin(d*x+c))^m,x,9,a^3*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)/sqrt(cos(d*x+c)^2)+3*a^3*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+a^3*hypergeom([2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+3*a^3*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sec(d*x+c)*(e*sin(d*x+c))^(1+m)/d/e/(1+m),1],
[(a+a*sec(d*x+c))^2*(e*sin(d*x+c))^m,x,7,a^2*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)/sqrt(cos(d*x+c)^2)+2*a^2*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+a^2*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sec(d*x+c)*(e*sin(d*x+c))^(1+m)/d/e/(1+m),1],
[(a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x,5,a*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)/sqrt(cos(d*x+c)^2)+a*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m),1],
[(e*sin(d*x+c))^m/(a+a*sec(d*x+c)),x,5,-e*(e*sin(d*x+c))^(-1+m)/a/d/(1-m)+e*cos(d*x+c)*hypergeom([-1/2, -1/2+1/2*m],[1/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(-1+m)/a/d/(1-m)/sqrt(cos(d*x+c)^2),1],
[(e*sin(d*x+c))^m/(a+a*sec(d*x+c))^2,x,9,2*e^3*(e*sin(d*x+c))^(-3+m)/a^2/d/(3-m)-e^3*cos(d*x+c)*hypergeom([-3/2, -3/2+1/2*m],[-1/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(-3+m)/a^2/d/(3-m)/sqrt(cos(d*x+c)^2)-e^3*cos(d*x+c)*hypergeom([-1/2, -3/2+1/2*m],[-1/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(-3+m)/a^2/d/(3-m)/sqrt(cos(d*x+c)^2)-2*e*(e*sin(d*x+c))^(-1+m)/a^2/d/(1-m),1],
[(e*sin(d*x+c))^m/(a+a*sec(d*x+c))^3,x,12,-4*e^5*(e*sin(d*x+c))^(-5+m)/a^3/d/(5-m)+e^5*cos(d*x+c)*hypergeom([-5/2, -5/2+1/2*m],[-3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(-5+m)/a^3/d/(5-m)/sqrt(cos(d*x+c)^2)+3*e^5*cos(d*x+c)*hypergeom([-3/2, -5/2+1/2*m],[-3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(-5+m)/a^3/d/(5-m)/sqrt(cos(d*x+c)^2)+7*e^3*(e*sin(d*x+c))^(-3+m)/a^3/d/(3-m)-3*e*(e*sin(d*x+c))^(-1+m)/a^3/d/(1-m),1],
[(a+a*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x,4,2*a*e*AppellF1(-1/2,1/2-1/2*m,-1-1/2*m,1/2,cos(d*x+c),-cos(d*x+c))*(1-cos(d*x+c))^(1/2-1/2*m)*sqrt(a+a*sec(d*x+c))*(e*sin(d*x+c))^(-1+m)/d/((1+cos(d*x+c))^(1/2*m)),1],
[sqrt(a+a*sec(d*x+c))*(e*sin(d*x+c))^m,x,4,-2*e*AppellF1(1/2,1/2-1/2*m,-1/2*m,3/2,cos(d*x+c),-cos(d*x+c))*(1-cos(d*x+c))^(1/2-1/2*m)*cos(d*x+c)*sqrt(a+a*sec(d*x+c))*(e*sin(d*x+c))^(-1+m)/d/((1+cos(d*x+c))^(1/2*m)),1],
[(e*sin(d*x+c))^m/sqrt(a+a*sec(d*x+c)),x,4,-2/3*e*AppellF1(3/2,1/2-1/2*m,1-1/2*m,5/2,cos(d*x+c),-cos(d*x+c))*(1-cos(d*x+c))^(1/2-1/2*m)*cos(d*x+c)*(1+cos(d*x+c))^(1-1/2*m)*(e*sin(d*x+c))^(-1+m)/d/sqrt(a+a*sec(d*x+c)),1],
[(e*sin(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x,4,-2/5*e*AppellF1(5/2,1/2-1/2*m,2-1/2*m,7/2,cos(d*x+c),-cos(d*x+c))*(1-cos(d*x+c))^(1/2-1/2*m)*cos(d*x+c)^2*(1+cos(d*x+c))^(1-1/2*m)*(e*sin(d*x+c))^(-1+m)/a/d/sqrt(a+a*sec(d*x+c)),1],
[(a+a*sec(d*x+c))^n*(e*sin(d*x+c))^m,x,4,-2^(1/2+1/2*m)*e*AppellF1(1/2+1/2*m+n,n,1/2-1/2*m,3/2+1/2*m+n,1+cos(d*x+c),1/2+1/2*cos(d*x+c))*(1-cos(d*x+c))^(1/2-1/2*m)*(-cos(d*x+c))^n*(1+cos(d*x+c))*(a+a*sec(d*x+c))^n*(e*sin(d*x+c))^(-1+m)/d/(1+m+2*n),1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^7,x,5,-1/42*(n^2-25*n+108)*cos(d*x+c)^6*(a+a*sec(d*x+c))^(4+n)/a^4/d/(1-n)+1/7*(8-n)*cos(d*x+c)^7*(a+a*sec(d*x+c))^(4+n)/a^4/d/(1-n)-1/42*(3-n)*(8-n)*(16-n)*hypergeom([6, 4+n],[5+n],1+sec(d*x+c))*(a+a*sec(d*x+c))^(4+n)/a^4/d/(1-n)/(4+n)-cos(d*x+c)^7*(1-sec(d*x+c))^2*(a+a*sec(d*x+c))^(4+n)/a^4/d/(1-n),1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^5,x,4,1/20*(12-n)*cos(d*x+c)^4*(a+a*sec(d*x+c))^(3+n)/a^3/d-1/5*cos(d*x+c)^5*(a+a*sec(d*x+c))^(3+n)/a^3/d+1/20*(n^2-13*n+32)*hypergeom([4, 3+n],[4+n],1+sec(d*x+c))*(a+a*sec(d*x+c))^(3+n)/a^3/d/(3+n),1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^3,x,3,1/3*cos(d*x+c)^3*(a+a*sec(d*x+c))^(2+n)/a^2/d-1/3*(4-n)*hypergeom([3, 2+n],[3+n],1+sec(d*x+c))*(a+a*sec(d*x+c))^(2+n)/a^2/d/(2+n),1],
[(a+a*sec(d*x+c))^n*sin(d*x+c),x,2,hypergeom([2, 1+n],[2+n],1+sec(d*x+c))*(a+a*sec(d*x+c))^(1+n)/a/d/(1+n),1],
[csc(d*x+c)*(a+a*sec(d*x+c))^n,x,2,-1/2*hypergeom([1, n],[1+n],1/2+1/2*sec(d*x+c))*(a+a*sec(d*x+c))^n/d/n,1],
[csc(d*x+c)^3*(a+a*sec(d*x+c))^n,x,4,-1/4*a*(2-n)*(a+a*sec(d*x+c))^(-1+n)/d/(1-n)+1/2*a*(a+a*sec(d*x+c))^(-1+n)/d/(1-sec(d*x+c))-1/8*(2+n)*hypergeom([1, n],[1+n],1/2+1/2*sec(d*x+c))*(a+a*sec(d*x+c))^n/d/n,1],
[csc(d*x+c)^5*(a+a*sec(d*x+c))^n,x,6,-1/16*a^2*(-n^2-5*n+12)*(a+a*sec(d*x+c))^(-2+n)/d/(2-n)-1/8*a^2*n*(7+n)*(a+a*sec(d*x+c))^(-2+n)/d/(1-n)/(1-sec(d*x+c))+1/4*a^2*(3+n)*sec(d*x+c)^2*(a+a*sec(d*x+c))^(-2+n)/d/(1-n)/(1-sec(d*x+c))^2-a^2*sec(d*x+c)^3*(a+a*sec(d*x+c))^(-2+n)/d/(1-n)/(1-sec(d*x+c))^2+1/32*a*(n^2+9*n+12)*hypergeom([1, -1+n],[n],1/2+1/2*sec(d*x+c))*(a+a*sec(d*x+c))^(-1+n)/d/(1-n),1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^4,x,10,1/3*2^(1/2+n)*AppellF1(3/2,n,1/2-n,5/2,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(1/2-n)*(n-n*cos(d*x+c))^2*csc(d*x+c)*(a+a*sec(d*x+c))^n/d/n-cos(d*x+c)*(a+a*sec(d*x+c))^n*sin(d*x+c)/d+2^(1/2+n)*AppellF1(1/2,-4+n,1/2-n,3/2,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(-1/2-n)*(a+a*sec(d*x+c))^n*sin(d*x+c)/d,1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^2,x,5,1/3*2^(3/2+n)*AppellF1(3/2,n,-1/2-n,5/2,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*(1-cos(d*x+c))^2*cos(d*x+c)^n*(1+cos(d*x+c))^(1/2-n)*csc(d*x+c)*(a+a*sec(d*x+c))^n/d,1],
[csc(d*x+c)^2*(a+a*sec(d*x+c))^n,x,4,-cot(d*x+c)*(a+a*sec(d*x+c))^n/d+2^(-1/2+n)*n*hypergeom([1/2, 3/2-n],[3/2],1/2-1/2*sec(d*x+c))*(1+sec(d*x+c))^(-1/2-n)*(a+a*sec(d*x+c))^n*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+a*sec(d*x+c))^n,x,7,(n^2-n+2)*cos(d*x+c)*(a+a*sec(d*x+c))^n*sin(d*x+c)/d/(3-2*n)/(-4*n^2+1)/(1-cos(d*x+c))^2-a^4*cos(d*x+c)*(a+a*sec(d*x+c))^n*sin(d*x+c)/d/(3-2*n)/(a-a*cos(d*x+c))^2/(a+a*cos(d*x+c))^2-a^3*(4-n)*cos(d*x+c)*(a+a*sec(d*x+c))^n*sin(d*x+c)/d/(4*n^2-8*n+3)/(a-a*cos(d*x+c))^2/(a+a*cos(d*x+c))+n*(-n^2-3*n+7)*cos(d*x+c)*((1+cos(d*x+c))/(1-cos(d*x+c)))^(-1/2-n)*hypergeom([-1/2-n, 1-n],[2-n],-2*cos(d*x+c)/(1-cos(d*x+c)))*(a+a*sec(d*x+c))^n*sin(d*x+c)/d/(1-2*n)/(3-2*n)/(1-n)/(1+2*n)/(1-cos(d*x+c))^2,1],
[(a+a*sec(d*x+c))^n*sin(d*x+c)^(3/2),x,4,1/5*2^(9/4+n)*AppellF1(5/4,n,-1/4-n,9/4,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*(1-cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(-1/4-n)*(a+a*sec(d*x+c))^n*sqrt(sin(d*x+c))/d,1],
[(a+a*sec(d*x+c))^n*sqrt(sin(d*x+c)),x,4,1/3*2^(7/4+n)*AppellF1(3/4,n,1/4-n,7/4,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*(1-cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(1/4-n)*(a+a*sec(d*x+c))^n/d/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))^n/sqrt(sin(d*x+c)),x,4,2^(5/4+n)*AppellF1(1/4,n,3/4-n,5/4,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*(1-cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(3/4-n)*(a+a*sec(d*x+c))^n/d/sin(d*x+c)^(3/2),1],
[(a+a*sec(d*x+c))^n/sin(d*x+c)^(3/2),x,4,-2^(3/4+n)*AppellF1(-1/4,n,5/4-n,3/4,1-cos(d*x+c),1/2-1/2*cos(d*x+c))*(1-cos(d*x+c))*cos(d*x+c)^n*(1+cos(d*x+c))^(5/4-n)*(a+a*sec(d*x+c))^n/d/sin(d*x+c)^(5/2),1],
[(a+b*sec(d*x+c))*sin(d*x+c)^7,x,5,-a*cos(d*x+c)/d+3/2*b*cos(d*x+c)^2/d+a*cos(d*x+c)^3/d-3/4*b*cos(d*x+c)^4/d-3/5*a*cos(d*x+c)^5/d+1/6*b*cos(d*x+c)^6/d+1/7*a*cos(d*x+c)^7/d-b*ln(cos(d*x+c))/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c)^5,x,5,-a*cos(d*x+c)/d+b*cos(d*x+c)^2/d+2/3*a*cos(d*x+c)^3/d-1/4*b*cos(d*x+c)^4/d-1/5*a*cos(d*x+c)^5/d-b*ln(cos(d*x+c))/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c)^3,x,5,-a*cos(d*x+c)/d+1/2*b*cos(d*x+c)^2/d+1/3*a*cos(d*x+c)^3/d-b*ln(cos(d*x+c))/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c),x,4,-a*cos(d*x+c)/d-b*ln(cos(d*x+c))/d,1],
[csc(d*x+c)*(a+b*sec(d*x+c)),x,5,-a*arctanh(cos(d*x+c))/d+b*ln(tan(d*x+c))/d,1],
[csc(d*x+c)^3*(a+b*sec(d*x+c)),x,7,-1/2*a*arctanh(cos(d*x+c))/d-1/2*b*cot(d*x+c)^2/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+b*ln(tan(d*x+c))/d,1],
[csc(d*x+c)^5*(a+b*sec(d*x+c)),x,9,-3/8*a*arctanh(cos(d*x+c))/d-b*cot(d*x+c)^2/d-1/4*b*cot(d*x+c)^4/d-3/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d+b*ln(tan(d*x+c))/d,1],
[csc(d*x+c)^7*(a+b*sec(d*x+c)),x,10,-5/16*a*arctanh(cos(d*x+c))/d-3/2*b*cot(d*x+c)^2/d-3/4*b*cot(d*x+c)^4/d-1/6*b*cot(d*x+c)^6/d-5/16*a*cot(d*x+c)*csc(d*x+c)/d-5/24*a*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a*cot(d*x+c)*csc(d*x+c)^5/d+b*ln(tan(d*x+c))/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c)^6,x,10,5/16*a*x+b*arctanh(sin(d*x+c))/d-b*sin(d*x+c)/d-5/16*a*cos(d*x+c)*sin(d*x+c)/d-1/3*b*sin(d*x+c)^3/d-5/24*a*cos(d*x+c)*sin(d*x+c)^3/d-1/5*b*sin(d*x+c)^5/d-1/6*a*cos(d*x+c)*sin(d*x+c)^5/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c)^4,x,9,3/8*a*x+b*arctanh(sin(d*x+c))/d-b*sin(d*x+c)/d-3/8*a*cos(d*x+c)*sin(d*x+c)/d-1/3*b*sin(d*x+c)^3/d-1/4*a*cos(d*x+c)*sin(d*x+c)^3/d,1],
[(a+b*sec(d*x+c))*sin(d*x+c)^2,x,7,1/2*a*x+b*arctanh(sin(d*x+c))/d-b*sin(d*x+c)/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*sec(d*x+c)),x,7,b*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-b*csc(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*sec(d*x+c)),x,8,b*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-b*csc(d*x+c)/d-1/3*b*csc(d*x+c)^3/d,1],
[csc(d*x+c)^6*(a+b*sec(d*x+c)),x,8,b*arctanh(sin(d*x+c))/d-a*cot(d*x+c)/d-2/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d-b*csc(d*x+c)/d-1/3*b*csc(d*x+c)^3/d-1/5*b*csc(d*x+c)^5/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c)^5,x,5,-(a^2-2*b^2)*cos(d*x+c)/d+2*a*b*cos(d*x+c)^2/d+1/3*(2*a^2-b^2)*cos(d*x+c)^3/d-1/2*a*b*cos(d*x+c)^4/d-1/5*a^2*cos(d*x+c)^5/d-2*a*b*ln(cos(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c)^3,x,5,-(a^2-b^2)*cos(d*x+c)/d+a*b*cos(d*x+c)^2/d+1/3*a^2*cos(d*x+c)^3/d-2*a*b*ln(cos(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c),x,5,-a^2*cos(d*x+c)/d-2*a*b*ln(cos(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[csc(d*x+c)*(a+b*sec(d*x+c))^2,x,5,1/2*(a+b)^2*ln(1-cos(d*x+c))/d-2*a*b*ln(cos(d*x+c))/d-1/2*(a-b)^2*ln(1+cos(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[csc(d*x+c)^3*(a+b*sec(d*x+c))^2,x,6,-1/2*(2*a*b+(a^2+b^2)*cos(d*x+c))*csc(d*x+c)^2/d+1/4*(a+b)*(a+3*b)*ln(1-cos(d*x+c))/d-2*a*b*ln(cos(d*x+c))/d-1/4*(a-3*b)*(a-b)*ln(1+cos(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c)^6,x,12,5/16*(a^2-6*b^2)*x+2*a*b*arctanh(sin(d*x+c))/d-2*a*b*sin(d*x+c)/d-1/16*(11*a^2-18*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/24*(13*a^2-6*b^2)*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a^2*cos(d*x+c)^5*sin(d*x+c)/d-2/3*a*b*sin(d*x+c)^3/d-2/5*a*b*sin(d*x+c)^5/d+b^2*tan(d*x+c)/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c)^4,x,7,3/8*(a^2-4*b^2)*x+2*a*b*arctanh(sin(d*x+c))/d-1/6*b*(28*a^2+b^2)*sin(d*x+c)/a/d-1/24*(39*a^2+2*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/12*(12*a^2+b^2)*(b+a*cos(d*x+c))^2*sin(d*x+c)/a/b/d+1/4*(b+a*cos(d*x+c))^3*sin(d*x+c)/a/d+(b+a*cos(d*x+c))^3*tan(d*x+c)/b/d,1],
[(a+b*sec(d*x+c))^2*sin(d*x+c)^2,x,10,1/2*a^2*x-b^2*x+2*a*b*arctanh(sin(d*x+c))/d-2*a*b*sin(d*x+c)/d-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d+b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*sec(d*x+c))^2,x,8,2*a*b*arctanh(sin(d*x+c))/d-(a^2+b^2)*cot(d*x+c)/d-2*a*b*csc(d*x+c)/d+b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*sec(d*x+c))^2,x,9,2*a*b*arctanh(sin(d*x+c))/d-(a^2+2*b^2)*cot(d*x+c)/d-1/3*(a^2+b^2)*cot(d*x+c)^3/d-2*a*b*csc(d*x+c)/d-2/3*a*b*csc(d*x+c)^3/d+b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^6*(a+b*sec(d*x+c))^2,x,9,2*a*b*arctanh(sin(d*x+c))/d-(a^2+3*b^2)*cot(d*x+c)/d-1/3*(2*a^2+3*b^2)*cot(d*x+c)^3/d-1/5*(a^2+b^2)*cot(d*x+c)^5/d-2*a*b*csc(d*x+c)/d-2/3*a*b*csc(d*x+c)^3/d-2/5*a*b*csc(d*x+c)^5/d+b^2*tan(d*x+c)/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c)^5,x,5,-a*(a^2-6*b^2)*cos(d*x+c)/d+1/2*b*(6*a^2-b^2)*cos(d*x+c)^2/d+1/3*a*(2*a^2-3*b^2)*cos(d*x+c)^3/d-3/4*a^2*b*cos(d*x+c)^4/d-1/5*a^3*cos(d*x+c)^5/d-b*(3*a^2-2*b^2)*ln(cos(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)^2/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c)^3,x,4,-a*(a^2-3*b^2)*cos(d*x+c)/d+3/2*a^2*b*cos(d*x+c)^2/d+1/3*a^3*cos(d*x+c)^3/d-b*(3*a^2-b^2)*ln(cos(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)^2/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c),x,5,-a^3*cos(d*x+c)/d-3*a^2*b*ln(cos(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)*(a+b*sec(d*x+c))^3,x,5,1/2*(a+b)^3*ln(1-cos(d*x+c))/d-b*(3*a^2+b^2)*ln(cos(d*x+c))/d-1/2*(a-b)^3*ln(1+cos(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)^2/d,1],
[csc(d*x+c)^3*(a+b*sec(d*x+c))^3,x,6,-1/2*a^2*(b*(3+b^2/a^2)+a*(1+3*b^2/a^2)*cos(d*x+c))*csc(d*x+c)^2/d+1/4*(a+b)^2*(a+4*b)*ln(1-cos(d*x+c))/d-b*(3*a^2+2*b^2)*ln(cos(d*x+c))/d-1/4*(a-4*b)*(a-b)^2*ln(1+cos(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)^2/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c)^6,x,21,5/16*a^3*x-45/8*a*b^2*x+3*a^2*b*arctanh(sin(d*x+c))/d-5/2*b^3*arctanh(sin(d*x+c))/d-3*a^2*b*sin(d*x+c)/d+5/2*b^3*sin(d*x+c)/d-5/16*a^3*cos(d*x+c)*sin(d*x+c)/d-a^2*b*sin(d*x+c)^3/d+5/6*b^3*sin(d*x+c)^3/d-5/24*a^3*cos(d*x+c)*sin(d*x+c)^3/d-3/5*a^2*b*sin(d*x+c)^5/d-1/6*a^3*cos(d*x+c)*sin(d*x+c)^5/d+45/8*a*b^2*tan(d*x+c)/d-15/8*a*b^2*sin(d*x+c)^2*tan(d*x+c)/d-3/4*a*b^2*sin(d*x+c)^4*tan(d*x+c)/d+1/2*b^3*sin(d*x+c)^3*tan(d*x+c)^2/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c)^4,x,8,3/8*a*(a^2-12*b^2)*x+3/2*b*(2*a^2-b^2)*arctanh(sin(d*x+c))/d-1/2*b*(17*a^2-b^2)*sin(d*x+c)/d-1/8*a*(21*a^2-2*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/4*(6*a^2-b^2)*(b+a*cos(d*x+c))^2*sin(d*x+c)/b/d-1/4*(4*a^2-b^2)*(b+a*cos(d*x+c))^3*sin(d*x+c)/b^2/d+a*(b+a*cos(d*x+c))^4*tan(d*x+c)/b^2/d+1/2*(b+a*cos(d*x+c))^4*sec(d*x+c)*tan(d*x+c)/b/d,1],
[(a+b*sec(d*x+c))^3*sin(d*x+c)^2,x,8,1/2*a*(a^2-6*b^2)*x+1/2*b*(6*a^2-b^2)*arctanh(sin(d*x+c))/d-15/2*a^2*b*sin(d*x+c)/d-5/2*a^3*cos(d*x+c)*sin(d*x+c)/d+3/2*a*(b+a*cos(d*x+c))^2*tan(d*x+c)/d+1/2*(b+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*sec(d*x+c))^3,x,15,3*a^2*b*arctanh(sin(d*x+c))/d+3/2*b^3*arctanh(sin(d*x+c))/d-a^3*cot(d*x+c)/d-3*a*b^2*cot(d*x+c)/d-3*a^2*b*csc(d*x+c)/d-3/2*b^3*csc(d*x+c)/d+1/2*b^3*csc(d*x+c)*sec(d*x+c)^2/d+3*a*b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*sec(d*x+c))^3,x,17,3*a^2*b*arctanh(sin(d*x+c))/d+5/2*b^3*arctanh(sin(d*x+c))/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-3*a^2*b*csc(d*x+c)/d-5/2*b^3*csc(d*x+c)/d-a^2*b*csc(d*x+c)^3/d-5/6*b^3*csc(d*x+c)^3/d+1/2*b^3*csc(d*x+c)^3*sec(d*x+c)^2/d+3*a*b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^6*(a+b*sec(d*x+c))^3,x,17,3*a^2*b*arctanh(sin(d*x+c))/d+7/2*b^3*arctanh(sin(d*x+c))/d-a^3*cot(d*x+c)/d-9*a*b^2*cot(d*x+c)/d-2/3*a^3*cot(d*x+c)^3/d-3*a*b^2*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d-3/5*a*b^2*cot(d*x+c)^5/d-3*a^2*b*csc(d*x+c)/d-7/2*b^3*csc(d*x+c)/d-a^2*b*csc(d*x+c)^3/d-7/6*b^3*csc(d*x+c)^3/d-3/5*a^2*b*csc(d*x+c)^5/d-7/10*b^3*csc(d*x+c)^5/d+1/2*b^3*csc(d*x+c)^5*sec(d*x+c)^2/d+3*a*b^2*tan(d*x+c)/d,1],
[sin(d*x+c)^7/(a+b*sec(d*x+c)),x,5,-(a^2-b^2)^3*cos(d*x+c)/a^7/d-1/2*b*(3*a^4-3*a^2*b^2+b^4)*cos(d*x+c)^2/a^6/d+1/3*(3*a^4-3*a^2*b^2+b^4)*cos(d*x+c)^3/a^5/d+1/4*b*(3*a^2-b^2)*cos(d*x+c)^4/a^4/d-1/5*(3*a^2-b^2)*cos(d*x+c)^5/a^3/d-1/6*b*cos(d*x+c)^6/a^2/d+1/7*cos(d*x+c)^7/a/d+b*(a^2-b^2)^3*ln(b+a*cos(d*x+c))/a^8/d,1],
[sin(d*x+c)^5/(a+b*sec(d*x+c)),x,5,-(a^2-b^2)^2*cos(d*x+c)/a^5/d-1/2*b*(2*a^2-b^2)*cos(d*x+c)^2/a^4/d+1/3*(2*a^2-b^2)*cos(d*x+c)^3/a^3/d+1/4*b*cos(d*x+c)^4/a^2/d-1/5*cos(d*x+c)^5/a/d+b*(a^2-b^2)^2*ln(b+a*cos(d*x+c))/a^6/d,1],
[sin(d*x+c)^3/(a+b*sec(d*x+c)),x,5,-(a^2-b^2)*cos(d*x+c)/a^3/d-1/2*b*cos(d*x+c)^2/a^2/d+1/3*cos(d*x+c)^3/a/d+b*(a^2-b^2)*ln(b+a*cos(d*x+c))/a^4/d,1],
[sin(d*x+c)/(a+b*sec(d*x+c)),x,5,-cos(d*x+c)/a/d+b*ln(b+a*cos(d*x+c))/a^2/d,1],
[csc(d*x+c)/(a+b*sec(d*x+c)),x,4,1/2*ln(1-cos(d*x+c))/(a+b)/d-1/2*ln(1+cos(d*x+c))/(a-b)/d+b*ln(b+a*cos(d*x+c))/(a^2-b^2)/d,1],
[csc(d*x+c)^3/(a+b*sec(d*x+c)),x,6,1/2*(b-a*cos(d*x+c))*csc(d*x+c)^2/(a^2-b^2)/d+1/4*a*ln(1-cos(d*x+c))/(a+b)^2/d-1/4*a*ln(1+cos(d*x+c))/(a-b)^2/d+a^2*b*ln(b+a*cos(d*x+c))/(a^2-b^2)^2/d,1],
[csc(d*x+c)^5/(a+b*sec(d*x+c)),x,6,-1/16*a^5*(3*a-b)/(a-b)/(a+b)^2/d/(a^4-a^4*cos(d*x+c))+1/16*a^5*(3*a+b)/(a-b)^2/(a+b)/d/(a^4+a^4*cos(d*x+c))+1/4*(b-a*cos(d*x+c))*csc(d*x+c)^4/(a^2-b^2)/d+1/16*a*(3*a+b)*ln(1-cos(d*x+c))/(a+b)^3/d-1/16*a*(3*a-b)*ln(1+cos(d*x+c))/(a-b)^3/d+a^4*b*ln(b+a*cos(d*x+c))/(a^2-b^2)^3/d,1],
[sin(d*x+c)^6/(a+b*sec(d*x+c)),x,7,1/16*(5*a^6-30*a^4*b^2+40*a^2*b^4-16*b^6)*x/a^7-2*(a-b)^(5/2)*b*(a+b)^(5/2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^7/d+1/16*(16*b*(a^2-b^2)^2-a*(5*a^4-14*a^2*b^2+8*b^4)*cos(d*x+c))*sin(d*x+c)/a^6/d+1/24*(8*b*(a^2-b^2)-a*(5*a^2-6*b^2)*cos(d*x+c))*sin(d*x+c)^3/a^4/d+1/30*(6*b-5*a*cos(d*x+c))*sin(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^4/(a+b*sec(d*x+c)),x,6,1/8*(3*a^4-12*a^2*b^2+8*b^4)*x/a^5-2*(a-b)^(3/2)*b*(a+b)^(3/2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/d+1/8*(8*b*(a^2-b^2)-a*(3*a^2-4*b^2)*cos(d*x+c))*sin(d*x+c)/a^4/d+1/12*(4*b-3*a*cos(d*x+c))*sin(d*x+c)^3/a^2/d,1],
[sin(d*x+c)^2/(a+b*sec(d*x+c)),x,5,1/2*(a^2-2*b^2)*x/a^3-2*sqrt(a-b)*b*sqrt(a+b)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/d+1/2*(2*b-a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[csc(d*x+c)^2/(a+b*sec(d*x+c)),x,5,-2*a*b*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/d+(b-a*cos(d*x+c))*csc(d*x+c)/(a^2-b^2)/d,1],
[csc(d*x+c)^4/(a+b*sec(d*x+c)),x,6,-2*a^3*b*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d+1/3*(3*a^2*b-a*(2*a^2+b^2)*cos(d*x+c))*csc(d*x+c)/(a^2-b^2)^2/d+1/3*(b-a*cos(d*x+c))*csc(d*x+c)^3/(a^2-b^2)/d,1],
[csc(d*x+c)^6/(a+b*sec(d*x+c)),x,7,-2*a^5*b*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d+1/15*(15*a^4*b-a*(8*a^4+9*a^2*b^2-2*b^4)*cos(d*x+c))*csc(d*x+c)/(a^2-b^2)^3/d+1/15*(5*a^2*b-a*(4*a^2+b^2)*cos(d*x+c))*csc(d*x+c)^3/(a^2-b^2)^2/d+1/5*(b-a*cos(d*x+c))*csc(d*x+c)^5/(a^2-b^2)/d,1],
[sin(d*x+c)^7/(a+b*sec(d*x+c))^2,x,5,-(a^2-7*b^2)*(a^2-b^2)^2*cos(d*x+c)/a^8/d-3*b*(a^2-b^2)^2*cos(d*x+c)^2/a^7/d+1/3*(3*a^4-9*a^2*b^2+5*b^4)*cos(d*x+c)^3/a^6/d+1/2*b*(3*a^2-2*b^2)*cos(d*x+c)^4/a^5/d-3/5*(a^2-b^2)*cos(d*x+c)^5/a^4/d-1/3*b*cos(d*x+c)^6/a^3/d+1/7*cos(d*x+c)^7/a^2/d+b^2*(a^2-b^2)^3/a^9/d/(b+a*cos(d*x+c))+2*b*(a^2-4*b^2)*(a^2-b^2)^2*ln(b+a*cos(d*x+c))/a^9/d,1],
[sin(d*x+c)^5/(a+b*sec(d*x+c))^2,x,5,-(a^4-6*a^2*b^2+5*b^4)*cos(d*x+c)/a^6/d-2*b*(a^2-b^2)*cos(d*x+c)^2/a^5/d+1/3*(2*a^2-3*b^2)*cos(d*x+c)^3/a^4/d+1/2*b*cos(d*x+c)^4/a^3/d-1/5*cos(d*x+c)^5/a^2/d+b^2*(a^2-b^2)^2/a^7/d/(b+a*cos(d*x+c))+2*b*(a^4-4*a^2*b^2+3*b^4)*ln(b+a*cos(d*x+c))/a^7/d,1],
[sin(d*x+c)^3/(a+b*sec(d*x+c))^2,x,5,-(a^2-3*b^2)*cos(d*x+c)/a^4/d-b*cos(d*x+c)^2/a^3/d+1/3*cos(d*x+c)^3/a^2/d+b^2*(a^2-b^2)/a^5/d/(b+a*cos(d*x+c))+2*b*(a^2-2*b^2)*ln(b+a*cos(d*x+c))/a^5/d,1],
[sin(d*x+c)/(a+b*sec(d*x+c))^2,x,5,-cos(d*x+c)/a^2/d+b^2/a^3/d/(b+a*cos(d*x+c))+2*b*ln(b+a*cos(d*x+c))/a^3/d,1],
[csc(d*x+c)/(a+b*sec(d*x+c))^2,x,5,b^2/a/(a^2-b^2)/d/(b+a*cos(d*x+c))+1/2*ln(1-cos(d*x+c))/(a+b)^2/d-1/2*ln(1+cos(d*x+c))/(a-b)^2/d+2*a*b*ln(b+a*cos(d*x+c))/(a^2-b^2)^2/d,1],
[csc(d*x+c)^3/(a+b*sec(d*x+c))^2,x,6,a*b^2/(a^2-b^2)^2/d/(b+a*cos(d*x+c))+1/2*(2*a*b-(a^2+b^2)*cos(d*x+c))*csc(d*x+c)^2/(a^2-b^2)^2/d+1/4*(a-b)*ln(1-cos(d*x+c))/(a+b)^3/d-1/4*(a+b)*ln(1+cos(d*x+c))/(a-b)^3/d+2*a*b*(a^2+b^2)*ln(b+a*cos(d*x+c))/(a^2-b^2)^3/d,1],
[csc(d*x+c)^5/(a+b*sec(d*x+c))^2,x,6,-1/16*(3*a^3-5*a^2*b+7*a*b^2-b^3)/(a-b)^2/(a+b)^3/d/(1-cos(d*x+c))+1/16*(3*a^3+5*a^2*b+7*a*b^2+b^3)/(a-b)^3/(a+b)^2/d/(1+cos(d*x+c))+a^3*b^2/(a^2-b^2)^3/d/(b+a*cos(d*x+c))+1/4*(2*a*b-(a^2+b^2)*cos(d*x+c))*csc(d*x+c)^4/(a^2-b^2)^2/d+1/16*(3*a^2-4*a*b-b^2)*ln(1-cos(d*x+c))/(a+b)^4/d-1/16*(3*a^2+4*a*b-b^2)*ln(1+cos(d*x+c))/(a-b)^4/d+2*a^3*b*(a^2+2*b^2)*ln(b+a*cos(d*x+c))/(a^2-b^2)^4/d,1],
[sin(d*x+c)^6/(a+b*sec(d*x+c))^2,x,10,1/16*(5*a^6-90*a^4*b^2+200*a^2*b^4-112*b^6)*x/a^8-2*(a-b)^(3/2)*b*(a+b)^(3/2)*(2*a^2-7*b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^8/d+1/15*b*(61*a^4-170*a^2*b^2+105*b^4)*sin(d*x+c)/a^7/d-1/16*(27*a^4-86*a^2*b^2+56*b^4)*cos(d*x+c)*sin(d*x+c)/a^6/d+1/15*(15*a^4-52*a^2*b^2+35*b^4)*cos(d*x+c)^2*sin(d*x+c)/a^5/b/d-1/24*(16*a^4-61*a^2*b^2+42*b^4)*cos(d*x+c)^3*sin(d*x+c)/a^4/b^2/d-1/3*cos(d*x+c)^3*sin(d*x+c)/b/d/(b+a*cos(d*x+c))+1/6*a*cos(d*x+c)^4*sin(d*x+c)/b^2/d/(b+a*cos(d*x+c))+1/10*(5*a^4-20*a^2*b^2+14*b^4)*cos(d*x+c)^4*sin(d*x+c)/a^3/b^2/d/(b+a*cos(d*x+c))+7/30*b*cos(d*x+c)^5*sin(d*x+c)/a^2/d/(b+a*cos(d*x+c))-1/6*cos(d*x+c)^6*sin(d*x+c)/a/d/(b+a*cos(d*x+c)),1],
[sin(d*x+c)^4/(a+b*sec(d*x+c))^2,x,8,1/8*(3*a^4-36*a^2*b^2+40*b^4)*x/a^6-2*sqrt(a-b)*b*sqrt(a+b)*(2*a^2-5*b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^6/d+1/3*b*(11*a^2-15*b^2)*sin(d*x+c)/a^5/d-1/8*(13*a^2-20*b^2)*cos(d*x+c)*sin(d*x+c)/a^4/d+1/3*(3*a^2-5*b^2)*cos(d*x+c)^2*sin(d*x+c)/a^3/b/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a^2/d-(a^2-b^2)*cos(d*x+c)^3*sin(d*x+c)/a^2/b/d/(b+a*cos(d*x+c)),1],
[sin(d*x+c)^2/(a+b*sec(d*x+c))^2,x,8,1/2*(a^2-6*b^2)*x/a^4-2*b*(2*a^2-3*b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/sqrt(a-b)/sqrt(a+b)/d+3*b*sin(d*x+c)/a^3/d-3/2*cos(d*x+c)*sin(d*x+c)/a^2/d+cos(d*x+c)^2*sin(d*x+c)/a/d/(b+a*cos(d*x+c)),1],
[csc(d*x+c)^2/(a+b*sec(d*x+c))^2,x,11,-4*a^2*b*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-2*b^3*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-1/2*sin(d*x+c)/(a+b)^2/d/(1-cos(d*x+c))+1/2*sin(d*x+c)/(a-b)^2/d/(1+cos(d*x+c))+a*b^2*sin(d*x+c)/(a^2-b^2)^2/d/(b+a*cos(d*x+c)),1],
[csc(d*x+c)^4/(a+b*sec(d*x+c))^2,x,15,-2*a^2*b^3*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-4*a^2*b*(a^2+b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-1/12*sin(d*x+c)/(a+b)^2/d/(1-cos(d*x+c))^2-1/4*(a-b)*sin(d*x+c)/(a+b)^3/d/(1-cos(d*x+c))-1/12*sin(d*x+c)/(a+b)^2/d/(1-cos(d*x+c))+1/12*sin(d*x+c)/(a-b)^2/d/(1+cos(d*x+c))^2+1/12*sin(d*x+c)/(a-b)^2/d/(1+cos(d*x+c))+1/4*(a+b)*sin(d*x+c)/(a-b)^3/d/(1+cos(d*x+c))+a^3*b^2*sin(d*x+c)/(a^2-b^2)^3/d/(b+a*cos(d*x+c)),1],
[sin(d*x+c)^7/(a+b*sec(d*x+c))^3,x,5,-(a^6-18*a^4*b^2+45*a^2*b^4-28*b^6)*cos(d*x+c)/a^9/d-3/2*b*(3*a^4-10*a^2*b^2+7*b^4)*cos(d*x+c)^2/a^8/d+(a^4-6*a^2*b^2+5*b^4)*cos(d*x+c)^3/a^7/d+1/4*b*(9*a^2-10*b^2)*cos(d*x+c)^4/a^6/d-3/5*(a^2-2*b^2)*cos(d*x+c)^5/a^5/d-1/2*b*cos(d*x+c)^6/a^4/d+1/7*cos(d*x+c)^7/a^3/d-1/2*b^3*(a^2-b^2)^3/a^10/d/(b+a*cos(d*x+c))^2+3*b^2*(a^2-3*b^2)*(a^2-b^2)^2/a^10/d/(b+a*cos(d*x+c))+3*b*(a^2-b^2)*(a^4-9*a^2*b^2+12*b^4)*ln(b+a*cos(d*x+c))/a^10/d,1],
[sin(d*x+c)^5/(a+b*sec(d*x+c))^3,x,5,-(a^4-12*a^2*b^2+15*b^4)*cos(d*x+c)/a^7/d-b*(3*a^2-5*b^2)*cos(d*x+c)^2/a^6/d+2/3*(a^2-3*b^2)*cos(d*x+c)^3/a^5/d+3/4*b*cos(d*x+c)^4/a^4/d-1/5*cos(d*x+c)^5/a^3/d-1/2*b^3*(a^2-b^2)^2/a^8/d/(b+a*cos(d*x+c))^2+b^2*(3*a^4-10*a^2*b^2+7*b^4)/a^8/d/(b+a*cos(d*x+c))+b*(3*a^4-20*a^2*b^2+21*b^4)*ln(b+a*cos(d*x+c))/a^8/d,1],
[sin(d*x+c)^3/(a+b*sec(d*x+c))^3,x,5,-(a^2-6*b^2)*cos(d*x+c)/a^5/d-3/2*b*cos(d*x+c)^2/a^4/d+1/3*cos(d*x+c)^3/a^3/d-1/2*b^3*(a^2-b^2)/a^6/d/(b+a*cos(d*x+c))^2+b^2*(3*a^2-5*b^2)/a^6/d/(b+a*cos(d*x+c))+b*(3*a^2-10*b^2)*ln(b+a*cos(d*x+c))/a^6/d,1],
[sin(d*x+c)/(a+b*sec(d*x+c))^3,x,5,-cos(d*x+c)/a^3/d-1/2*b^3/a^4/d/(b+a*cos(d*x+c))^2+3*b^2/a^4/d/(b+a*cos(d*x+c))+3*b*ln(b+a*cos(d*x+c))/a^4/d,1],
[csc(d*x+c)/(a+b*sec(d*x+c))^3,x,5,-1/2*b^3/a^2/(a^2-b^2)/d/(b+a*cos(d*x+c))^2+b^2*(3*a^2-b^2)/a^2/(a^2-b^2)^2/d/(b+a*cos(d*x+c))+1/2*ln(1-cos(d*x+c))/(a+b)^3/d-1/2*ln(1+cos(d*x+c))/(a-b)^3/d+b*(3*a^2+b^2)*ln(b+a*cos(d*x+c))/(a^2-b^2)^3/d,1],
[csc(d*x+c)^3/(a+b*sec(d*x+c))^3,x,5,-1/2*b^3/(a^2-b^2)^2/d/(b+a*cos(d*x+c))^2+b^2*(3*a^2+b^2)/(a^2-b^2)^3/d/(b+a*cos(d*x+c))+1/2*(b*(3*a^2+b^2)-a*(a^2+3*b^2)*cos(d*x+c))*csc(d*x+c)^2/(a^2-b^2)^3/d+1/4*(a-2*b)*ln(1-cos(d*x+c))/(a+b)^4/d-1/4*(a+2*b)*ln(1+cos(d*x+c))/(a-b)^4/d+b*(3*a^4+8*a^2*b^2+b^4)*ln(b+a*cos(d*x+c))/(a^2-b^2)^4/d,1],
[csc(d*x+c)^5/(a+b*sec(d*x+c))^3,x,6,-1/16*(3*a^4-9*a^3*b+21*a^2*b^2-11*a*b^3+4*b^4)/(a-b)^3/(a+b)^4/d/(1-cos(d*x+c))+1/16*(3*a^4+9*a^3*b+21*a^2*b^2+11*a*b^3+4*b^4)/(a-b)^4/(a+b)^3/d/(1+cos(d*x+c))-1/2*a^2*b^3/(a^2-b^2)^3/d/(b+a*cos(d*x+c))^2+3*a^2*b^2*(a^2+b^2)/(a^2-b^2)^4/d/(b+a*cos(d*x+c))+1/4*(b*(3*a^2+b^2)-a*(a^2+3*b^2)*cos(d*x+c))*csc(d*x+c)^4/(a^2-b^2)^3/d+3/16*a*(a-3*b)*ln(1-cos(d*x+c))/(a+b)^5/d-3/16*a*(a+3*b)*ln(1+cos(d*x+c))/(a-b)^5/d+3*a^2*b*(a^4+5*a^2*b^2+2*b^4)*ln(b+a*cos(d*x+c))/(a^2-b^2)^5/d,1],
[sin(d*x+c)^6/(a+b*sec(d*x+c))^3,x,11,1/16*(5*a^6-180*a^4*b^2+600*a^2*b^4-448*b^6)*x/a^9-sqrt(a-b)*b*sqrt(a+b)*(6*a^4-47*a^2*b^2+56*b^4)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^9/d+1/30*b*(213*a^4-985*a^2*b^2+840*b^4)*sin(d*x+c)/a^8/d-1/16*(43*a^4-244*a^2*b^2+224*b^4)*cos(d*x+c)*sin(d*x+c)/a^7/d+1/30*(45*a^4-291*a^2*b^2+280*b^4)*cos(d*x+c)^2*sin(d*x+c)/a^6/b/d-1/24*(24*a^4-169*a^2*b^2+168*b^4)*cos(d*x+c)^3*sin(d*x+c)/a^5/b^2/d-1/4*cos(d*x+c)^4*sin(d*x+c)/b/d/(b+a*cos(d*x+c))^2+1/10*a*cos(d*x+c)^5*sin(d*x+c)/b^2/d/(b+a*cos(d*x+c))^2+1/60*(9*a^4-60*a^2*b^2+56*b^4)*cos(d*x+c)^5*sin(d*x+c)/a^3/b^2/d/(b+a*cos(d*x+c))^2+4/15*b*cos(d*x+c)^6*sin(d*x+c)/a^2/d/(b+a*cos(d*x+c))^2-1/6*cos(d*x+c)^7*sin(d*x+c)/a/d/(b+a*cos(d*x+c))^2+1/20*(15*a^4-110*a^2*b^2+112*b^4)*cos(d*x+c)^4*sin(d*x+c)/a^4/b^2/d/(b+a*cos(d*x+c)),1],
[sin(d*x+c)^4/(a+b*sec(d*x+c))^3,x,9,3/8*(a^4-24*a^2*b^2+40*b^4)*x/a^7-3*b*(2*a^4-11*a^2*b^2+10*b^4)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^7/sqrt(a-b)/sqrt(a+b)/d+1/2*b*(13*a^2-30*b^2)*sin(d*x+c)/a^6/d-3/8*(7*a^2-20*b^2)*cos(d*x+c)*sin(d*x+c)/a^5/d+1/2*(3*a^2-10*b^2)*cos(d*x+c)^2*sin(d*x+c)/a^4/b/d-1/4*(4*a^2-15*b^2)*cos(d*x+c)^3*sin(d*x+c)/a^3/b^2/d-1/2*(a^2-b^2)*cos(d*x+c)^4*sin(d*x+c)/a^2/b/d/(b+a*cos(d*x+c))^2+1/2*(2*a^2-7*b^2)*cos(d*x+c)^4*sin(d*x+c)/a^2/b^2/d/(b+a*cos(d*x+c)),1],
[sin(d*x+c)^2/(a+b*sec(d*x+c))^3,x,9,1/2*(a^2-12*b^2)*x/a^5-b*(6*a^4-19*a^2*b^2+12*b^4)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(3/2)/(a+b)^(3/2)/d+1/2*b*(11*a^2-12*b^2)*sin(d*x+c)/a^4/(a^2-b^2)/d-1/2*(5*a^2-6*b^2)*cos(d*x+c)*sin(d*x+c)/a^3/(a^2-b^2)/d+1/2*cos(d*x+c)^3*sin(d*x+c)/a/d/(b+a*cos(d*x+c))^2+1/2*(3*a^2-4*b^2)*cos(d*x+c)^2*sin(d*x+c)/a^2/(a^2-b^2)/d/(b+a*cos(d*x+c)),1],
[csc(d*x+c)^2/(a+b*sec(d*x+c))^3,x,16,-2*b^3*(3*a^2-b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/(a-b)^(7/2)/(a+b)^(7/2)/d-2*a*b*(3*a^2+b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-b^3*(a^2+2*b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/(a-b)^(7/2)/(a+b)^(7/2)/d-1/2*sin(d*x+c)/(a+b)^3/d/(1-cos(d*x+c))+1/2*sin(d*x+c)/(a-b)^3/d/(1+cos(d*x+c))-1/2*b^3*sin(d*x+c)/(a^2-b^2)^2/d/(b+a*cos(d*x+c))^2+3/2*b^4*sin(d*x+c)/(a^2-b^2)^3/d/(b+a*cos(d*x+c))+b^2*(3*a^2-b^2)*sin(d*x+c)/(a^2-b^2)^3/d/(b+a*cos(d*x+c)),1],
[csc(d*x+c)^4/(a+b*sec(d*x+c))^3,x,20,-2*a*b^3*(3*a^2+b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(9/2)/(a+b)^(9/2)/d-a*b^3*(a^2+2*b^2)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(9/2)/(a+b)^(9/2)/d-2*a*b*(3*a^4+8*a^2*b^2+b^4)*arctanh(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(9/2)/(a+b)^(9/2)/d-1/12*sin(d*x+c)/(a+b)^3/d/(1-cos(d*x+c))^2-1/4*(a-2*b)*sin(d*x+c)/(a+b)^4/d/(1-cos(d*x+c))-1/12*sin(d*x+c)/(a+b)^3/d/(1-cos(d*x+c))+1/12*sin(d*x+c)/(a-b)^3/d/(1+cos(d*x+c))^2+1/12*sin(d*x+c)/(a-b)^3/d/(1+cos(d*x+c))+1/4*(a+2*b)*sin(d*x+c)/(a-b)^4/d/(1+cos(d*x+c))-1/2*a^2*b^3*sin(d*x+c)/(a^2-b^2)^3/d/(b+a*cos(d*x+c))^2+3/2*a^2*b^4*sin(d*x+c)/(a^2-b^2)^4/d/(b+a*cos(d*x+c))+a^2*b^2*(3*a^2+b^2)*sin(d*x+c)/(a^2-b^2)^4/d/(b+a*cos(d*x+c)),1],
[(e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c)),x,15,-b*(a^2-b^2)^(5/4)*e^(7/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/d-b*(a^2-b^2)^(5/4)*e^(7/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/d+2/21*(5*a^4-28*a^2*b^2+21*b^4)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^5/d/sqrt(e*sin(d*x+c))+b^2*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+b^2*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2/21*e^3*(21*b*(a^2-b^2)-a*(5*a^2-7*b^2)*cos(d*x+c))*sqrt(e*sin(d*x+c))/a^4/d+2/35*e*(7*b-5*a*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/a^2/d,1],
[(e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x,14,b*(a^2-b^2)^(3/4)*e^(5/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/d-b*(a^2-b^2)^(3/4)*e^(5/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/d-b^2*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-b^2*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2/5*(3*a^2-5*b^2)*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^3/d/sqrt(sin(d*x+c))+2/15*e*(5*b-3*a*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/a^2/d,1],
[(e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x,14,-b*(a^2-b^2)^(1/4)*e^(3/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/d-b*(a^2-b^2)^(1/4)*e^(3/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/d+2/3*(a^2-3*b^2)*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^3/d/sqrt(e*sin(d*x+c))+b^2*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+b^2*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2/3*e*(3*b-a*cos(d*x+c))*sqrt(e*sin(d*x+c))/a^2/d,1],
[sqrt(e*sin(d*x+c))/(a+b*sec(d*x+c)),x,13,b*sqrt(e)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(1/4)/d-b*sqrt(e)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(1/4)/d-b^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-b^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a/d/sqrt(sin(d*x+c)),1],
[1/(a+b*sec(d*x+c))/sqrt(e*sin(d*x+c)),x,13,-b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(3/4)/d/sqrt(e)-b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(3/4)/d/sqrt(e)+2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d/sqrt(e*sin(d*x+c))+b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c)),1],
[1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(3/2),x,14,sqrt(a)*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(5/4)/d/e^(3/2)-sqrt(a)*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(5/4)/d/e^(3/2)+2*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/sqrt(e*sin(d*x+c))-b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a-sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a+sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(5/2),x,14,-a^(3/2)*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(7/4)/d/e^(5/2)-a^(3/2)*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(7/4)/d/e^(5/2)+2/3*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/(e*sin(d*x+c))^(3/2)+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/d/e^2/sqrt(e*sin(d*x+c))+a*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b^2-a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c))+a*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b^2+a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c)),1],
[1/(a+b*sec(d*x+c))/(e*sin(d*x+c))^(7/2),x,15,a^(5/2)*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(9/4)/d/e^(7/2)-a^(5/2)*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(9/4)/d/e^(7/2)+2/5*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/(e*sin(d*x+c))^(5/2)+2/5*(5*a^2*b-a*(3*a^2+2*b^2)*cos(d*x+c))/(a^2-b^2)^2/d/e^3/sqrt(e*sin(d*x+c))-a^2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a-sqrt(a^2-b^2))/d/e^3/sqrt(e*sin(d*x+c))-a^2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a+sqrt(a^2-b^2))/d/e^3/sqrt(e*sin(d*x+c))-2/5*a*(3*a^2+2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^2/d/e^4/sqrt(sin(d*x+c)),1],
[(e*sin(d*x+c))^(9/2)/(a+b*sec(d*x+c))^2,x,35,-7/2*b^3*(a^2-b^2)^(3/4)*e^(9/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(13/2)/d+2*b*(a^2-b^2)^(7/4)*e^(9/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(13/2)/d+7/2*b^3*(a^2-b^2)^(3/4)*e^(9/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(13/2)/d-2*b*(a^2-b^2)^(7/4)*e^(9/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(13/2)/d+7/2*b^4*(a^2-b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^7/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-2*b^2*(a^2-b^2)^2*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^7/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+7/2*b^4*(a^2-b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^7/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-2*b^2*(a^2-b^2)^2*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^7/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+14/15*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/sqrt(sin(d*x+c))-7/5*b^2*(3*a^2-5*b^2)*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^6/d/sqrt(sin(d*x+c))-4/5*b^2*(8*a^2-5*b^2)*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^6/d/sqrt(sin(d*x+c))-14/45*e^3*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/a^2/d-7/15*b^2*e^3*(5*b-3*a*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/a^5/d+4/15*b*e^3*(5*a^2-5*b^2+3*a*b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/a^5/d+4/7*b*e*(e*sin(d*x+c))^(7/2)/a^3/d-2/9*e*cos(d*x+c)*(e*sin(d*x+c))^(7/2)/a^2/d+b^2*e*(e*sin(d*x+c))^(7/2)/a^3/d/(b+a*cos(d*x+c)),1],
[(e*sin(d*x+c))^(7/2)/(a+b*sec(d*x+c))^2,x,35,5/2*b^3*(a^2-b^2)^(1/4)*e^(7/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(11/2)/d-2*b*(a^2-b^2)^(5/4)*e^(7/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(11/2)/d+5/2*b^3*(a^2-b^2)^(1/4)*e^(7/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(11/2)/d-2*b*(a^2-b^2)^(5/4)*e^(7/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(11/2)/d+10/21*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c))-5/3*b^2*(a^2-3*b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^6/d/sqrt(e*sin(d*x+c))-4/3*b^2*(4*a^2-3*b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^6/d/sqrt(e*sin(d*x+c))-5/2*b^4*(a^2-b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^6/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*b^2*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^6/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-5/2*b^4*(a^2-b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^6/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*b^2*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^6/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-10/21*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/a^2/d-5/3*b^2*e^3*(3*b-a*cos(d*x+c))*sqrt(e*sin(d*x+c))/a^5/d+4/3*b*e^3*(3*a^2-3*b^2+a*b*cos(d*x+c))*sqrt(e*sin(d*x+c))/a^5/d+4/5*b*e*(e*sin(d*x+c))^(5/2)/a^3/d-2/7*e*cos(d*x+c)*(e*sin(d*x+c))^(5/2)/a^2/d+b^2*e*(e*sin(d*x+c))^(5/2)/a^3/d/(b+a*cos(d*x+c)),1],
[(e*sin(d*x+c))^(5/2)/(a+b*sec(d*x+c))^2,x,32,-3/2*b^3*e^(5/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/(a^2-b^2)^(1/4)/d+2*b*(a^2-b^2)^(3/4)*e^(5/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/d+3/2*b^3*e^(5/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/(a^2-b^2)^(1/4)/d-2*b*(a^2-b^2)^(3/4)*e^(5/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(9/2)/d+3/2*b^4*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-2*b^2*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+3/2*b^4*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-2*b^2*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^5/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+6/5*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/sqrt(sin(d*x+c))-7*b^2*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^4/d/sqrt(sin(d*x+c))+4/3*b*e*(e*sin(d*x+c))^(3/2)/a^3/d-2/5*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/a^2/d+b^2*e*(e*sin(d*x+c))^(3/2)/a^3/d/(b+a*cos(d*x+c)),1],
[(e*sin(d*x+c))^(3/2)/(a+b*sec(d*x+c))^2,x,32,1/2*b^3*e^(3/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/(a^2-b^2)^(3/4)/d-2*b*(a^2-b^2)^(1/4)*e^(3/2)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/d+1/2*b^3*e^(3/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/(a^2-b^2)^(3/4)/d-2*b*(a^2-b^2)^(1/4)*e^(3/2)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(7/2)/d+2/3*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c))-5*b^2*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^4/d/sqrt(e*sin(d*x+c))-1/2*b^4*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*b^2*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-1/2*b^4*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*b^2*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^4/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+4*b*e*sqrt(e*sin(d*x+c))/a^3/d-2/3*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/a^2/d+b^2*e*sqrt(e*sin(d*x+c))/a^3/d/(b+a*cos(d*x+c)),1],
[sqrt(e*sin(d*x+c))/(a+b*sec(d*x+c))^2,x,27,1/2*b^3*sqrt(e)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/(a^2-b^2)^(5/4)/d+2*b*sqrt(e)*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/(a^2-b^2)^(1/4)/d-1/2*b^3*sqrt(e)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/(a^2-b^2)^(5/4)/d-2*b*sqrt(e)*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(5/2)/(a^2-b^2)^(1/4)/d-2*b^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-1/2*b^4*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a^2-b^2)/(a-sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-2*b^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))-1/2*b^4*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^3/(a^2-b^2)/(a+sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/sqrt(sin(d*x+c))-b^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/(a^2-b^2)/d/sqrt(sin(d*x+c))+b^2*(e*sin(d*x+c))^(3/2)/a/(a^2-b^2)/d/e/(b+a*cos(d*x+c)),1],
[1/(a+b*sec(d*x+c))^2/sqrt(e*sin(d*x+c)),x,27,-3/2*b^3*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(7/4)/d/sqrt(e)-2*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(3/4)/d/sqrt(e)-3/2*b^3*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(7/4)/d/sqrt(e)-2*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/a^(3/2)/(a^2-b^2)^(3/4)/d/sqrt(e)+2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/sqrt(e*sin(d*x+c))+b^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2)/d/sqrt(e*sin(d*x+c))+2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+3/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2)/(a^2-b^2-a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+3/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2)/(a^2-b^2+a*sqrt(a^2-b^2))/d/sqrt(e*sin(d*x+c))+b^2*sqrt(e*sin(d*x+c))/a/(a^2-b^2)/d/e/(b+a*cos(d*x+c)),1],
[1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(3/2),x,33,5/2*b^3*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(9/4)/d/e^(3/2)+2*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(5/4)/d/e^(3/2)-5/2*b^3*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(9/4)/d/e^(3/2)-2*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/sqrt(a)/(a^2-b^2)^(5/4)/d/e^(3/2)-2*cos(d*x+c)/a^2/d/e/sqrt(e*sin(d*x+c))+b^2/a/(a^2-b^2)/d/e/(b+a*cos(d*x+c))/sqrt(e*sin(d*x+c))+4*b*(a-b*cos(d*x+c))/a^2/(a^2-b^2)/d/e/sqrt(e*sin(d*x+c))+b^2*(5*a*b-(3*a^2+2*b^2)*cos(d*x+c))/a^2/(a^2-b^2)^2/d/e/sqrt(e*sin(d*x+c))-5/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2)^2/(a-sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2)/(a-sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-5/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2)^2/(a+sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/a/(a^2-b^2)/(a+sqrt(a^2-b^2))/d/e/sqrt(e*sin(d*x+c))-2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/d/e^2/sqrt(sin(d*x+c))-4*b^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/(a^2-b^2)/d/e^2/sqrt(sin(d*x+c))-b^2*(3*a^2+2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/a^2/(a^2-b^2)^2/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+b*sec(d*x+c))^2/(e*sin(d*x+c))^(5/2),x,33,-7/2*sqrt(a)*b^3*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(11/4)/d/e^(5/2)-2*sqrt(a)*b*arctan(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(7/4)/d/e^(5/2)-7/2*sqrt(a)*b^3*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(11/4)/d/e^(5/2)-2*sqrt(a)*b*arctanh(sqrt(a)*sqrt(e*sin(d*x+c))/(a^2-b^2)^(1/4)/sqrt(e))/(a^2-b^2)^(7/4)/d/e^(5/2)-2/3*cos(d*x+c)/a^2/d/e/(e*sin(d*x+c))^(3/2)+b^2/a/(a^2-b^2)/d/e/(b+a*cos(d*x+c))/(e*sin(d*x+c))^(3/2)+4/3*b*(a-b*cos(d*x+c))/a^2/(a^2-b^2)/d/e/(e*sin(d*x+c))^(3/2)+1/3*b^2*(7*a*b-(5*a^2+2*b^2)*cos(d*x+c))/a^2/(a^2-b^2)^2/d/e/(e*sin(d*x+c))^(3/2)+2/3*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d/e^2/sqrt(e*sin(d*x+c))+4/3*b^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2)/d/e^2/sqrt(e*sin(d*x+c))+1/3*b^2*(5*a^2+2*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/(a^2-b^2)^2/d/e^2/sqrt(e*sin(d*x+c))+7/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b^2-a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c))+2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a-sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b^2-a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c))+7/2*b^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b^2+a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c))+2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*a/(a+sqrt(a^2-b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b^2+a*sqrt(a^2-b^2))/d/e^2/sqrt(e*sin(d*x+c)),1],
[sqrt(a+b*sec(f*x+e)),x,1,-2*cot(f*x+e)*EllipticPi(sin(arcsin(sqrt(a+b)/sqrt(a+b*sec(f*x+e)))),a/(a+b),sqrt((a-b)/(a+b)))*sqrt(-b*(1-sec(f*x+e))/(a+b*sec(f*x+e)))*sqrt(b*(1+sec(f*x+e))/(a+b*sec(f*x+e)))*(a+b*sec(f*x+e))/sqrt(a+b)/f,1],
[csc(f*x+e)^2*sqrt(a+b*sec(f*x+e)),x,2,sqrt(a+b)*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f-cot(f*x+e)*sqrt(a+b*sec(f*x+e))/f,1],
[(a+b*sec(f*x+e))^(3/2),x,5,-2*(a-b)*sqrt(a+b)*cot(f*x+e)*EllipticE(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f+2*(2*a-b)*sqrt(a+b)*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f-2*a*sqrt(a+b)*cot(f*x+e)*EllipticPi(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),(a+b)/a,sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f,1],
[csc(f*x+e)^2*(a+b*sec(f*x+e))^(3/2),x,4,-3*(a-b)*sqrt(a+b)*cot(f*x+e)*EllipticE(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f+3*(a-b)*sqrt(a+b)*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/f-cot(f*x+e)*(a+b*sec(f*x+e))^(3/2)/f,1],
[1/sqrt(a+b*sec(f*x+e)),x,1,-2*sqrt(a+b)*cot(f*x+e)*EllipticPi(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),(a+b)/a,sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/a/f,1],
[csc(f*x+e)^2/sqrt(a+b*sec(f*x+e)),x,6,cot(f*x+e)*EllipticE(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/sqrt(a+b)/f-cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/sqrt(a+b)/f-cot(f*x+e)/f/sqrt(a+b*sec(f*x+e))+b^2*tan(f*x+e)/(a^2-b^2)/f/sqrt(a+b*sec(f*x+e)),1],
[1/(a+b*sec(f*x+e))^(3/2),x,6,2*cot(f*x+e)*EllipticE(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/a/sqrt(a+b)/f-2*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/a/sqrt(a+b)/f-2*sqrt(a+b)*cot(f*x+e)*EllipticPi(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),(a+b)/a,sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/a^2/f+2*b^2*tan(f*x+e)/a/(a^2-b^2)/f/sqrt(a+b*sec(f*x+e)),1],
[csc(f*x+e)^2/(a+b*sec(f*x+e))^(3/2),x,6,4*a*cot(f*x+e)*EllipticE(sin(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b))),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/(a-b)/(a+b)^(3/2)/f-(3*a-b)*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(a+b*sec(f*x+e))/sqrt(a+b)),sqrt((a+b)/(a-b)))*sqrt(b*(1-sec(f*x+e))/(a+b))*sqrt(-b*(1+sec(f*x+e))/(a-b))/(a-b)/(a+b)^(3/2)/f-cot(f*x+e)/f/(a+b*sec(f*x+e))^(3/2)+b^2*tan(f*x+e)/(a^2-b^2)/f/(a+b*sec(f*x+e))^(3/2)+4*a*b^2*tan(f*x+e)/(a^2-b^2)^2/f/sqrt(a+b*sec(f*x+e)),1],
[(a+b*sec(d*x+c))^3*(e*sin(d*x+c))^m,x,9,a^3*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)/sqrt(cos(d*x+c)^2)+3*a^2*b*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+b^3*hypergeom([2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+3*a*b^2*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sec(d*x+c)*(e*sin(d*x+c))^(1+m)/d/e/(1+m),1],
[(a+b*sec(d*x+c))^2*(e*sin(d*x+c))^m,x,9,a^2*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)*(e*sin(d*x+c))^m/d/(1+m)/sqrt(cos(d*x+c)^2)+2*a*b*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)+b^2*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^m*tan(d*x+c)/d/(1+m),1],
[(a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x,5,a*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m)/sqrt(cos(d*x+c)^2)+b*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/d/e/(1+m),1],
[(e*sin(d*x+c))^m/(a+b*sec(d*x+c)),x,4,-b*e*AppellF1(1-m,1/2-1/2*m,1/2-1/2*m,2-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^2/d/(1-m)+cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/a/d/e/(1+m)/sqrt(cos(d*x+c)^2),1],
[(e*sin(d*x+c))^m/(a+b*sec(d*x+c))^2,x,6,-2*b*e*AppellF1(1-m,1/2-1/2*m,1/2-1/2*m,2-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^3/d/(1-m)+b^2*e*AppellF1(2-m,1/2-1/2*m,1/2-1/2*m,3-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^3/d/(2-m)/(b+a*cos(d*x+c))+cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/a^2/d/e/(1+m)/sqrt(cos(d*x+c)^2),1],
[(e*sin(d*x+c))^m/(a+b*sec(d*x+c))^3,x,7,-3*b*e*AppellF1(1-m,1/2-1/2*m,1/2-1/2*m,2-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^4/d/(1-m)-b^3*e*AppellF1(3-m,1/2-1/2*m,1/2-1/2*m,4-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^4/d/(3-m)/(b+a*cos(d*x+c))^2+3*b^2*e*AppellF1(2-m,1/2-1/2*m,1/2-1/2*m,3-m,-(a-b)/(b+a*cos(d*x+c)),(a+b)/(b+a*cos(d*x+c)))*(-a*(1-cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(a*(1+cos(d*x+c))/(b+a*cos(d*x+c)))^(1/2-1/2*m)*(e*sin(d*x+c))^(-1+m)/a^4/d/(2-m)/(b+a*cos(d*x+c))+cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*(e*sin(d*x+c))^(1+m)/a^3/d/e/(1+m)/sqrt(cos(d*x+c)^2),1],
[(a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x,0,Defer(Int)((a+b*sec(d*x+c))^(3/2)*(e*sin(d*x+c))^m,x),0],
[sqrt(a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x,0,Defer(Int)(sqrt(a+b*sec(d*x+c))*(e*sin(d*x+c))^m,x),0],
[(e*sin(d*x+c))^m/sqrt(a+b*sec(d*x+c)),x,0,Defer(Int)((e*sin(d*x+c))^m/sqrt(a+b*sec(d*x+c)),x),0],
[(e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x,0,Defer(Int)((e*sin(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x),0],
[(a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x,0,Defer(Int)((a+b*sec(d*x+c))^n*(e*sin(d*x+c))^m,x),0],
[(a+b*sec(d*x+c))^n*sin(d*x+c)^5,x,7,-1/120*b*(2-n)*(40*a^2-b^2*(n^2-7*n+12))*cos(d*x+c)^2*(a+b*sec(d*x+c))^(1+n)/a^4/d+1/60*(40*a^2-b^2*(n^2-7*n+12))*cos(d*x+c)^3*(a+b*sec(d*x+c))^(1+n)/a^3/d+1/20*b*(4-n)*cos(d*x+c)^4*(a+b*sec(d*x+c))^(1+n)/a^2/d-1/5*cos(d*x+c)^5*(a+b*sec(d*x+c))^(1+n)/a/d+1/120*b*(120*a^4-b^2*(1-n)*(2-n)*(40*a^2-b^2*(n^2-7*n+12)))*hypergeom([2, 1+n],[2+n],(a+b*sec(d*x+c))/a)*(a+b*sec(d*x+c))^(1+n)/a^6/d/(1+n),1],
[(a+b*sec(d*x+c))^n*sin(d*x+c)^3,x,5,-1/6*b*(2-n)*cos(d*x+c)^2*(a+b*sec(d*x+c))^(1+n)/a^2/d+1/3*cos(d*x+c)^3*(a+b*sec(d*x+c))^(1+n)/a/d+1/6*b*(6*a^2-b^2*(n^2-3*n+2))*hypergeom([2, 1+n],[2+n],(a+b*sec(d*x+c))/a)*(a+b*sec(d*x+c))^(1+n)/a^4/d/(1+n),1],
[(a+b*sec(d*x+c))^n*sin(d*x+c),x,2,b*hypergeom([2, 1+n],[2+n],(a+b*sec(d*x+c))/a)*(a+b*sec(d*x+c))^(1+n)/a^2/d/(1+n),1],
[csc(d*x+c)*(a+b*sec(d*x+c))^n,x,6,1/2*hypergeom([1, 1+n],[2+n],(a+b*sec(d*x+c))/(a-b))*(a+b*sec(d*x+c))^(1+n)/(a-b)/d/(1+n)-1/2*hypergeom([1, 1+n],[2+n],(a+b*sec(d*x+c))/(a+b))*(a+b*sec(d*x+c))^(1+n)/(a+b)/d/(1+n),1],
[csc(d*x+c)^3*(a+b*sec(d*x+c))^n,x,7,1/4*(a-b*(1+n))*hypergeom([1, 1+n],[2+n],(a+b*sec(d*x+c))/(a-b))*(a+b*sec(d*x+c))^(1+n)/(a-b)^2/d/(1+n)-1/4*(b*n+a+b)*hypergeom([1, 1+n],[2+n],(a+b*sec(d*x+c))/(a+b))*(a+b*sec(d*x+c))^(1+n)/(a+b)^2/d/(1+n)+1/2*cot(d*x+c)^2*(b-a*sec(d*x+c))*(a+b*sec(d*x+c))^(1+n)/(a^2-b^2)/d,1],
[(a+b*sec(d*x+c))^n*sin(d*x+c)^4,x,0,Defer(Int)((a+b*sec(d*x+c))^n*sin(d*x+c)^4,x),0],
[(a+b*sec(d*x+c))^n*sin(d*x+c)^2,x,0,Defer(Int)((a+b*sec(d*x+c))^n*sin(d*x+c)^2,x),0],
[csc(d*x+c)^2*(a+b*sec(d*x+c))^n,x,3,-cot(d*x+c)*(a+b*sec(d*x+c))^n/d+sqrt(2)*b*n*AppellF1(1/2,1/2,1-n,3/2,1/2-1/2*sec(d*x+c),b*(1-sec(d*x+c))/(a+b))*(a+b*sec(d*x+c))^(-1+n)*((a+b*sec(d*x+c))/(a+b))^(1-n)*tan(d*x+c)/d/sqrt(1+sec(d*x+c)),1],
[csc(d*x+c)^4*(a+b*sec(d*x+c))^n,x,-1,-3/2*AppellF1(-1/2,5/2,-n,1/2,1/2-1/2*sec(d*x+c),b*(1-sec(d*x+c))/(a+b))*cot(d*x+c)*sqrt(1+sec(d*x+c))*(a+b*sec(d*x+c))^n/sqrt(2)/d/(((a+b*sec(d*x+c))/(a+b))^n)-1/6*AppellF1(-3/2,5/2,-n,-1/2,1/2-1/2*sec(d*x+c),b*(1-sec(d*x+c))/(a+b))*cot(d*x+c)^3*(1+sec(d*x+c))^(3/2)*(a+b*sec(d*x+c))^n/sqrt(2)/d/(((a+b*sec(d*x+c))/(a+b))^n)+AppellF1(1/2,3/2,-n,3/2,1/2-1/2*sec(d*x+c),b*(1-sec(d*x+c))/(a+b))*(a+b*sec(d*x+c))^n*tan(d*x+c)/sqrt(2)/d/sqrt(1+sec(d*x+c))/(((a+b*sec(d*x+c))/(a+b))^n)+1/2*AppellF1(1/2,5/2,-n,3/2,1/2-1/2*sec(d*x+c),b*(1-sec(d*x+c))/(a+b))*(a+b*sec(d*x+c))^n*tan(d*x+c)/sqrt(2)/d/sqrt(1+sec(d*x+c))/(((a+b*sec(d*x+c))/(a+b))^n),1],
[(a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x,0,Defer(Int)((a+b*sec(d*x+c))^n*sin(d*x+c)^(3/2),x),0],
[(a+b*sec(d*x+c))^n*sqrt(sin(d*x+c)),x,0,Defer(Int)((a+b*sec(d*x+c))^n*sqrt(sin(d*x+c)),x),0],
[(a+b*sec(d*x+c))^n/sqrt(sin(d*x+c)),x,0,Defer(Int)((a+b*sec(d*x+c))^n/sqrt(sin(d*x+c)),x),0],
[(a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x,0,Defer(Int)((a+b*sec(d*x+c))^n/sin(d*x+c)^(3/2),x),0],
[(e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x,11,-2/3*a*e^2*cot(d*x+c)*sqrt(e*csc(d*x+c))/d-2/3*a*e^2*csc(d*x+c)*sqrt(e*csc(d*x+c))/d+a*e^2*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+a*e^2*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+2/3*a*e^2*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d,1],
[(e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x,11,-2*a*e*sqrt(e*csc(d*x+c))/d-2*a*e*cos(d*x+c)*sqrt(e*csc(d*x+c))/d-a*e*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+a*e*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d-2*a*e*sqrt(e*csc(d*x+c))*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(sin(d*x+c))/d,1],
[sqrt(e*csc(d*x+c))*(a+a*sec(d*x+c)),x,9,a*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+a*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+2*a*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d,1],
[(a+a*sec(d*x+c))/sqrt(e*csc(d*x+c)),x,9,-a*arctan(sqrt(sin(d*x+c)))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+a*arctanh(sqrt(sin(d*x+c)))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))/(e*csc(d*x+c))^(3/2),x,11,-2*a/d/e/sqrt(e*csc(d*x+c))-2/3*a*cos(d*x+c)/d/e/sqrt(e*csc(d*x+c))+a*arctan(sqrt(sin(d*x+c)))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+a*arctanh(sqrt(sin(d*x+c)))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))/(e*csc(d*x+c))^(5/2),x,11,-a*arctan(sqrt(sin(d*x+c)))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+a*arctanh(sqrt(sin(d*x+c)))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+6/5*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))-2/3*a*sin(d*x+c)/d/e^2/sqrt(e*csc(d*x+c))-2/5*a*cos(d*x+c)*sin(d*x+c)/d/e^2/sqrt(e*csc(d*x+c)),1],
[(e*csc(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x,15,-2/3*a^2*e^2*cot(d*x+c)*sqrt(e*csc(d*x+c))/d-4/3*a^2*e^2*csc(d*x+c)*sqrt(e*csc(d*x+c))/d-2/3*a^2*e^2*csc(d*x+c)*sqrt(e*csc(d*x+c))*sec(d*x+c)/d+2*a^2*e^2*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+2*a^2*e^2*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+7/3*a^2*e^2*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d+5/3*a^2*e^2*sqrt(e*csc(d*x+c))*tan(d*x+c)/d,1],
[(e*csc(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x,15,-4*a^2*e*sqrt(e*csc(d*x+c))/d-2*a^2*e*cos(d*x+c)*sqrt(e*csc(d*x+c))/d-2*a^2*e*sqrt(e*csc(d*x+c))*sec(d*x+c)/d-2*a^2*e*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+2*a^2*e*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d-5*a^2*e*sqrt(e*csc(d*x+c))*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(sin(d*x+c))/d+3*a^2*e*sqrt(e*csc(d*x+c))*sin(d*x+c)*tan(d*x+c)/d,1],
[sqrt(e*csc(d*x+c))*(a+a*sec(d*x+c))^2,x,12,2*a^2*arctan(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+2*a^2*arctanh(sqrt(sin(d*x+c)))*sqrt(e*csc(d*x+c))*sqrt(sin(d*x+c))/d+3*a^2*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d+a^2*sqrt(e*csc(d*x+c))*tan(d*x+c)/d,1],
[(a+a*sec(d*x+c))^2/sqrt(e*csc(d*x+c)),x,12,-2*a^2*arctan(sqrt(sin(d*x+c)))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2*a^2*arctanh(sqrt(sin(d*x+c)))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+a^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+a^2*tan(d*x+c)/d/sqrt(e*csc(d*x+c)),1],
[(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(3/2),x,14,-4*a^2/d/e/sqrt(e*csc(d*x+c))-2/3*a^2*cos(d*x+c)/d/e/sqrt(e*csc(d*x+c))+a^2*sec(d*x+c)/d/e/sqrt(e*csc(d*x+c))+2*a^2*arctan(sqrt(sin(d*x+c)))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2*a^2*arctanh(sqrt(sin(d*x+c)))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))-1/3*a^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[(a+a*sec(d*x+c))^2/(e*csc(d*x+c))^(5/2),x,14,-2*a^2*arctan(sqrt(sin(d*x+c)))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2*a^2*arctanh(sqrt(sin(d*x+c)))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))-9/5*a^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))-4/3*a^2*sin(d*x+c)/d/e^2/sqrt(e*csc(d*x+c))-2/5*a^2*cos(d*x+c)*sin(d*x+c)/d/e^2/sqrt(e*csc(d*x+c))+a^2*tan(d*x+c)/d/e^2/sqrt(e*csc(d*x+c)),1],
[(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x,8,-4/21*e^2*cot(d*x+c)*sqrt(e*csc(d*x+c))/a/d+2/7*e^2*cot(d*x+c)*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a/d-2/7*e^2*csc(d*x+c)^3*sqrt(e*csc(d*x+c))/a/d+4/21*e^2*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d,1],
[(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x,8,-4/5*e*cos(d*x+c)*sqrt(e*csc(d*x+c))/a/d+2/5*e*cot(d*x+c)*csc(d*x+c)*sqrt(e*csc(d*x+c))/a/d-2/5*e*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a/d-4/5*e*sqrt(e*csc(d*x+c))*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(sin(d*x+c))/a/d,1],
[sqrt(e*csc(d*x+c))/(a+a*sec(d*x+c)),x,7,2/3*cot(d*x+c)*sqrt(e*csc(d*x+c))/a/d-2/3*csc(d*x+c)*sqrt(e*csc(d*x+c))/a/d+4/3*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a/d,1],
[1/sqrt(e*csc(d*x+c))/(a+a*sec(d*x+c)),x,7,2*cot(d*x+c)/a/d/sqrt(e*csc(d*x+c))-2*csc(d*x+c)/a/d/sqrt(e*csc(d*x+c))+4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/a/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x,7,2/a/d/e/sqrt(e*csc(d*x+c))-2/3*cos(d*x+c)/a/d/e/sqrt(e*csc(d*x+c))-4/3*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/a/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x,7,-4/5*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/a/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2/3*sin(d*x+c)/a/d/e^2/sqrt(e*csc(d*x+c))-2/5*cos(d*x+c)*sin(d*x+c)/a/d/e^2/sqrt(e*csc(d*x+c)),1],
[1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x,8,-2/21*cos(d*x+c)/a/d/e^3/sqrt(e*csc(d*x+c))+2/7*cos(d*x+c)^3/a/d/e^3/sqrt(e*csc(d*x+c))-4/21*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/a/d/e^3/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+2/5*sin(d*x+c)^2/a/d/e^3/sqrt(e*csc(d*x+c)),1],
[(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x,16,-4/231*e^2*cot(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d+16/77*e^2*cot(d*x+c)*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a^2/d-2/11*e^2*cot(d*x+c)^3*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a^2/d-4/7*e^2*csc(d*x+c)^3*sqrt(e*csc(d*x+c))/a^2/d-2/11*e^2*cot(d*x+c)*csc(d*x+c)^4*sqrt(e*csc(d*x+c))/a^2/d+4/11*e^2*csc(d*x+c)^5*sqrt(e*csc(d*x+c))/a^2/d+4/231*e^2*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d,1],
[(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x,16,-4/15*e*cos(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d+16/45*e*cot(d*x+c)*csc(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d-2/9*e*cot(d*x+c)^3*csc(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d-4/5*e*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a^2/d-2/9*e*cot(d*x+c)*csc(d*x+c)^3*sqrt(e*csc(d*x+c))/a^2/d+4/9*e*csc(d*x+c)^4*sqrt(e*csc(d*x+c))/a^2/d-4/15*e*sqrt(e*csc(d*x+c))*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(sin(d*x+c))/a^2/d,1],
[sqrt(e*csc(d*x+c))/(a+a*sec(d*x+c))^2,x,14,16/21*cot(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d-2/7*cot(d*x+c)^3*sqrt(e*csc(d*x+c))/a^2/d-4/3*csc(d*x+c)*sqrt(e*csc(d*x+c))/a^2/d-2/7*cot(d*x+c)*csc(d*x+c)^2*sqrt(e*csc(d*x+c))/a^2/d+4/7*csc(d*x+c)^3*sqrt(e*csc(d*x+c))/a^2/d+20/21*sqrt(e*csc(d*x+c))*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/a^2/d,1],
[1/sqrt(e*csc(d*x+c))/(a+a*sec(d*x+c))^2,x,14,16/5*cot(d*x+c)/a^2/d/sqrt(e*csc(d*x+c))-2/5*cot(d*x+c)^3/a^2/d/sqrt(e*csc(d*x+c))-4*csc(d*x+c)/a^2/d/sqrt(e*csc(d*x+c))-2/5*cot(d*x+c)*csc(d*x+c)^2/a^2/d/sqrt(e*csc(d*x+c))+4/5*csc(d*x+c)^3/a^2/d/sqrt(e*csc(d*x+c))+28/5*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/a^2/d/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[1/(e*csc(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x,13,4/a^2/d/e/sqrt(e*csc(d*x+c))-4/3*cos(d*x+c)/a^2/d/e/sqrt(e*csc(d*x+c))-2/3*cos(d*x+c)*cot(d*x+c)^2/a^2/d/e/sqrt(e*csc(d*x+c))-2/3*cot(d*x+c)*csc(d*x+c)/a^2/d/e/sqrt(e*csc(d*x+c))+4/3*csc(d*x+c)^2/a^2/d/e/sqrt(e*csc(d*x+c))-4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/a^2/d/e/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c)),1],
[1/(e*csc(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x,13,-2*cot(d*x+c)/a^2/d/e^2/sqrt(e*csc(d*x+c))-2*cos(d*x+c)^2*cot(d*x+c)/a^2/d/e^2/sqrt(e*csc(d*x+c))+4*csc(d*x+c)/a^2/d/e^2/sqrt(e*csc(d*x+c))-44/5*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))/a^2/d/e^2/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+4/3*sin(d*x+c)/a^2/d/e^2/sqrt(e*csc(d*x+c))-12/5*cos(d*x+c)*sin(d*x+c)/a^2/d/e^2/sqrt(e*csc(d*x+c)),1],
[1/(e*csc(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x,13,-4/a^2/d/e^3/sqrt(e*csc(d*x+c))+26/21*cos(d*x+c)/a^2/d/e^3/sqrt(e*csc(d*x+c))+2/7*cos(d*x+c)^3/a^2/d/e^3/sqrt(e*csc(d*x+c))+52/21*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))/a^2/d/e^3/sqrt(e*csc(d*x+c))/sqrt(sin(d*x+c))+4/5*sin(d*x+c)^2/a^2/d/e^3/sqrt(e*csc(d*x+c)),1]]: