lst:=[[(a+b*csc(d*x+c)^2)^4,x,4,a^4*x-b*(2*a+b)*(2*a^2+2*a*b+b^2)*cot(d*x+c)/d-1/3*b^2*(6*a^2+8*a*b+3*b^2)*cot(d*x+c)^3/d-1/5*b^3*(4*a+3*b)*cot(d*x+c)^5/d-1/7*b^4*cot(d*x+c)^7/d,1],
[(a+b*csc(d*x+c)^2)^3,x,4,a^3*x-b*(3*a^2+3*a*b+b^2)*cot(d*x+c)/d-1/3*b^2*(3*a+2*b)*cot(d*x+c)^3/d-1/5*b^3*cot(d*x+c)^5/d,1],
[(a+b*csc(d*x+c)^2)^2,x,4,a^2*x-b*(2*a+b)*cot(d*x+c)/d-1/3*b^2*cot(d*x+c)^3/d,1],
[a+b*csc(d*x+c)^2,x,3,a*x-b*cot(d*x+c)/d,1],
[1/(a+b*csc(d*x+c)^2),x,3,x/a-sqrt(b)*arctan(sqrt(a+b)*tan(d*x+c)/sqrt(b))/a/sqrt(a+b)/d,1],
[1/(a+b*csc(d*x+c)^2)^2,x,5,x/a^2+1/2*sqrt(b)*(3*a+2*b)*arctan(sqrt(b)*cot(d*x+c)/sqrt(a+b))/a^2/(a+b)^(3/2)/d+1/2*b*cot(d*x+c)/a/(a+b)/d/(a+b+b*cot(d*x+c)^2),1],
[1/(a+b*csc(d*x+c)^2)^3,x,6,x/a^3+1/8*sqrt(b)*(15*a^2+20*a*b+8*b^2)*arctan(sqrt(b)*cot(d*x+c)/sqrt(a+b))/a^3/(a+b)^(5/2)/d+1/4*b*cot(d*x+c)/a/(a+b)/d/(a+b+b*cot(d*x+c)^2)^2+1/8*b*(7*a+4*b)*cot(d*x+c)/a^2/(a+b)^2/d/(a+b+b*cot(d*x+c)^2),1],
[1/(a+b*csc(d*x+c)^2)^4,x,7,x/a^4+1/16*sqrt(b)*(35*a^3+70*a^2*b+56*a*b^2+16*b^3)*arctan(sqrt(b)*cot(d*x+c)/sqrt(a+b))/a^4/(a+b)^(7/2)/d+1/6*b*cot(d*x+c)/a/(a+b)/d/(a+b+b*cot(d*x+c)^2)^3+1/24*b*(11*a+6*b)*cot(d*x+c)/a^2/(a+b)^2/d/(a+b+b*cot(d*x+c)^2)^2+1/16*b*(19*a^2+22*a*b+8*b^2)*cot(d*x+c)/a^3/(a+b)^3/d/(a+b+b*cot(d*x+c)^2),1],
[(a+b*csc(d*x+c)^2)^(5/2),x,8,-a^(5/2)*arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d-1/8*sqrt(b)*(15*a^2+10*a*b+3*b^2)*arctanh(sqrt(b)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d-1/8*b*(7*a+3*b)*cot(d*x+c)*sqrt(a+b+b*cot(d*x+c)^2)/d-1/4*b*cot(d*x+c)*(a+b+b*cot(d*x+c)^2)^(3/2)/d,1],
[(a+b*csc(d*x+c)^2)^(3/2),x,7,-a^(3/2)*arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d-1/2*sqrt(b)*(3*a+b)*arctanh(sqrt(b)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d-1/2*b*cot(d*x+c)*sqrt(a+b+b*cot(d*x+c)^2)/d,1],
[sqrt(a+b*csc(d*x+c)^2),x,6,-sqrt(a)*arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d-sqrt(b)*arctanh(sqrt(b)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/d,1],
[1/sqrt(a+b*csc(d*x+c)^2),x,3,-arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b*csc(d*x+c)^2))/sqrt(a)/d,1],
[1/(a+b*csc(d*x+c)^2)^(3/2),x,4,-arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/a^(3/2)/d+b*cot(d*x+c)/a/(a+b)/d/sqrt(a+b+b*cot(d*x+c)^2),1],
[1/(a+b*csc(d*x+c)^2)^(5/2),x,6,-arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/a^(5/2)/d+1/3*b*cot(d*x+c)/a/(a+b)/d/(a+b+b*cot(d*x+c)^2)^(3/2)+1/3*b*(5*a+3*b)*cot(d*x+c)/a^2/(a+b)^2/d/sqrt(a+b+b*cot(d*x+c)^2),1],
[1/(a+b*csc(d*x+c)^2)^(7/2),x,7,-arctan(sqrt(a)*cot(d*x+c)/sqrt(a+b+b*cot(d*x+c)^2))/a^(7/2)/d+1/5*b*cot(d*x+c)/a/(a+b)/d/(a+b+b*cot(d*x+c)^2)^(5/2)+1/15*b*(9*a+5*b)*cot(d*x+c)/a^2/(a+b)^2/d/(a+b+b*cot(d*x+c)^2)^(3/2)+1/15*b*(33*a^2+40*a*b+15*b^2)*cot(d*x+c)/a^3/(a+b)^3/d/sqrt(a+b+b*cot(d*x+c)^2),1],
[(1+csc(x)^2)^(3/2),x,6,-2*arcsinh(cot(x)/sqrt(2))-arctan(cot(x)/sqrt(2+cot(x)^2))-1/2*cot(x)*sqrt(2+cot(x)^2),1],
[sqrt(1+csc(x)^2),x,5,-arcsinh(cot(x)/sqrt(2))-arctan(cot(x)/sqrt(2+cot(x)^2)),1],
[1/sqrt(1+csc(x)^2),x,3,-arctan(cot(x)/sqrt(2+cot(x)^2)),1],
[(1-csc(x)^2)^(3/2),x,4,1/2*cot(x)*sqrt(-cot(x)^2)+sqrt(-cot(x)^2)*ln(sin(x))*tan(x),1],
[sqrt(1-csc(x)^2),x,3,sqrt(-cot(x)^2)*ln(sin(x))*tan(x),1],
[1/sqrt(1-csc(x)^2),x,3,-cot(x)*ln(cos(x))/sqrt(-cot(x)^2),1],
[(-1+csc(x)^2)^(3/2),x,4,-1/2*(cot(x)^2)^(3/2)*tan(x)-sqrt(cot(x)^2)*ln(sin(x))*tan(x),1],
[sqrt(-1+csc(x)^2),x,3,sqrt(cot(x)^2)*ln(sin(x))*tan(x),1],
[1/sqrt(-1+csc(x)^2),x,3,-cot(x)*ln(cos(x))/sqrt(cot(x)^2),1],
[(-1-csc(x)^2)^(3/2),x,7,-2*arctan(cot(x)/sqrt(-2-cot(x)^2))-arctanh(cot(x)/sqrt(-2-cot(x)^2))+1/2*cot(x)*sqrt(-2-cot(x)^2),1],
[sqrt(-1-csc(x)^2),x,6,arctan(cot(x)/sqrt(-2-cot(x)^2))+arctanh(cot(x)/sqrt(-2-cot(x)^2)),1],
[1/sqrt(-1-csc(x)^2),x,3,-arctanh(cot(x)/sqrt(-2-cot(x)^2)),1]]: