lst:=[[(a+I*a*cot(d*x+c))^n,x,2,1/2*I*(a+I*a*cot(d*x+c))^n*hypergeom([1, n],[1+n],1/2+1/2*I*cot(d*x+c))/d/n,1],
[(e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c)),x,5,-sqrt(2)*a*e^(5/2)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d+2*a*e^2*sqrt(e*cot(d*x+c))/d-2/3*a*e*(e*cot(d*x+c))^(3/2)/d-2/5*a*(e*cot(d*x+c))^(5/2)/d,1],
[(e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c)),x,4,-sqrt(2)*a*e^(3/2)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d-2*a*e*sqrt(e*cot(d*x+c))/d-2/3*a*(e*cot(d*x+c))^(3/2)/d,1],
[sqrt(e*cot(d*x+c))*(a+a*cot(d*x+c)),x,3,sqrt(2)*a*sqrt(e)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d-2*a*sqrt(e*cot(d*x+c))/d,1],
[(a+a*cot(d*x+c))/sqrt(e*cot(d*x+c)),x,2,sqrt(2)*a*arctan(sqrt(e)*(1-cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/sqrt(e),1],
[(a+a*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x,3,-sqrt(2)*a*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(3/2)+2*a/d/e/sqrt(e*cot(d*x+c)),1],
[(a+a*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x,4,-sqrt(2)*a*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(5/2)+2/3*a/d/e/(e*cot(d*x+c))^(3/2)+2*a/d/e^2/sqrt(e*cot(d*x+c)),1],
[(e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^2,x,15,sqrt(2)*a^2*e^(5/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d-sqrt(2)*a^2*e^(5/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d-sqrt(2)*a^2*e^(5/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d+4*a^2*e^2*sqrt(e*cot(d*x+c))/d-4/5*a^2*(e*cot(d*x+c))^(5/2)/d-2/7*a^2*(e*cot(d*x+c))^(7/2)/d/e,1],
[(e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^2,x,14,-sqrt(2)*a^2*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d+sqrt(2)*a^2*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d-sqrt(2)*a^2*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d-4/3*a^2*(e*cot(d*x+c))^(3/2)/d-2/5*a^2*(e*cot(d*x+c))^(5/2)/d/e,1],
[sqrt(e*cot(d*x+c))*(a+a*cot(d*x+c))^2,x,14,-sqrt(2)*a^2*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d+sqrt(2)*a^2*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d+sqrt(2)*a^2*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d-4*a^2*sqrt(e*cot(d*x+c))/d-2/3*a^2*(e*cot(d*x+c))^(3/2)/d/e,1],
[(a+a*cot(d*x+c))^2/sqrt(e*cot(d*x+c)),x,13,sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/sqrt(e)-sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/sqrt(e)+sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d/sqrt(e)-2*a^2*sqrt(e*cot(d*x+c))/d/e,1],
[(a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x,12,sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(3/2)-sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(3/2)-sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d/e^(3/2)+2*a^2/d/e/sqrt(e*cot(d*x+c)),1],
[(a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x,13,-sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(5/2)+sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(5/2)-sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d/e^(5/2)+2/3*a^2/d/e/(e*cot(d*x+c))^(3/2)+4*a^2/d/e^2/sqrt(e*cot(d*x+c)),1],
[(a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x,13,-sqrt(2)*a^2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(7/2)+sqrt(2)*a^2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/d/e^(7/2)+sqrt(2)*a^2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/d/e^(7/2)+2/5*a^2/d/e/(e*cot(d*x+c))^(5/2)+4/3*a^2/d/e^2/(e*cot(d*x+c))^(3/2),1],
[(e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^3,x,7,2*sqrt(2)*a^3*e^(5/2)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d+4*a^3*e^2*sqrt(e*cot(d*x+c))/d+4/3*a^3*e*(e*cot(d*x+c))^(3/2)/d-4/5*a^3*(e*cot(d*x+c))^(5/2)/d-40/63*a^3*(e*cot(d*x+c))^(7/2)/d/e-2/9*(e*cot(d*x+c))^(7/2)*(a^3+a^3*cot(d*x+c))/d/e,1],
[(e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^3,x,6,-2*sqrt(2)*a^3*e^(3/2)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d+4*a^3*e*sqrt(e*cot(d*x+c))/d-4/3*a^3*(e*cot(d*x+c))^(3/2)/d-32/35*a^3*(e*cot(d*x+c))^(5/2)/d/e-2/7*(e*cot(d*x+c))^(5/2)*(a^3+a^3*cot(d*x+c))/d/e,1],
[sqrt(e*cot(d*x+c))*(a+a*cot(d*x+c))^3,x,5,-2*sqrt(2)*a^3*sqrt(e)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d-4*a^3*sqrt(e*cot(d*x+c))/d-8/5*a^3*(e*cot(d*x+c))^(3/2)/d/e-2/5*(e*cot(d*x+c))^(3/2)*(a^3+a^3*cot(d*x+c))/d/e,1],
[(a+a*cot(d*x+c))^3/sqrt(e*cot(d*x+c)),x,4,2*sqrt(2)*a^3*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/sqrt(e)-16/3*a^3*sqrt(e*cot(d*x+c))/d/e-2/3*sqrt(e*cot(d*x+c))*(a^3+a^3*cot(d*x+c))/d/e,1],
[(a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x,4,2*sqrt(2)*a^3*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(3/2)-4*a^3*sqrt(e*cot(d*x+c))/d/e^2+2*(a^3+a^3*cot(d*x+c))/d/e/sqrt(e*cot(d*x+c)),1],
[(a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x,4,-2*sqrt(2)*a^3*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(5/2)+16/3*a^3/d/e^2/sqrt(e*cot(d*x+c))+2/3*(a^3+a^3*cot(d*x+c))/d/e/(e*cot(d*x+c))^(3/2),1],
[(a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x,5,-2*sqrt(2)*a^3*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(7/2)+8/5*a^3/d/e^2/(e*cot(d*x+c))^(3/2)+4*a^3/d/e^3/sqrt(e*cot(d*x+c))+2/5*(a^3+a^3*cot(d*x+c))/d/e/(e*cot(d*x+c))^(5/2),1],
[(a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x,6,2*sqrt(2)*a^3*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/d/e^(9/2)+32/35*a^3/d/e^2/(e*cot(d*x+c))^(5/2)+4/3*a^3/d/e^3/(e*cot(d*x+c))^(3/2)-4*a^3/d/e^4/sqrt(e*cot(d*x+c))+2/7*(a^3+a^3*cot(d*x+c))/d/e/(e*cot(d*x+c))^(7/2),1],
[(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x,7,e^(5/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d-e^(5/2)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d-2*e^2*sqrt(e*cot(d*x+c))/a/d,1],
[(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x,6,-e^(3/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d+e^(3/2)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d,1],
[sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c)),x,6,sqrt(e)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d+sqrt(e)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d,1],
[1/sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c)),x,6,-arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d/sqrt(e)-arctanh(sqrt(e)*(1+cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d/sqrt(e),1],
[1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x,7,arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d/e^(3/2)-arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d/e^(3/2)+2/a/d/e/sqrt(e*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x,10,-arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a/d/e^(5/2)+arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a/d/e^(5/2)+2/3/a/d/e/(e*cot(d*x+c))^(3/2)-2/a/d/e^2/sqrt(e*cot(d*x+c)),1],
[(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x,16,-3/2*e^(5/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d-1/2*e^(5/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d+1/2*e^(5/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d+1/2*e^(5/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d+1/2*e^2*sqrt(e*cot(d*x+c))/d/(a^2+a^2*cot(d*x+c)),1],
[(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x,17,1/2*e^(3/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d+1/2*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d-1/2*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d+1/2*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d-1/2*e*sqrt(e*cot(d*x+c))/d/(a^2+a^2*cot(d*x+c)),1],
[sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c))^2,x,16,1/2*sqrt(e)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d+1/2*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d-1/2*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d-1/2*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d+1/2*sqrt(e*cot(d*x+c))/d/(a^2+a^2*cot(d*x+c)),1],
[1/sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c))^2,x,17,-3/2*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d/sqrt(e)-1/2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/sqrt(e)+1/2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/sqrt(e)-1/2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d/sqrt(e)-1/2*sqrt(e*cot(d*x+c))/d/e/(a^2+a^2*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x,17,5/2*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d/e^(3/2)-1/2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/e^(3/2)+1/2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/e^(3/2)+1/2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d/e^(3/2)+5/2/a^2/d/e/sqrt(e*cot(d*x+c))-1/2/d/e/sqrt(e*cot(d*x+c))/(a^2+a^2*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x,19,-7/2*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^2/d/e^(5/2)+1/2*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/e^(5/2)-1/2*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/a^2/d/e^(5/2)+1/2*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/a^2/d/e^(5/2)+7/6/a^2/d/e/(e*cot(d*x+c))^(3/2)-9/2/a^2/d/e^2/sqrt(e*cot(d*x+c))-1/2/d/e/(e*cot(d*x+c))^(3/2)/(a^2+a^2*cot(d*x+c)),1],
[(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x,8,-1/8*e^(5/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d+1/2*e^(5/2)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d-5/8*e^2*sqrt(e*cot(d*x+c))/a^3/d/(1+cot(d*x+c))+1/4*e^2*sqrt(e*cot(d*x+c))/a/d/(a+a*cot(d*x+c))^2,1],
[(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x,8,5/8*e^(3/2)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d+1/2*e^(3/2)*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d-1/4*e*sqrt(e*cot(d*x+c))/a/d/(a+a*cot(d*x+c))^2+1/8*e*sqrt(e*cot(d*x+c))/d/(a^3+a^3*cot(d*x+c)),1],
[sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c))^3,x,8,-1/8*sqrt(e)*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d-1/2*sqrt(e)*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d+1/4*sqrt(e*cot(d*x+c))/a/d/(a+a*cot(d*x+c))^2+3/8*sqrt(e*cot(d*x+c))/d/(a^3+a^3*cot(d*x+c)),1],
[1/sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c))^3,x,8,-11/8*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d/sqrt(e)-1/2*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d/sqrt(e)-7/8*sqrt(e*cot(d*x+c))/a^3/d/e/(1+cot(d*x+c))-1/4*sqrt(e*cot(d*x+c))/a/d/e/(a+a*cot(d*x+c))^2,1],
[1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x,9,31/8*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d/e^(3/2)+1/2*arctanh((sqrt(e)+sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d/e^(3/2)+27/8/a^3/d/e/sqrt(e*cot(d*x+c))-9/8/a^3/d/e/sqrt(e*cot(d*x+c))/(1+cot(d*x+c))-1/4/a/d/e/sqrt(e*cot(d*x+c))/(a+a*cot(d*x+c))^2,1],
[1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x,10,-59/8*arctan(sqrt(e*cot(d*x+c))/sqrt(e))/a^3/d/e^(5/2)+1/2*arctan((sqrt(e)-sqrt(e)*cot(d*x+c))/sqrt(2)/sqrt(e*cot(d*x+c)))/sqrt(2)/a^3/d/e^(5/2)+55/24/a^3/d/e/(e*cot(d*x+c))^(3/2)-63/8/a^3/d/e^2/sqrt(e*cot(d*x+c))-11/8/a^3/d/e/(e*cot(d*x+c))^(3/2)/(1+cot(d*x+c))-1/4/a/d/e/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,1],
[cot(x)^2*sqrt(1+cot(x)),x,11,-sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))-arctanh(sqrt(2+2*sqrt(2))*sqrt(1+cot(x))/(1+sqrt(2)+cot(x)))/sqrt(2+2*sqrt(2))-2/3*(1+cot(x))^(3/2),1],
[cot(x)*sqrt(1+cot(x)),x,6,sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*cot(x))/sqrt(-7+5*sqrt(2))/sqrt(1+cot(x)))+sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*cot(x))/sqrt(7+5*sqrt(2))/sqrt(1+cot(x)))-2*sqrt(1+cot(x)),1],
[cot(x)^2*(1+cot(x))^(3/2),x,8,-sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*cot(x))/sqrt(-14+10*sqrt(2))/sqrt(1+cot(x)))-sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*cot(x))/sqrt(14+10*sqrt(2))/sqrt(1+cot(x)))+2*sqrt(1+cot(x))-2/5*(1+cot(x))^(5/2),1],
[cot(x)*(1+cot(x))^(3/2),x,13,-sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+arctanh(sqrt(2+2*sqrt(2))*sqrt(1+cot(x))/(1+sqrt(2)+cot(x)))/sqrt(1+sqrt(2))-2*sqrt(1+cot(x))-2/3*(1+cot(x))^(3/2),1],
[cot(x)^2/sqrt(1+cot(x)),x,11,-1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+1/2*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+cot(x))/(1+sqrt(2)+cot(x)))/sqrt(1+sqrt(2))-2*sqrt(1+cot(x)),1],
[cot(x)/sqrt(1+cot(x)),x,5,1/2*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*cot(x))/sqrt(-14+10*sqrt(2))/sqrt(1+cot(x)))+1/2*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*cot(x))/sqrt(14+10*sqrt(2))/sqrt(1+cot(x))),1],
[cot(x)^2/(1+cot(x))^(3/2),x,6,1/2*sqrt(-1/2+1/2*sqrt(2))*arctan(1/2*(4-3*sqrt(2)+(2-sqrt(2))*cot(x))/sqrt(-7+5*sqrt(2))/sqrt(1+cot(x)))+1/2*sqrt(1/2+1/2*sqrt(2))*arctanh(1/2*(4+3*sqrt(2)+(2+sqrt(2))*cot(x))/sqrt(7+5*sqrt(2))/sqrt(1+cot(x)))+1/sqrt(1+cot(x)),1],
[cot(x)/(1+cot(x))^(3/2),x,12,1/2*sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))-1/2*sqrt(1/2+1/2*sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))+1/2*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+cot(x))/(1+sqrt(2)+cot(x)))/sqrt(2+2*sqrt(2))-1/sqrt(1+cot(x)),1],
[cot(x)^2/(1+cot(x))^(5/2),x,8,1/4*sqrt(-1+sqrt(2))*arctan((3-2*sqrt(2)+(1-sqrt(2))*cot(x))/sqrt(-14+10*sqrt(2))/sqrt(1+cot(x)))+1/4*sqrt(1+sqrt(2))*arctanh((3+2*sqrt(2)+(1+sqrt(2))*cot(x))/sqrt(14+10*sqrt(2))/sqrt(1+cot(x)))+1/3/(1+cot(x))^(3/2)-1/sqrt(1+cot(x)),1],
[cot(x)/(1+cot(x))^(5/2),x,12,1/4*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))-2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))-1/4*sqrt(1+sqrt(2))*arctan((sqrt(2+2*sqrt(2))+2*sqrt(1+cot(x)))/sqrt(-2+2*sqrt(2)))-1/4*arctanh(sqrt(2+2*sqrt(2))*sqrt(1+cot(x))/(1+sqrt(2)+cot(x)))/sqrt(1+sqrt(2))-1/3/(1+cot(x))^(3/2),1],
[(e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c)),x,11,-(a+b)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a+b)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a-b)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-2*a*e*sqrt(e*cot(d*x+c))/d-2/3*b*(e*cot(d*x+c))^(3/2)/d,1],
[sqrt(e*cot(d*x+c))*(a+b*cot(d*x+c)),x,10,(a-b)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d-(a-b)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a+b)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-2*b*sqrt(e*cot(d*x+c))/d,1],
[(a+b*cot(d*x+c))/sqrt(e*cot(d*x+c)),x,9,(a+b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a+b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a-b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/sqrt(e),1],
[(a+b*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x,10,-(a-b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)+(a-b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)-(a+b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(3/2)+2*a/d/e/sqrt(e*cot(d*x+c)),1],
[(a+b*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x,11,-(a+b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a+b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a-b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(5/2)+2/3*a/d/e/(e*cot(d*x+c))^(3/2)+2*b/d/e^2/sqrt(e*cot(d*x+c)),1],
[(e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^2,x,12,-(a^2+2*a*b-b^2)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a^2+2*a*b-b^2)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a^2-2*a*b-b^2)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-2*(a^2-b^2)*e*sqrt(e*cot(d*x+c))/d-4/3*a*b*(e*cot(d*x+c))^(3/2)/d-2/5*b^2*(e*cot(d*x+c))^(5/2)/d/e,1],
[sqrt(e*cot(d*x+c))*(a+b*cot(d*x+c))^2,x,11,(a^2-2*a*b-b^2)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d-(a^2-2*a*b-b^2)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a^2+2*a*b-b^2)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-4*a*b*sqrt(e*cot(d*x+c))/d-2/3*b^2*(e*cot(d*x+c))^(3/2)/d/e,1],
[(a+b*cot(d*x+c))^2/sqrt(e*cot(d*x+c)),x,10,(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/sqrt(e)-2*b^2*sqrt(e*cot(d*x+c))/d/e,1],
[(a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x,10,-(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)+(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(3/2)+2*a^2/d/e/sqrt(e*cot(d*x+c)),1],
[(a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x,11,-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(5/2)+2/3*a^2/d/e/(e*cot(d*x+c))^(3/2)+4*a*b/d/e^2/sqrt(e*cot(d*x+c)),1],
[(a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x,12,(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(7/2)-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(7/2)+(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(7/2)+2/5*a^2/d/e/(e*cot(d*x+c))^(5/2)+4/3*a*b/d/e^2/(e*cot(d*x+c))^(3/2)-2*(a^2-b^2)/d/e^3/sqrt(e*cot(d*x+c)),1],
[(e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^3,x,13,-(a-b)*(a^2+4*a*b+b^2)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a+b)*(a^2-4*a*b+b^2)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-2*a*(a^2-3*b^2)*e*sqrt(e*cot(d*x+c))/d-2/3*b*(3*a^2-b^2)*(e*cot(d*x+c))^(3/2)/d-32/35*a*b^2*(e*cot(d*x+c))^(5/2)/d/e-2/7*b^2*(e*cot(d*x+c))^(5/2)*(a+b*cot(d*x+c))/d/e,1],
[sqrt(e*cot(d*x+c))*(a+b*cot(d*x+c))^3,x,12,(a+b)*(a^2-4*a*b+b^2)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d-(a+b)*(a^2-4*a*b+b^2)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d+(a-b)*(a^2+4*a*b+b^2)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d-2*b*(3*a^2-b^2)*sqrt(e*cot(d*x+c))/d-8/5*a*b^2*(e*cot(d*x+c))^(3/2)/d/e-2/5*b^2*(e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))/d/e,1],
[(a+b*cot(d*x+c))^3/sqrt(e*cot(d*x+c)),x,11,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/sqrt(e)-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/sqrt(e)-16/3*a*b^2*sqrt(e*cot(d*x+c))/d/e-2/3*b^2*sqrt(e*cot(d*x+c))*(a+b*cot(d*x+c))/d/e,1],
[(a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x,11,-(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)+(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(3/2)-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(3/2)-2*b*(a^2+b^2)*sqrt(e*cot(d*x+c))/d/e^2+2*a^2*(a+b*cot(d*x+c))/d/e/sqrt(e*cot(d*x+c)),1],
[(a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x,11,-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(5/2)+(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(5/2)+16/3*a^2*b/d/e^2/sqrt(e*cot(d*x+c))+2/3*a^2*(a+b*cot(d*x+c))/d/e/(e*cot(d*x+c))^(3/2),1],
[(a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x,12,(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(7/2)-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(7/2)+(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(7/2)+8/5*a^2*b/d/e^2/(e*cot(d*x+c))^(3/2)-2*a*(a^2-3*b^2)/d/e^3/sqrt(e*cot(d*x+c))+2/5*a^2*(a+b*cot(d*x+c))/d/e/(e*cot(d*x+c))^(5/2),1],
[(a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x,13,(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(9/2)-(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/d/e^(9/2)-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/d/e^(9/2)+32/35*a^2*b/d/e^2/(e*cot(d*x+c))^(5/2)-2/3*a*(a^2-3*b^2)/d/e^3/(e*cot(d*x+c))^(3/2)-2*b*(3*a^2-b^2)/d/e^4/sqrt(e*cot(d*x+c))+2/7*a^2*(a+b*cot(d*x+c))/d/e/(e*cot(d*x+c))^(7/2),1],
[(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x,14,2*a^(5/2)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(3/2)/(a^2+b^2)/d-(a+b)*e^(5/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d+(a+b)*e^(5/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d-(a-b)*e^(5/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d-2*e^2*sqrt(e*cot(d*x+c))/b/d,1],
[(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x,13,-2*a^(3/2)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/sqrt(b)/(a^2+b^2)/d-(a-b)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d+(a-b)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d+(a+b)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c)),x,13,2*sqrt(a)*sqrt(b)*sqrt(e)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/(a^2+b^2)/d+(a+b)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d-(a+b)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d+(a-b)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d,1],
[1/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c)),x,13,-2*b^(3/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/sqrt(a)/(a^2+b^2)/d/sqrt(e)+(a-b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/sqrt(e)-(a-b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/sqrt(e)-(a+b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d/sqrt(e),1],
[1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x,14,2*b^(5/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(3/2)/(a^2+b^2)/d/e^(3/2)-(a+b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/e^(3/2)+(a+b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/e^(3/2)-(a-b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d/e^(3/2)+2/a/d/e/sqrt(e*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x,15,-2*b^(7/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(5/2)/(a^2+b^2)/d/e^(5/2)-(a-b)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/e^(5/2)+(a-b)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)/d/e^(5/2)+(a+b)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)/d/e^(5/2)+2/3/a/d/e/(e*cot(d*x+c))^(3/2)-2*b/a^2/d/e^2/sqrt(e*cot(d*x+c)),1],
[(e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^2,x,15,a^(5/2)*(3*a^2+7*b^2)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(5/2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*e^(7/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*e^(7/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*e^(7/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-(3*a^2+2*b^2)*e^3*sqrt(e*cot(d*x+c))/b^2/(a^2+b^2)/d+a^2*e^2*(e*cot(d*x+c))^(3/2)/b/(a^2+b^2)/d/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^2,x,14,-a^(3/2)*(a^2+5*b^2)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(3/2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*e^(5/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*e^(5/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*e^(5/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+a^2*e^2*sqrt(e*cot(d*x+c))/b/(a^2+b^2)/d/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x,14,-sqrt(a)*(a^2-3*b^2)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/sqrt(b)/(a^2+b^2)^2/d-(a^2-2*a*b-b^2)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d-a*e*sqrt(e*cot(d*x+c))/(a^2+b^2)/d/(a+b*cot(d*x+c)),1],
[sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c))^2,x,14,sqrt(b)*(3*a^2-b^2)*sqrt(e)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/sqrt(a)/(a^2+b^2)^2/d+(a^2+2*a*b-b^2)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d-(a^2+2*a*b-b^2)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d+(a^2-2*a*b-b^2)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d+b*sqrt(e*cot(d*x+c))/(a^2+b^2)/d/(a+b*cot(d*x+c)),1],
[1/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c))^2,x,14,-b^(3/2)*(5*a^2+b^2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(3/2)/(a^2+b^2)^2/d/sqrt(e)+(a^2-2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d/sqrt(e)-(a^2-2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d/sqrt(e)-(a^2+2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d/sqrt(e)-b^2*sqrt(e*cot(d*x+c))/a/(a^2+b^2)/d/e/(a+b*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x,15,b^(5/2)*(7*a^2+3*b^2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(5/2)/(a^2+b^2)^2/d/e^(3/2)-(a^2+2*a*b-b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d/e^(3/2)+(a^2+2*a*b-b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^2/d/e^(3/2)-(a^2-2*a*b-b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^2/d/e^(3/2)+(2*a^2+3*b^2)/a^2/(a^2+b^2)/d/e/sqrt(e*cot(d*x+c))-b^2/a/(a^2+b^2)/d/e/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(9/2)/(a+b*cot(d*x+c))^3,x,16,1/4*a^(5/2)*(15*a^4+46*a^2*b^2+63*b^4)*e^(9/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(7/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*e^(9/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*e^(9/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*e^(9/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/4*(15*a^4+31*a^2*b^2+8*b^4)*e^4*sqrt(e*cot(d*x+c))/b^3/(a^2+b^2)^2/d+1/2*a^2*e^2*(e*cot(d*x+c))^(5/2)/b/(a^2+b^2)/d/(a+b*cot(d*x+c))^2+1/4*a^2*(5*a^2+13*b^2)*e^3*(e*cot(d*x+c))^(3/2)/b^2/(a^2+b^2)^2/d/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^3,x,15,-1/4*a^(3/2)*(3*a^4+6*a^2*b^2+35*b^4)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(5/2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*e^(7/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*e^(7/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*e^(7/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*a^2*e^2*(e*cot(d*x+c))^(3/2)/b/(a^2+b^2)/d/(a+b*cot(d*x+c))^2+1/4*a^2*(3*a^2+11*b^2)*e^3*sqrt(e*cot(d*x+c))/b^2/(a^2+b^2)^2/d/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^3,x,15,-1/4*sqrt(a)*(a^4+18*a^2*b^2-15*b^4)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/b^(3/2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*e^(5/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*e^(5/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*e^(5/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*a^2*e^2*sqrt(e*cot(d*x+c))/b/(a^2+b^2)/d/(a+b*cot(d*x+c))^2-1/4*a*(a^2+9*b^2)*e^2*sqrt(e*cot(d*x+c))/b/(a^2+b^2)^2/d/(a+b*cot(d*x+c)),1],
[(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x,15,-1/4*(3*a^4-26*a^2*b^2+3*b^4)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/sqrt(a)/sqrt(b)/(a^2+b^2)^3/d-(a+b)*(a^2-4*a*b+b^2)*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*e^(3/2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d-1/2*a*e*sqrt(e*cot(d*x+c))/(a^2+b^2)/d/(a+b*cot(d*x+c))^2-1/4*(3*a^2-5*b^2)*e*sqrt(e*cot(d*x+c))/(a^2+b^2)^2/d/(a+b*cot(d*x+c)),1],
[sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c))^3,x,15,1/4*sqrt(b)*(15*a^4-18*a^2*b^2-b^4)*sqrt(e)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(3/2)/(a^2+b^2)^3/d+(a-b)*(a^2+4*a*b+b^2)*sqrt(e)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d-(a-b)*(a^2+4*a*b+b^2)*sqrt(e)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d+(a+b)*(a^2-4*a*b+b^2)*sqrt(e)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d+1/2*b*sqrt(e*cot(d*x+c))/(a^2+b^2)/d/(a+b*cot(d*x+c))^2+1/4*b*(7*a^2-b^2)*sqrt(e*cot(d*x+c))/a/(a^2+b^2)^2/d/(a+b*cot(d*x+c)),1],
[1/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c))^3,x,15,-1/4*b^(3/2)*(35*a^4+6*a^2*b^2+3*b^4)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(5/2)/(a^2+b^2)^3/d/sqrt(e)+(a+b)*(a^2-4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d/sqrt(e)-(a+b)*(a^2-4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d/sqrt(e)-(a-b)*(a^2+4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d/sqrt(e)-1/2*b^2*sqrt(e*cot(d*x+c))/a/(a^2+b^2)/d/e/(a+b*cot(d*x+c))^2-1/4*b^2*(11*a^2+3*b^2)*sqrt(e*cot(d*x+c))/a^2/(a^2+b^2)^2/d/e/(a+b*cot(d*x+c)),1],
[1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x,16,1/4*b^(5/2)*(63*a^4+46*a^2*b^2+15*b^4)*arctan(sqrt(b)*sqrt(e*cot(d*x+c))/sqrt(a)/sqrt(e))/a^(7/2)/(a^2+b^2)^3/d/e^(3/2)-(a-b)*(a^2+4*a*b+b^2)*arctan(1-sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d/e^(3/2)+(a-b)*(a^2+4*a*b+b^2)*arctan(1+sqrt(2)*sqrt(e*cot(d*x+c))/sqrt(e))/sqrt(2)/(a^2+b^2)^3/d/e^(3/2)-(a+b)*(a^2-4*a*b+b^2)*arctanh(sqrt(2)*sqrt(e*cot(d*x+c))/(sqrt(e)+sqrt(e)*cot(d*x+c)))/sqrt(2)/(a^2+b^2)^3/d/e^(3/2)+1/4*(8*a^4+31*a^2*b^2+15*b^4)/a^3/(a^2+b^2)^2/d/e/sqrt(e*cot(d*x+c))-1/2*b^2/a/(a^2+b^2)/d/e/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c))^2-1/4*b^2*(13*a^2+5*b^2)/a^2/(a^2+b^2)^2/d/e/sqrt(e*cot(d*x+c))/(a+b*cot(d*x+c)),1],
[(a+b*cot(d*x+c))^n,x,5,-1/2*b*(a+b*cot(d*x+c))^(1+n)*hypergeom([1, 1+n],[2+n],(a+b*cot(d*x+c))/(a-sqrt(-b^2)))/sqrt(-b^2)/(a-sqrt(-b^2))/d/(1+n)+1/2*b*(a+b*cot(d*x+c))^(1+n)*hypergeom([1, 1+n],[2+n],(a+b*cot(d*x+c))/(a+sqrt(-b^2)))/sqrt(-b^2)/(a+sqrt(-b^2))/d/(1+n),1],
[(a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n,x,8,-1/2*AppellF1(1-n,-m,1,2-n,-b*cot(f*x+e)/a,-I*cot(f*x+e))*cot(f*x+e)*(a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n/f/(1-n)/(((a+b*cot(f*x+e))/a)^m)-1/2*AppellF1(1-n,-m,1,2-n,-b*cot(f*x+e)/a,I*cot(f*x+e))*cot(f*x+e)*(a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n/f/(1-n)/(((a+b*cot(f*x+e))/a)^m),1],
[(1+I*cot(d*x+c))/sqrt(a+b*cot(d*x+c)),x,3,2*I*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d,1],
[(1-I*cot(d*x+c))/sqrt(a+b*cot(d*x+c)),x,3,-2*I*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d,1],
[(A+B*cot(d*x+c))/(a+b*cot(d*x+c)),x,2,(A*a+B*b)*x/(a^2+b^2)-(A*b-B*a)*ln(b*cos(d*x+c)+a*sin(d*x+c))/(a^2+b^2)/d,1],
[(A+B*cot(d*x+c))/(a+b*cot(d*x+c))^2,x,3,(A*a^2-A*b^2+2*B*a*b)*x/(a^2+b^2)^2+(A*b-B*a)/(a^2+b^2)/d/(a+b*cot(d*x+c))-(2*A*a*b-B*a^2+B*b^2)*ln(b*cos(d*x+c)+a*sin(d*x+c))/(a^2+b^2)^2/d,1],
[(A+B*cot(d*x+c))/(a+b*cot(d*x+c))^3,x,4,(A*a^3-3*A*a*b^2+3*B*a^2*b-B*b^3)*x/(a^2+b^2)^3+1/2*(A*b-B*a)/(a^2+b^2)/d/(a+b*cot(d*x+c))^2+(2*A*a*b-B*a^2+B*b^2)/(a^2+b^2)^2/d/(a+b*cot(d*x+c))-(3*A*a^2*b-A*b^3-B*a^3+3*B*a*b^2)*ln(b*cos(d*x+c)+a*sin(d*x+c))/(a^2+b^2)^3/d,1],
[(a+b*cot(d*x+c))^(5/2)*(A+B*cot(d*x+c)),x,10,(a-I*b)^(5/2)*(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(5/2)*(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/d-2*(2*A*a*b+B*a^2-B*b^2)*sqrt(a+b*cot(d*x+c))/d-2/3*(A*b+B*a)*(a+b*cot(d*x+c))^(3/2)/d-2/5*B*(a+b*cot(d*x+c))^(5/2)/d,1],
[(a+b*cot(d*x+c))^(3/2)*(A+B*cot(d*x+c)),x,9,(a-I*b)^(3/2)*(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/d-(a+I*b)^(3/2)*(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/d-2*(A*b+B*a)*sqrt(a+b*cot(d*x+c))/d-2/3*B*(a+b*cot(d*x+c))^(3/2)/d,1],
[sqrt(a+b*cot(d*x+c))*(A+B*cot(d*x+c)),x,8,sqrt(a-I*b)*(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/d-sqrt(a+I*b)*(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/d-2*B*sqrt(a+b*cot(d*x+c))/d,1],
[(-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(5/2),x,10,-(I*a-b)*(a-I*b)^(5/2)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/d+(a+I*b)^(5/2)*(I*a+b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/d+2*b*(a^2+b^2)*sqrt(a+b*cot(d*x+c))/d-2/5*b*(a+b*cot(d*x+c))^(5/2)/d,1],
[(-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(3/2),x,12,-b*(a^2+b^2)*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*cot(d*x+c))/(a+sqrt(a^2+b^2)+b*cot(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d+b*(a^2+b^2)*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*cot(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-b*(a^2+b^2)*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*cot(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-2/3*b*(a+b*cot(d*x+c))^(3/2)/d,1],
[(-a+b*cot(d*x+c))*sqrt(a+b*cot(d*x+c)),x,12,b*sqrt(a^2+b^2)*arctanh(sqrt(2)*sqrt(a+sqrt(a^2+b^2))*sqrt(a+b*cot(d*x+c))/(a+sqrt(a^2+b^2)+b*cot(d*x+c)))/sqrt(2)/sqrt(a+sqrt(a^2+b^2))/d+b*sqrt(a^2+b^2)*arctanh((sqrt(a+sqrt(a^2+b^2))-sqrt(2)*sqrt(a+b*cot(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-b*sqrt(a^2+b^2)*arctanh((sqrt(a+sqrt(a^2+b^2))+sqrt(2)*sqrt(a+b*cot(d*x+c)))/sqrt(a-sqrt(a^2+b^2)))/sqrt(2)/sqrt(a-sqrt(a^2+b^2))/d-2*b*sqrt(a+b*cot(d*x+c))/d,1],
[(A+B*cot(d*x+c))/sqrt(a+b*cot(d*x+c)),x,7,(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d-(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d,1],
[(A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x,8,(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d-(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d+2*(A*b-B*a)/(a^2+b^2)/d/sqrt(a+b*cot(d*x+c)),1],
[(A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x,9,(I*A+B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d-(I*A-B)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d+2/3*(A*b-B*a)/(a^2+b^2)/d/(a+b*cot(d*x+c))^(3/2)+2*(2*A*a*b-B*a^2+B*b^2)/(a^2+b^2)^2/d/sqrt(a+b*cot(d*x+c)),1],
[(-a+b*cot(d*x+c))/sqrt(a+b*cot(d*x+c)),x,7,-(I*a-b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/sqrt(a-I*b)/d+(I*a+b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/sqrt(a+I*b)/d,1],
[(-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x,8,-(I*a-b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/(a-I*b)^(3/2)/d+(I*a+b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/(a+I*b)^(3/2)/d-4*a*b/(a^2+b^2)/d/sqrt(a+b*cot(d*x+c)),1],
[(-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x,9,-(I*a-b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a-I*b))/(a-I*b)^(5/2)/d+(I*a+b)*arctanh(sqrt(a+b*cot(d*x+c))/sqrt(a+I*b))/(a+I*b)^(5/2)/d-4/3*a*b/(a^2+b^2)/d/(a+b*cot(d*x+c))^(3/2)-2*b*(3*a^2-b^2)/(a^2+b^2)^2/d/sqrt(a+b*cot(d*x+c)),1]]: