1,1,240,82,0.862000," ","int(x^3*cot(b*x+a),x)","-\frac{i x^{4}}{4}-\frac{3 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{2 i a^{3} x}{b^{3}}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{4}}{2 b^{4}}+\frac{2 a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}"," ",0,"-1/4*I*x^4-3*I/b^2*polylog(2,-exp(I*(b*x+a)))*x^2-3*I/b^2*polylog(2,exp(I*(b*x+a)))*x^2-2*I/b^3*a^3*x+1/b^4*ln(1-exp(I*(b*x+a)))*a^3+1/b*ln(1-exp(I*(b*x+a)))*x^3+1/b*ln(exp(I*(b*x+a))+1)*x^3+6*I/b^4*polylog(4,-exp(I*(b*x+a)))+6*I/b^4*polylog(4,exp(I*(b*x+a)))-3/2*I/b^4*a^4+2/b^4*a^3*ln(exp(I*(b*x+a)))-1/b^4*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*polylog(3,-exp(I*(b*x+a)))*x","B"
2,1,198,62,0.798000," ","int(x^2*cot(b*x+a),x)","-\frac{i x^{3}}{3}+\frac{2 i a^{2} x}{b^{2}}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{4 i a^{3}}{3 b^{3}}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{2 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{2 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{2 a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-1/3*I*x^3+2*I/b^2*a^2*x-1/b^3*ln(1-exp(I*(b*x+a)))*a^2+4/3*I/b^3*a^3+1/b*ln(exp(I*(b*x+a))+1)*x^2-2*I/b^2*polylog(2,-exp(I*(b*x+a)))*x+2/b^3*polylog(3,-exp(I*(b*x+a)))+1/b*ln(1-exp(I*(b*x+a)))*x^2-2*I/b^2*polylog(2,exp(I*(b*x+a)))*x+2/b^3*polylog(3,exp(I*(b*x+a)))+1/b^3*a^2*ln(exp(I*(b*x+a))-1)-2/b^3*a^2*ln(exp(I*(b*x+a)))","B"
3,1,150,43,0.823000," ","int(x*cot(b*x+a),x)","-\frac{i x^{2}}{2}-\frac{2 i a x}{b}-\frac{i a^{2}}{b^{2}}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"-1/2*I*x^2-2*I/b*a*x-I/b^2*a^2+1/b*ln(exp(I*(b*x+a))+1)*x-I/b^2*polylog(2,-exp(I*(b*x+a)))+1/b*ln(1-exp(I*(b*x+a)))*x+1/b^2*ln(1-exp(I*(b*x+a)))*a-I/b^2*polylog(2,exp(I*(b*x+a)))+2/b^2*a*ln(exp(I*(b*x+a)))-1/b^2*a*ln(exp(I*(b*x+a))-1)","B"
4,0,0,12,0.896000," ","int(cot(b*x+a)/x,x)","\int \frac{\cot \left(b x +a \right)}{x}\, dx"," ",0,"int(cot(b*x+a)/x,x)","F"
5,0,0,12,1.083000," ","int(cot(b*x+a)/x^2,x)","\int \frac{\cot \left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(cot(b*x+a)/x^2,x)","F"
6,1,231,85,0.952000," ","int(x^3*cot(b*x+a)^2,x)","-\frac{x^{4}}{4}-\frac{2 i x^{3}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{6 i a^{2} x}{b^{3}}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}-\frac{6 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}-\frac{6 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{6 a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{2 i x^{3}}{b}+\frac{4 i a^{3}}{b^{4}}"," ",0,"-1/4*x^4-2*I*x^3/b/(exp(2*I*(b*x+a))-1)+6*I/b^3*a^2*x+3/b^2*ln(exp(I*(b*x+a))+1)*x^2-6*I/b^3*polylog(2,-exp(I*(b*x+a)))*x+6/b^4*polylog(3,-exp(I*(b*x+a)))+3/b^2*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*ln(1-exp(I*(b*x+a)))*a^2-6*I/b^3*polylog(2,exp(I*(b*x+a)))*x+6/b^4*polylog(3,exp(I*(b*x+a)))+3/b^4*a^2*ln(exp(I*(b*x+a))-1)-6/b^4*a^2*ln(exp(I*(b*x+a)))-2*I/b*x^3+4*I/b^4*a^3","B"
7,1,183,66,0.898000," ","int(x^2*cot(b*x+a)^2,x)","-\frac{x^{3}}{3}-\frac{2 i x^{2}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{2 i x^{2}}{b}-\frac{4 i a x}{b^{2}}-\frac{2 i a^{2}}{b^{3}}+\frac{2 \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{2 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}"," ",0,"-1/3*x^3-2*I*x^2/b/(exp(2*I*(b*x+a))-1)-2*I/b*x^2-4*I/b^2*a*x-2*I/b^3*a^2+2/b^2*ln(exp(I*(b*x+a))+1)*x-2*I/b^3*polylog(2,-exp(I*(b*x+a)))+2/b^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*ln(1-exp(I*(b*x+a)))*a-2*I/b^3*polylog(2,exp(I*(b*x+a)))+4/b^3*a*ln(exp(I*(b*x+a)))-2/b^3*a*ln(exp(I*(b*x+a))-1)","B"
8,1,30,29,0.719000," ","int(x*cot(b*x+a)^2,x)","-\frac{x^{2}}{2}-\frac{x \cot \left(b x +a \right)}{b}+\frac{\ln \left(\sin \left(b x +a \right)\right)}{b^{2}}"," ",0,"-1/2*x^2-x*cot(b*x+a)/b+ln(sin(b*x+a))/b^2","A"
9,0,0,14,1.052000," ","int(cot(b*x+a)^2/x,x)","\int \frac{\cot^{2}\left(b x +a \right)}{x}\, dx"," ",0,"int(cot(b*x+a)^2/x,x)","F"
10,0,0,14,1.118000," ","int(cot(b*x+a)^2/x^2,x)","\int \frac{\cot^{2}\left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(cot(b*x+a)^2/x^2,x)","F"
11,1,444,167,1.060000," ","int(x^3*cot(b*x+a)^3,x)","\frac{3 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{x^{2} \left(2 b x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i {\mathrm e}^{2 i \left(b x +a \right)}+3 i\right)}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{2 i a^{3} x}{b^{3}}+\frac{3 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{6 i a x}{b^{3}}-\frac{3 i x^{2}}{b^{2}}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{3 a \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{2}}{b^{4}}+\frac{a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{3 i a^{4}}{2 b^{4}}-\frac{2 a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}-\frac{6 i \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{i x^{4}}{4}"," ",0,"-3*I/b^2*x^2-6*I/b^3*a*x+3*I/b^2*polylog(2,-exp(I*(b*x+a)))*x^2+3*I/b^2*polylog(2,exp(I*(b*x+a)))*x^2+2*I/b^3*a^3*x+1/4*I*x^4-1/b*ln(1-exp(I*(b*x+a)))*x^3-1/b*ln(exp(I*(b*x+a))+1)*x^3+3/b^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*ln(1-exp(I*(b*x+a)))*x-6/b^3*polylog(3,exp(I*(b*x+a)))*x-6/b^3*polylog(3,-exp(I*(b*x+a)))*x+6/b^4*a*ln(exp(I*(b*x+a)))-1/b^4*ln(1-exp(I*(b*x+a)))*a^3+x^2*(2*b*x*exp(2*I*(b*x+a))-3*I*exp(2*I*(b*x+a))+3*I)/b^2/(exp(2*I*(b*x+a))-1)^2-3/b^4*a*ln(exp(I*(b*x+a))-1)-2/b^4*a^3*ln(exp(I*(b*x+a)))+3/b^4*a*ln(1-exp(I*(b*x+a)))-3*I/b^4*a^2+3/2*I/b^4*a^4-3*I/b^4*polylog(2,exp(I*(b*x+a)))-3*I/b^4*polylog(2,-exp(I*(b*x+a)))-6*I/b^4*polylog(4,exp(I*(b*x+a)))-6*I/b^4*polylog(4,-exp(I*(b*x+a)))+1/b^4*a^3*ln(exp(I*(b*x+a))-1)","B"
12,1,293,110,1.008000," ","int(x^2*cot(b*x+a)^3,x)","\frac{2 i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 x \left(b x \,{\mathrm e}^{2 i \left(b x +a \right)}-i {\mathrm e}^{2 i \left(b x +a \right)}+i\right)}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}-\frac{2 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i a^{2} x}{b^{2}}+\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{2 i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{i x^{3}}{3}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{4 i a^{3}}{3 b^{3}}-\frac{2 \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{2 a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-2*I/b^2*a^2*x+2*x*(b*x*exp(2*I*(b*x+a))-I*exp(2*I*(b*x+a))+I)/b^2/(exp(2*I*(b*x+a))-1)^2-2/b^3*polylog(3,exp(I*(b*x+a)))-2/b^3*polylog(3,-exp(I*(b*x+a)))-4/3*I/b^3*a^3+1/b^3*ln(1-exp(I*(b*x+a)))*a^2+1/b^3*ln(exp(I*(b*x+a))-1)+2*I/b^2*polylog(2,-exp(I*(b*x+a)))*x-1/b*ln(exp(I*(b*x+a))+1)*x^2+1/3*I*x^3-1/b*ln(1-exp(I*(b*x+a)))*x^2+2*I/b^2*polylog(2,exp(I*(b*x+a)))*x-2/b^3*ln(exp(I*(b*x+a)))+1/b^3*ln(exp(I*(b*x+a))+1)-1/b^3*a^2*ln(exp(I*(b*x+a))-1)+2/b^3*a^2*ln(exp(I*(b*x+a)))","B"
13,1,197,75,0.803000," ","int(x*cot(b*x+a)^3,x)","\frac{i x^{2}}{2}+\frac{2 b x \,{\mathrm e}^{2 i \left(b x +a \right)}-i {\mathrm e}^{2 i \left(b x +a \right)}+i}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{2 i a x}{b}+\frac{i a^{2}}{b^{2}}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{i \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{\ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{i \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"1/2*I*x^2+(2*b*x*exp(2*I*(b*x+a))-I*exp(2*I*(b*x+a))+I)/b^2/(exp(2*I*(b*x+a))-1)^2+2*I/b*a*x+I/b^2*a^2-1/b*ln(exp(I*(b*x+a))+1)*x+I/b^2*polylog(2,-exp(I*(b*x+a)))-1/b*ln(1-exp(I*(b*x+a)))*x-1/b^2*ln(1-exp(I*(b*x+a)))*a+I/b^2*polylog(2,exp(I*(b*x+a)))-2/b^2*a*ln(exp(I*(b*x+a)))+1/b^2*a*ln(exp(I*(b*x+a))-1)","B"
14,0,0,14,2.916000," ","int(cot(b*x+a)^3/x,x)","\int \frac{\cot^{3}\left(b x +a \right)}{x}\, dx"," ",0,"int(cot(b*x+a)^3/x,x)","F"
15,0,0,14,3.788000," ","int(cot(b*x+a)^3/x^2,x)","\int \frac{\cot^{3}\left(b x +a \right)}{x^{2}}\, dx"," ",0,"int(cot(b*x+a)^3/x^2,x)","F"
16,1,170,165,2.069000," ","int((d*x+c)^3/(a+I*a*cot(f*x+e)),x)","\frac{d^{3} x^{4}}{8 a}+\frac{d^{2} c \,x^{3}}{2 a}+\frac{3 d \,c^{2} x^{2}}{4 a}+\frac{c^{3} x}{2 a}+\frac{c^{4}}{8 d a}+\frac{i \left(4 d^{3} x^{3} f^{3}+12 c \,d^{2} f^{3} x^{2}+6 i d^{3} f^{2} x^{2}+12 c^{2} d \,f^{3} x +12 i c \,d^{2} f^{2} x +4 c^{3} f^{3}+6 i c^{2} d \,f^{2}-6 d^{3} f x -6 c \,d^{2} f -3 i d^{3}\right) {\mathrm e}^{2 i \left(f x +e \right)}}{16 a \,f^{4}}"," ",0,"1/8*d^3/a*x^4+1/2*d^2/a*c*x^3+3/4*d/a*c^2*x^2+1/2*c^3*x/a+1/8/d/a*c^4+1/16*I*(4*d^3*x^3*f^3+6*I*d^3*f^2*x^2+12*c*d^2*f^3*x^2+12*I*c*d^2*f^2*x+12*c^2*d*f^3*x+6*I*c^2*d*f^2+4*c^3*f^3-6*d^3*f*x-3*I*d^3-6*c*d^2*f)/a/f^4*exp(2*I*(f*x+e))","A"
17,1,108,119,1.864000," ","int((d*x+c)^2/(a+I*a*cot(f*x+e)),x)","\frac{d^{2} x^{3}}{6 a}+\frac{d c \,x^{2}}{2 a}+\frac{c^{2} x}{2 a}+\frac{c^{3}}{6 d a}+\frac{i \left(2 d^{2} f^{2} x^{2}+4 c d \,f^{2} x +2 i d^{2} f x +2 c^{2} f^{2}+2 i c d f -d^{2}\right) {\mathrm e}^{2 i \left(f x +e \right)}}{8 a \,f^{3}}"," ",0,"1/6*d^2/a*x^3+1/2*d/a*c*x^2+1/2*c^2*x/a+1/6/d/a*c^3+1/8*I*(2*d^2*f^2*x^2+2*I*d^2*f*x+4*c*d*f^2*x+2*I*c*d*f+2*c^2*f^2-d^2)/a/f^3*exp(2*I*(f*x+e))","A"
18,1,177,72,0.622000," ","int((d*x+c)/(a+I*a*cot(f*x+e)),x)","\frac{d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)+c f \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-i d \left(-\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{2}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}\right)+\frac{i c f \left(\cos^{2}\left(f x +e \right)\right)}{2}-\frac{i d e \left(\cos^{2}\left(f x +e \right)\right)}{2}}{f^{2} a}"," ",0,"1/f^2/a*(d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+c*f*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-I*d*(-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e)+1/2*I*c*f*cos(f*x+e)^2-1/2*I*d*e*cos(f*x+e)^2)","B"
19,1,204,149,0.597000," ","int(1/(d*x+c)/(a+I*a*cot(f*x+e)),x)","\frac{\ln \left(\left(f x +e \right) d +c f -d e \right)}{2 a d}-\frac{\Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{2 a d}-\frac{\Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{2 a d}-\frac{i \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{2 a d}+\frac{i \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{2 a d}"," ",0,"1/2/a*ln((f*x+e)*d+c*f-d*e)/d-1/2/a*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d-1/2/a*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-1/2*I/a*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d+1/2*I/a*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d","A"
20,1,271,164,0.575000," ","int(1/(d*x+c)^2/(a+I*a*cot(f*x+e)),x)","\frac{f \left(-\frac{1}{2 \left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\cos \left(2 f x +2 e \right)}{2 \left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{2 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}-\frac{2 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}}{2 d}-\frac{i \left(-\frac{2 \sin \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{4 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}+\frac{4 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}}{d}\right)}{4}\right)}{a}"," ",0,"f/a*(-1/2/((f*x+e)*d+c*f-d*e)/d+1/2*cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d+1/2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d)/d-1/4*I*(-2*sin(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d+2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d+2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d)/d))","A"
21,1,143,216,1.635000," ","int(1/(d*x+c)^3/(a+I*a*cot(f*x+e)),x)","-\frac{1}{4 d \left(d x +c \right)^{2} a}-\frac{f^{2} {\mathrm e}^{2 i \left(f x +e \right)}}{4 a \,d^{3} \left(i f x +\frac{i c f}{d}\right)^{2}}-\frac{f^{2} {\mathrm e}^{2 i \left(f x +e \right)}}{2 a \,d^{3} \left(i f x +\frac{i c f}{d}\right)}-\frac{f^{2} {\mathrm e}^{-\frac{2 i \left(c f -d e \right)}{d}} \Ei \left(1, -2 i f x -2 i e -\frac{2 \left(i c f -i d e \right)}{d}\right)}{a \,d^{3}}"," ",0,"-1/4/d/(d*x+c)^2/a-1/4*f^2/a/d^3*exp(2*I*(f*x+e))/(I*f*x+I/d*c*f)^2-1/2*f^2/a/d^3*exp(2*I*(f*x+e))/(I*f*x+I/d*c*f)-f^2/a/d^3*exp(-2*I*(c*f-d*e)/d)*Ei(1,-2*I*f*x-2*I*e-2*(I*c*f-I*d*e)/d)","A"
22,1,2261,224,2.155000," ","int((d*x+c)^3/(a+I*a*cot(f*x+e))^2,x)","\text{Expression too large to display}"," ",0,"-1/a^2/f*(1/2*I*c^3*sin(f*x+e)^4+6*I/f^2*c*d^2*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)+6*I/f*c^2*d*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-12/f^2*c*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)-6*I/f^3*d^3*e*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)+6*I/f^3*d^3*e^2*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-1/f^3*d^3*((f*x+e)^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3/4*(f*x+e)^2*cos(f*x+e)^2+3/2*(f*x+e)*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3/8*(f*x+e)^2-3/8*sin(f*x+e)^2-3/8*(f*x+e)^4)+2/f^3*d^3*((f*x+e)^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3/16*(f*x+e)^2*cos(f*x+e)^2+3/8*(f*x+e)*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-21/128*(f*x+e)^2-3/128*sin(f*x+e)^2-3/32*(f*x+e)^4-(f*x+e)^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2*sin(f*x+e)^4+3/8*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/128*sin(f*x+e)^4)+3/f*c^2*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+6/f^2*c*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+6/f^2*c*d^2*e^2*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-3/f^2*c*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-6/f*c^2*d*e*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-3/f*c^2*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+2*I/f^3*d^3*(1/4*(f*x+e)^3*sin(f*x+e)^4-3/4*(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/32*(f*x+e)*sin(f*x+e)^4-3/128*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-27/256*f*x-27/256*e+9/32*(f*x+e)*cos(f*x+e)^2-9/64*sin(f*x+e)*cos(f*x+e)+3/16*(f*x+e)^3)-2/f^3*d^3*e^3*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-3/f^3*d^3*e^2*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+6/f^2*c*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/8*(f*x+e)*cos(f*x+e)^2+1/16*sin(f*x+e)*cos(f*x+e)+7/64*f*x+7/64*e-1/12*(f*x+e)^3-(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/8*(f*x+e)*sin(f*x+e)^4-1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e))+3/f^3*d^3*e*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)-3/f^2*c*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)-6/f^3*d^3*e*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/8*(f*x+e)*cos(f*x+e)^2+1/16*sin(f*x+e)*cos(f*x+e)+7/64*f*x+7/64*e-1/12*(f*x+e)^3-(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/8*(f*x+e)*sin(f*x+e)^4-1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e))+6/f^3*d^3*e^2*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)+6/f*c^2*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)+1/f^3*d^3*e^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*I/f^3*d^3*e^3*sin(f*x+e)^4-3/2*I/f*c^2*d*e*sin(f*x+e)^4+3/2*I/f^2*c*d^2*e^2*sin(f*x+e)^4-12*I/f^2*c*d^2*e*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*c^3*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e))","B"
23,1,1073,166,1.948000," ","int((d*x+c)^2/(a+I*a*cot(f*x+e))^2,x)","-\frac{-\frac{i c d e \left(\sin^{4}\left(f x +e \right)\right)}{f}-\frac{4 i d^{2} e \left(\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{16}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f^{2}}+\frac{2 i d^{2} \left(\frac{\left(f x +e \right)^{2} \left(\sin^{4}\left(f x +e \right)\right)}{4}-\frac{\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{2}+\frac{3 \left(f x +e \right)^{2}}{32}-\frac{\left(\sin^{4}\left(f x +e \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(f x +e \right)\right)}{32}\right)}{f^{2}}+\frac{i d^{2} e^{2} \left(\sin^{4}\left(f x +e \right)\right)}{2 f^{2}}+\frac{4 i c d \left(\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{16}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f}+\frac{i c^{2} \left(\sin^{4}\left(f x +e \right)\right)}{2}+\frac{2 d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{8}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{16}+\frac{7 f x}{64}+\frac{7 e}{64}-\frac{\left(f x +e \right)^{3}}{12}-\left(f x +e \right)^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{8}-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{32}\right)}{f^{2}}+\frac{4 c d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{16}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{16}-\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{\left(\sin^{4}\left(f x +e \right)\right)}{16}\right)}{f}-\frac{4 d^{2} e \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{16}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{16}-\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{\left(\sin^{4}\left(f x +e \right)\right)}{16}\right)}{f^{2}}+2 c^{2} \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)-\frac{4 c d e \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)}{f}+\frac{2 d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)}{f^{2}}-\frac{d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{2}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{4}+\frac{f x}{4}+\frac{e}{4}-\frac{\left(f x +e \right)^{3}}{3}\right)}{f^{2}}-\frac{2 c d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{2 d^{2} e \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}-c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{2 c d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}-\frac{d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}}{a^{2} f}"," ",0,"-1/a^2/f*(-I/f*c*d*e*sin(f*x+e)^4-4*I/f^2*d^2*e*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+2*I/f^2*d^2*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)+1/2*I/f^2*d^2*e^2*sin(f*x+e)^4+4*I/f*c*d*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+1/2*I*c^2*sin(f*x+e)^4+2/f^2*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/8*(f*x+e)*cos(f*x+e)^2+1/16*sin(f*x+e)*cos(f*x+e)+7/64*f*x+7/64*e-1/12*(f*x+e)^3-(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/8*(f*x+e)*sin(f*x+e)^4-1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e))+4/f*c*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)-4/f^2*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)+2*c^2*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-4/f*c*d*e*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)+2/f^2*d^2*e^2*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-1/f^2*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)-2/f*c*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+2/f^2*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)-c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2/f*c*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/f^2*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
24,1,390,130,1.662000," ","int((d*x+c)/(a+I*a*cot(f*x+e))^2,x)","-\frac{\frac{2 i d \left(\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{16}-\frac{3 f x}{32}-\frac{3 e}{32}\right)}{f}+\frac{i c \left(\sin^{4}\left(f x +e \right)\right)}{2}-\frac{i d e \left(\sin^{4}\left(f x +e \right)\right)}{2 f}+\frac{2 d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{16}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{16}-\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{\left(\sin^{4}\left(f x +e \right)\right)}{16}\right)}{f}+2 c \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)-\frac{2 e d \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)}{f}-\frac{d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f}-c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{e d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}}{a^{2} f}"," ",0,"-1/a^2/f*(2*I/f*d*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+1/2*I*c*sin(f*x+e)^4-1/2*I/f*d*e*sin(f*x+e)^4+2/f*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/16*(f*x+e)^2+1/16*sin(f*x+e)^2-(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/16*sin(f*x+e)^4)+2*c*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-2*e/f*d*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-1/f*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)-c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+e/f*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
25,1,382,283,1.425000," ","int(1/(d*x+c)/(a+I*a*cot(f*x+e))^2,x)","-\frac{i \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{2 a^{2} d}+\frac{i \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{2 a^{2} d}+\frac{i \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{4 a^{2} d}-\frac{i \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{4 a^{2} d}+\frac{\ln \left(\left(f x +e \right) d +c f -d e \right)}{4 a^{2} d}+\frac{\Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{4 a^{2} d}+\frac{\Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{4 a^{2} d}-\frac{\Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{2 a^{2} d}-\frac{\Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{2 a^{2} d}"," ",0,"-1/2*I/a^2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d+1/2*I/a^2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d+1/4*I/a^2*Si(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d-1/4*I/a^2*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d+1/4/a^2*ln((f*x+e)*d+c*f-d*e)/d+1/4/a^2*Si(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d+1/4/a^2*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d-1/2/a^2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d-1/2/a^2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d","A"
26,1,537,416,1.429000," ","int(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^2,x)","-\frac{\frac{i f^{2} \left(-\frac{2 \sin \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{4 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}+\frac{4 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}}{d}\right)}{4}-\frac{i f^{2} \left(-\frac{4 \sin \left(4 f x +4 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{16 \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{d}+\frac{16 \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{d}}{d}\right)}{16}+\frac{f^{2}}{4 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{f^{2} \left(-\frac{4 \cos \left(4 f x +4 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}-\frac{4 \left(\frac{4 \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{d}-\frac{4 \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{d}\right)}{d}\right)}{16}+\frac{f^{2} \left(-\frac{2 \cos \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}-\frac{2 \left(\frac{2 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}-\frac{2 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}\right)}{d}\right)}{4}}{a^{2} f}"," ",0,"-1/a^2/f*(1/4*I*f^2*(-2*sin(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d+2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d+2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d)/d)-1/16*I*f^2*(-4*sin(4*f*x+4*e)/((f*x+e)*d+c*f-d*e)/d+4*(4*Si(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d+4*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d)/d)+1/4*f^2/((f*x+e)*d+c*f-d*e)/d-1/16*f^2*(-4*cos(4*f*x+4*e)/((f*x+e)*d+c*f-d*e)/d-4*(4*Si(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d-4*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d)/d)+1/4*f^2*(-2*cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d-2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d)/d))","A"
27,1,3997,328,1.721000," ","int((d*x+c)^3/(a+I*a*cot(f*x+e))^3,x)","\text{output too large to display}"," ",0,"1/f^4/a^3*(-3*d^3*e*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/8*(f*x+e)*sin(f*x+e)^4+1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+9/64*f*x+9/64*e-3/8*(f*x+e)*cos(f*x+e)^2+3/16*sin(f*x+e)*cos(f*x+e)-1/4*(f*x+e)^3)+3*d^3*e^2*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)+3*c*d^2*e^2*f*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+12*c^2*d*e*f^2*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+12*I*c*d^2*f*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/24*(f*x+e)^2-1/72*sin(f*x+e)^4-1/24*sin(f*x+e)^2-1/6*(f*x+e)^2*sin(f*x+e)^6+1/3*(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/108*sin(f*x+e)^6)-6*c*d^2*e*f*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)-3*c^2*d*e*f^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-12*c*d^2*e^2*f*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+12*I*c*d^2*e^2*f*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)+18*I*c*d^2*e*f*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-12*I*d^3*e*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/24*(f*x+e)^2-1/72*sin(f*x+e)^4-1/24*sin(f*x+e)^2-1/6*(f*x+e)^2*sin(f*x+e)^6+1/3*(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/108*sin(f*x+e)^6)+3*c^2*d*f^2*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)-3/4*I*c^3*f^3*sin(f*x+e)^4+4*I*c^3*f^3*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-9*I*d^3*e^2*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-12*d^3*e^2*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)+c^3*f^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-d^3*e^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3*I*d^3*(1/4*(f*x+e)^3*sin(f*x+e)^4-3/4*(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/32*(f*x+e)*sin(f*x+e)^4-3/128*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-27/256*f*x-27/256*e+9/32*(f*x+e)*cos(f*x+e)^2-9/64*sin(f*x+e)*cos(f*x+e)+3/16*(f*x+e)^3)+12*d^3*e*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/48*(f*x+e)*sin(f*x+e)^4+1/192*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+47/1152*f*x+47/1152*e-1/16*(f*x+e)*cos(f*x+e)^2+1/32*sin(f*x+e)*cos(f*x+e)-1/24*(f*x+e)^3-(f*x+e)^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/18*(f*x+e)*sin(f*x+e)^6-1/108*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+4*I*d^3*(1/4*(f*x+e)^3*sin(f*x+e)^4-3/4*(f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/24*(f*x+e)*sin(f*x+e)^4-1/96*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/18*f*x-1/18*e+1/8*(f*x+e)*cos(f*x+e)^2-1/16*sin(f*x+e)*cos(f*x+e)+1/12*(f*x+e)^3-1/6*(f*x+e)^3*sin(f*x+e)^6+1/2*(f*x+e)^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/36*(f*x+e)*sin(f*x+e)^6+1/216*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+4*d^3*e^3*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)-4*c^3*f^3*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+12*I*c^2*d*f^2*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))-9/4*I*c*d^2*e^2*f*sin(f*x+e)^4-12*I*c^2*d*e*f^2*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-9*I*c*d^2*f*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)-9*I*c^2*d*f^2*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+24*c*d^2*e*f*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)+9*I*d^3*e*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)-12*c^2*d*f^2*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)-4*I*d^3*e^3*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-12*c*d^2*f*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/48*(f*x+e)*sin(f*x+e)^4+1/192*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+47/1152*f*x+47/1152*e-1/16*(f*x+e)*cos(f*x+e)^2+1/32*sin(f*x+e)*cos(f*x+e)-1/24*(f*x+e)^3-(f*x+e)^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/18*(f*x+e)*sin(f*x+e)^6-1/108*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+12*I*d^3*e^2*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))-24*I*c*d^2*e*f*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+9/4*I*c^2*d*e*f^2*sin(f*x+e)^4+3/4*I*d^3*e^3*sin(f*x+e)^4+3*c*d^2*f*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/8*(f*x+e)*sin(f*x+e)^4+1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+9/64*f*x+9/64*e-3/8*(f*x+e)*cos(f*x+e)^2+3/16*sin(f*x+e)*cos(f*x+e)-1/4*(f*x+e)^3)-4*d^3*((f*x+e)^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/32*(f*x+e)^2*sin(f*x+e)^4-1/16*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-47/768*(f*x+e)^2+11/2304*sin(f*x+e)^4-25/768*sin(f*x+e)^2-3/32*(f*x+e)^2*cos(f*x+e)^2+3/16*(f*x+e)*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3/64*(f*x+e)^4-(f*x+e)^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/12*(f*x+e)^2*sin(f*x+e)^6+1/6*(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/216*sin(f*x+e)^6)+d^3*((f*x+e)^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/16*(f*x+e)^2*sin(f*x+e)^4-3/8*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-27/128*(f*x+e)^2-3/128*sin(f*x+e)^4-45/128*sin(f*x+e)^2-9/16*(f*x+e)^2*cos(f*x+e)^2+9/8*(f*x+e)*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-9/32*(f*x+e)^4))","B"
28,1,1843,241,1.481000," ","int((d*x+c)^2/(a+I*a*cot(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"1/f^3/a^3*(-6*I*c*d*f*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+4*I*c^2*f^2*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-8*I*d^2*e*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+8*I*c*d*f*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))-3*I*d^2*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3/32*(f*x+e)^2-1/32*sin(f*x+e)^4-3/32*sin(f*x+e)^2)+4*I*d^2*e^2*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-4*d^2*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/48*(f*x+e)*sin(f*x+e)^4+1/192*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+47/1152*f*x+47/1152*e-1/16*(f*x+e)*cos(f*x+e)^2+1/32*sin(f*x+e)*cos(f*x+e)-1/24*(f*x+e)^3-(f*x+e)^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/18*(f*x+e)*sin(f*x+e)^6-1/108*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))-8*c*d*f*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)+8*d^2*e*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)-4*c^2*f^2*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+8*c*d*e*f*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)-4*d^2*e^2*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+3/2*I*c*d*e*f*sin(f*x+e)^4-3/4*I*c^2*f^2*sin(f*x+e)^4+6*I*d^2*e*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)+4*I*d^2*(1/4*(f*x+e)^2*sin(f*x+e)^4-1/2*(f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/24*(f*x+e)^2-1/72*sin(f*x+e)^4-1/24*sin(f*x+e)^2-1/6*(f*x+e)^2*sin(f*x+e)^6+1/3*(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/108*sin(f*x+e)^6)-3/4*I*d^2*e^2*sin(f*x+e)^4-8*I*c*d*e*f*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)+d^2*((f*x+e)^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/8*(f*x+e)*sin(f*x+e)^4+1/32*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+9/64*f*x+9/64*e-3/8*(f*x+e)*cos(f*x+e)^2+3/16*sin(f*x+e)*cos(f*x+e)-1/4*(f*x+e)^3)+2*c*d*f*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)-2*d^2*e*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)+c^2*f^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*c*d*e*f*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+d^2*e^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e))","B"
29,1,653,181,1.061000," ","int((d*x+c)/(a+I*a*cot(f*x+e))^3,x)","\frac{4 i d \left(\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{16}-\frac{f x}{24}-\frac{e}{24}-\frac{\left(f x +e \right) \left(\sin^{6}\left(f x +e \right)\right)}{6}-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{36}\right)+4 i c f \left(-\frac{\left(\sin^{2}\left(f x +e \right)\right) \left(\cos^{4}\left(f x +e \right)\right)}{6}-\frac{\left(\cos^{4}\left(f x +e \right)\right)}{12}\right)-4 i d e \left(-\frac{\left(\sin^{2}\left(f x +e \right)\right) \left(\cos^{4}\left(f x +e \right)\right)}{6}-\frac{\left(\cos^{4}\left(f x +e \right)\right)}{12}\right)-4 d \left(\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{\left(f x +e \right)^{2}}{32}+\frac{\left(\sin^{4}\left(f x +e \right)\right)}{96}+\frac{\left(\sin^{2}\left(f x +e \right)\right)}{32}-\left(f x +e \right) \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{\left(\sin^{6}\left(f x +e \right)\right)}{36}\right)-4 c f \left(-\frac{\left(\sin^{3}\left(f x +e \right)\right) \left(\cos^{3}\left(f x +e \right)\right)}{6}-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{8}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{16}+\frac{f x}{16}+\frac{e}{16}\right)+4 d e \left(-\frac{\left(\sin^{3}\left(f x +e \right)\right) \left(\cos^{3}\left(f x +e \right)\right)}{6}-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{8}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{16}+\frac{f x}{16}+\frac{e}{16}\right)-3 i d \left(\frac{\left(f x +e \right) \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{16}-\frac{3 f x}{32}-\frac{3 e}{32}\right)-\frac{3 i c f \left(\sin^{4}\left(f x +e \right)\right)}{4}+\frac{3 i d e \left(\sin^{4}\left(f x +e \right)\right)}{4}+d \left(\left(f x +e \right) \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 \left(f x +e \right)^{2}}{16}+\frac{\left(\sin^{4}\left(f x +e \right)\right)}{16}+\frac{3 \left(\sin^{2}\left(f x +e \right)\right)}{16}\right)+c f \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-d e \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f^{2} a^{3}}"," ",0,"1/f^2/a^3*(4*I*d*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-1/24*f*x-1/24*e-1/6*(f*x+e)*sin(f*x+e)^6-1/36*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e))+4*I*c*f*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-4*I*d*e*(-1/6*sin(f*x+e)^2*cos(f*x+e)^4-1/12*cos(f*x+e)^4)-4*d*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/32*(f*x+e)^2+1/96*sin(f*x+e)^4+1/32*sin(f*x+e)^2-(f*x+e)*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/36*sin(f*x+e)^6)-4*c*f*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+4*d*e*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)-3*I*d*(1/4*(f*x+e)*sin(f*x+e)^4+1/16*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/32*f*x-3/32*e)-3/4*I*c*f*sin(f*x+e)^4+3/4*I*d*e*sin(f*x+e)^4+d*((f*x+e)*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/16*(f*x+e)^2+1/16*sin(f*x+e)^4+3/16*sin(f*x+e)^2)+c*f*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-d*e*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e))","B"
30,1,560,417,0.641000," ","int(1/(d*x+c)/(a+I*a*cot(f*x+e))^3,x)","\frac{3 i \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{8 a^{3} d}-\frac{3 i \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{8 a^{3} d}-\frac{3 i \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{8 a^{3} d}+\frac{3 i \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{8 a^{3} d}-\frac{3 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{8 a^{3} d}-\frac{3 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{8 a^{3} d}-\frac{\Si \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \sin \left(\frac{6 c f -6 d e}{d}\right)}{8 a^{3} d}-\frac{\Ci \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \cos \left(\frac{6 c f -6 d e}{d}\right)}{8 a^{3} d}+\frac{3 \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{8 a^{3} d}+\frac{3 \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{8 a^{3} d}+\frac{\ln \left(\left(f x +e \right) d +c f -d e \right)}{8 a^{3} d}-\frac{i \Si \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \cos \left(\frac{6 c f -6 d e}{d}\right)}{8 a^{3} d}+\frac{i \Ci \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \sin \left(\frac{6 c f -6 d e}{d}\right)}{8 a^{3} d}"," ",0,"3/8*I/a^3*Si(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d-3/8*I/a^3*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d-3/8*I/a^3*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d+3/8*I/a^3*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d-3/8/a^3*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d-3/8/a^3*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-1/8/a^3*Si(6*f*x+6*e+6*(c*f-d*e)/d)*sin(6*(c*f-d*e)/d)/d-1/8/a^3*Ci(6*f*x+6*e+6*(c*f-d*e)/d)*cos(6*(c*f-d*e)/d)/d+3/8/a^3*Si(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d+3/8/a^3*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d+1/8/a^3*ln((f*x+e)*d+c*f-d*e)/d-1/8*I/a^3*Si(6*f*x+6*e+6*(c*f-d*e)/d)*cos(6*(c*f-d*e)/d)/d+1/8*I/a^3*Ci(6*f*x+6*e+6*(c*f-d*e)/d)*sin(6*(c*f-d*e)/d)/d","A"
31,1,756,658,0.645000," ","int(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^3,x)","-\frac{f \left(\frac{3 i \left(-\frac{2 \sin \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{4 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}+\frac{4 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}}{d}\right)}{16}+\frac{i \left(-\frac{6 \sin \left(6 f x +6 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{36 \Si \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \sin \left(\frac{6 c f -6 d e}{d}\right)}{d}+\frac{36 \Ci \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \cos \left(\frac{6 c f -6 d e}{d}\right)}{d}}{d}\right)}{48}+\frac{3 \cos \left(4 f x +4 e \right)}{8 \left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{3 \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{2 d}-\frac{3 \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{2 d}}{d}+\frac{1}{8 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{3 \cos \left(2 f x +2 e \right)}{8 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{3 \left(\frac{2 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}-\frac{2 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}\right)}{8 d}-\frac{\cos \left(6 f x +6 e \right)}{8 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{\frac{6 \Si \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \cos \left(\frac{6 c f -6 d e}{d}\right)}{d}-\frac{6 \Ci \left(6 f x +6 e +\frac{6 c f -6 d e}{d}\right) \sin \left(\frac{6 c f -6 d e}{d}\right)}{d}}{8 d}-\frac{3 i \left(-\frac{4 \sin \left(4 f x +4 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{16 \Si \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \sin \left(\frac{4 c f -4 d e}{d}\right)}{d}+\frac{16 \Ci \left(4 f x +4 e +\frac{4 c f -4 d e}{d}\right) \cos \left(\frac{4 c f -4 d e}{d}\right)}{d}}{d}\right)}{32}\right)}{a^{3}}"," ",0,"-f/a^3*(3/16*I*(-2*sin(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d+2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d+2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d)/d)+1/48*I*(-6*sin(6*f*x+6*e)/((f*x+e)*d+c*f-d*e)/d+6*(6*Si(6*f*x+6*e+6*(c*f-d*e)/d)*sin(6*(c*f-d*e)/d)/d+6*Ci(6*f*x+6*e+6*(c*f-d*e)/d)*cos(6*(c*f-d*e)/d)/d)/d)+3/8*cos(4*f*x+4*e)/((f*x+e)*d+c*f-d*e)/d+3/8*(4*Si(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d-4*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d)/d+1/8/((f*x+e)*d+c*f-d*e)/d-3/8*cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d-3/8*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d)/d-1/8*cos(6*f*x+6*e)/((f*x+e)*d+c*f-d*e)/d-1/8*(6*Si(6*f*x+6*e+6*(c*f-d*e)/d)*cos(6*(c*f-d*e)/d)/d-6*Ci(6*f*x+6*e+6*(c*f-d*e)/d)*sin(6*(c*f-d*e)/d)/d)/d-3/32*I*(-4*sin(4*f*x+4*e)/((f*x+e)*d+c*f-d*e)/d+4*(4*Si(4*f*x+4*e+4*(c*f-d*e)/d)*sin(4*(c*f-d*e)/d)/d+4*Ci(4*f*x+4*e+4*(c*f-d*e)/d)*cos(4*(c*f-d*e)/d)/d)/d))","A"
32,0,0,24,0.706000," ","int((d*x+c)^m*(a+I*a*cot(f*x+e))^2,x)","\int \left(d x +c \right)^{m} \left(a +i a \cot \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*x+c)^m*(a+I*a*cot(f*x+e))^2,x)","F"
33,0,0,22,1.006000," ","int((d*x+c)^m*(a+I*a*cot(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +i a \cot \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+I*a*cot(f*x+e)),x)","F"
34,0,0,91,1.287000," ","int((d*x+c)^m/(a+I*a*cot(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +i a \cot \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+I*a*cot(f*x+e)),x)","F"
35,0,0,159,2.102000," ","int((d*x+c)^m/(a+I*a*cot(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +i a \cot \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^m/(a+I*a*cot(f*x+e))^2,x)","F"
36,0,0,234,2.342000," ","int((d*x+c)^m/(a+I*a*cot(f*x+e))^3,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +i a \cot \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*x+c)^m/(a+I*a*cot(f*x+e))^3,x)","F"
37,1,857,126,1.320000," ","int((d*x+c)^3*(a+b*cot(f*x+e)),x)","-\frac{3 i b \,c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{3 i b \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{3 i b \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}+\frac{4 i b c \,d^{2} e^{3}}{f^{3}}-\frac{3 i b \,c^{2} d \,e^{2}}{f^{2}}-\frac{2 i b \,d^{3} e^{3} x}{f^{3}}-\frac{3 i b \,c^{2} d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 b c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{3 b c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{3}}+\frac{3 b \,c^{2} d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{3 b c \,d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{3 b \,c^{2} d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{3 b \,c^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{6 b c \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{3 a \,c^{2} d \,x^{2}}{2}+\frac{6 i b c \,d^{2} e^{2} x}{f^{2}}-\frac{6 i b c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{6 i b c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{6 i b \,c^{2} d e x}{f}+a c \,d^{2} x^{3}+i b \,c^{3} x -\frac{i b \,d^{3} x^{4}}{4}+\frac{b \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}+\frac{b \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}-\frac{2 b \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{6 i b \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{2 b \,d^{3} e^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{b \,d^{3} e^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{4}}+a \,c^{3} x +\frac{a \,d^{3} x^{4}}{4}-\frac{3 i b \,d^{3} e^{4}}{2 f^{4}}+\frac{6 b c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{6 i b \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{3 b \,c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{6 b \,c^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 b c \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}+\frac{b \,d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}+\frac{6 b \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{b \,d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{3}}{f^{4}}+\frac{b \,d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}-i b c \,d^{2} x^{3}-\frac{3 i b \,c^{2} d \,x^{2}}{2}+\frac{6 b \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{6 b c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}"," ",0,"I*b*c^3*x-1/4*I*b*d^3*x^4+1/f^4*b*d^3*ln(1-exp(I*(f*x+e)))*e^3+1/f*b*d^3*ln(exp(I*(f*x+e))+1)*x^3-3*I/f^2*b*c^2*d*polylog(2,exp(I*(f*x+e)))+1/f*b*c^3*ln(exp(I*(f*x+e))+1)+1/f*b*c^3*ln(exp(I*(f*x+e))-1)-2/f*b*c^3*ln(exp(I*(f*x+e)))+3/2*a*c^2*d*x^2-3*I/f^2*b*c^2*d*polylog(2,-exp(I*(f*x+e)))+4*I/f^3*b*c*d^2*e^3-3*I/f^2*b*c^2*d*e^2-2*I/f^3*b*d^3*e^3*x-3*I/f^2*b*d^3*polylog(2,-exp(I*(f*x+e)))*x^2-3*I/f^2*b*d^3*polylog(2,exp(I*(f*x+e)))*x^2-I*b*c*d^2*x^3-3/2*I*b*c^2*d*x^2+a*c*d^2*x^3-6*I/f^2*b*c*d^2*polylog(2,exp(I*(f*x+e)))*x-6*I/f^2*b*c*d^2*polylog(2,-exp(I*(f*x+e)))*x+6*I/f^2*b*c*d^2*e^2*x-6*I/f*b*c^2*d*e*x+3/f*b*c*d^2*ln(1-exp(I*(f*x+e)))*x^2-3/f^3*b*c*d^2*ln(1-exp(I*(f*x+e)))*e^2+3/f*b*c^2*d*ln(1-exp(I*(f*x+e)))*x+3/f*b*c*d^2*ln(exp(I*(f*x+e))+1)*x^2+3/f^2*b*c^2*d*ln(1-exp(I*(f*x+e)))*e-3/f^2*b*c^2*d*e*ln(exp(I*(f*x+e))-1)-6/f^3*b*c*d^2*e^2*ln(exp(I*(f*x+e)))+a*c^3*x+1/4*a*d^3*x^4+3/f*b*c^2*d*ln(exp(I*(f*x+e))+1)*x+1/f*b*d^3*ln(1-exp(I*(f*x+e)))*x^3+6/f^2*b*c^2*d*e*ln(exp(I*(f*x+e)))+3/f^3*b*c*d^2*e^2*ln(exp(I*(f*x+e))-1)+6/f^3*b*d^3*polylog(3,-exp(I*(f*x+e)))*x+6/f^3*b*d^3*polylog(3,exp(I*(f*x+e)))*x+2/f^4*b*d^3*e^3*ln(exp(I*(f*x+e)))+6/f^3*b*c*d^2*polylog(3,exp(I*(f*x+e)))+6/f^3*b*c*d^2*polylog(3,-exp(I*(f*x+e)))-1/f^4*b*d^3*e^3*ln(exp(I*(f*x+e))-1)-3/2*I/f^4*b*d^3*e^4+6*I/f^4*b*d^3*polylog(4,-exp(I*(f*x+e)))+6*I/f^4*b*d^3*polylog(4,exp(I*(f*x+e)))","B"
38,1,516,98,1.221000," ","int((d*x+c)^2*(a+b*cot(f*x+e)),x)","a \,c^{2} x +a c d \,x^{2}+\frac{2 b c d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{2 b c d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{4 b c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 i b c d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 i b c d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 i b \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{2 i b \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{2 b \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{b \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}+i b \,c^{2} x -\frac{i b \,d^{2} x^{3}}{3}+\frac{b \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}-\frac{2 b \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{b \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}-\frac{b \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{3}}+\frac{b \,d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{a \,d^{2} x^{3}}{3}-\frac{4 i b c d e x}{f}+\frac{4 i b \,d^{2} e^{3}}{3 f^{3}}-\frac{2 b \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-i b c d \,x^{2}+\frac{b \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}+\frac{2 i b \,d^{2} e^{2} x}{f^{2}}-\frac{2 b c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{2 b c d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{2 i b c d \,e^{2}}{f^{2}}"," ",0,"a*c^2*x+a*c*d*x^2+I*b*c^2*x-1/3*I*b*d^2*x^3+2/f^3*b*d^2*polylog(3,-exp(I*(f*x+e)))+2/f^3*b*d^2*polylog(3,exp(I*(f*x+e)))+1/f*b*c^2*ln(exp(I*(f*x+e))+1)-2/f*b*c^2*ln(exp(I*(f*x+e)))+1/f*b*c^2*ln(exp(I*(f*x+e))-1)+4/3*I/f^3*b*d^2*e^3+1/3*a*d^2*x^3-2/f^3*b*d^2*e^2*ln(exp(I*(f*x+e)))+1/f^3*b*d^2*e^2*ln(exp(I*(f*x+e))-1)+1/f*b*d^2*ln(1-exp(I*(f*x+e)))*x^2-1/f^3*b*d^2*ln(1-exp(I*(f*x+e)))*e^2+1/f*b*d^2*ln(exp(I*(f*x+e))+1)*x^2-4*I/f*b*c*d*e*x-I*b*c*d*x^2-2*I/f^2*b*c*d*e^2-2*I/f^2*b*c*d*polylog(2,exp(I*(f*x+e)))+2*I/f^2*b*d^2*e^2*x-2*I/f^2*b*c*d*polylog(2,-exp(I*(f*x+e)))-2*I/f^2*b*d^2*polylog(2,-exp(I*(f*x+e)))*x-2*I/f^2*b*d^2*polylog(2,exp(I*(f*x+e)))*x-2/f^2*b*c*d*e*ln(exp(I*(f*x+e))-1)+2/f*b*c*d*ln(exp(I*(f*x+e))+1)*x+2/f^2*b*c*d*ln(1-exp(I*(f*x+e)))*e+4/f^2*b*c*d*e*ln(exp(I*(f*x+e)))+2/f*b*c*d*ln(1-exp(I*(f*x+e)))*x","B"
39,1,240,71,1.113000," ","int((d*x+c)*(a+b*cot(f*x+e)),x)","i b c x -\frac{i b d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{a d \,x^{2}}{2}+c a x -\frac{2 b c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{b c \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}+\frac{b c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}-\frac{i b d \,x^{2}}{2}-\frac{i b d \,e^{2}}{f^{2}}-\frac{i b d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{b d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{b d \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{2 i b d e x}{f}+\frac{b d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{2 b d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{b d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}"," ",0,"I*b*c*x-I/f^2*b*d*polylog(2,-exp(I*(f*x+e)))+1/2*a*d*x^2+c*a*x-2/f*b*c*ln(exp(I*(f*x+e)))+1/f*b*c*ln(exp(I*(f*x+e))-1)+1/f*b*c*ln(exp(I*(f*x+e))+1)-I/f^2*b*d*polylog(2,exp(I*(f*x+e)))-1/2*I*b*d*x^2-2*I/f*b*d*e*x+1/f*b*d*ln(1-exp(I*(f*x+e)))*x+1/f^2*b*d*ln(1-exp(I*(f*x+e)))*e-I/f^2*b*d*e^2+1/f*b*d*ln(exp(I*(f*x+e))+1)*x+2/f^2*b*d*e*ln(exp(I*(f*x+e)))-1/f^2*b*d*e*ln(exp(I*(f*x+e))-1)","B"
40,0,0,20,1.779000," ","int((a+b*cot(f*x+e))/(d*x+c),x)","\int \frac{a +b \cot \left(f x +e \right)}{d x +c}\, dx"," ",0,"int((a+b*cot(f*x+e))/(d*x+c),x)","F"
41,0,0,20,1.799000," ","int((a+b*cot(f*x+e))/(d*x+c)^2,x)","\int \frac{a +b \cot \left(f x +e \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*cot(f*x+e))/(d*x+c)^2,x)","F"
42,1,1571,266,1.819000," ","int((d*x+c)^3*(a+b*cot(f*x+e))^2,x)","a^{2} c^{3} x -b^{2} c^{3} x +\frac{3 b^{2} c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{12 i b a c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{12 i b a c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{12 i b a \,c^{2} d e x}{f}+\frac{12 i b a c \,d^{2} e^{2} x}{f^{2}}+\frac{3 b^{2} d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{4}}+\frac{2 b a \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}+a^{2} c \,d^{2} x^{3}-b^{2} c \,d^{2} x^{3}+\frac{3 a^{2} c^{2} d \,x^{2}}{2}-\frac{3 b^{2} c^{2} d \,x^{2}}{2}+\frac{4 i b^{2} d^{3} e^{3}}{f^{4}}+2 i a b \,c^{3} x -\frac{i a b \,d^{3} x^{4}}{2}-\frac{2 i b^{2} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{f \left({\mathrm e}^{2 i \left(f x +e \right)}-1\right)}+\frac{6 b^{2} d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{6 b^{2} d^{3} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{a^{2} d^{3} x^{4}}{4}-\frac{b^{2} d^{3} x^{4}}{4}+\frac{12 i b a \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{3 b^{2} c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{6 b^{2} c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 b a \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{2 b a \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}-\frac{6 b^{2} d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{3 b^{2} d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f^{2}}-\frac{2 i b^{2} d^{3} x^{3}}{f}+\frac{4 b a \,d^{3} e^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{12 b^{2} c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{6 b^{2} c \,d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f^{2}}+\frac{12 b a c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{12 b a c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{12 i b a \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{12 b a \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{12 b a \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i b^{2} c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 i b^{2} c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 i b^{2} d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i b^{2} d^{3} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i b a \,c^{2} d \,e^{2}}{f^{2}}-\frac{4 i b a \,d^{3} e^{3} x}{f^{3}}-\frac{12 i b^{2} c \,d^{2} e x}{f^{2}}+\frac{8 i b a c \,d^{2} e^{3}}{f^{3}}+\frac{6 b a c \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}-\frac{12 b a c \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{12 b a \,c^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 b a \,c^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{6 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a \,c^{2} d e}{f^{2}}-\frac{6 i b a \,c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 i b a \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{6 i b a \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{6 i b a \,c^{2} d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{6 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a \,c^{2} d x}{f}+\frac{6 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a \,c^{2} d x}{f}+\frac{6 b a c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{6 b a c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{3}}+\frac{6 b a c \,d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}-2 i a b c \,d^{2} x^{3}-3 i a b \,c^{2} d \,x^{2}+\frac{2 b a \,d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}+\frac{2 b a \,d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}+\frac{2 b a \,d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{3}}{f^{4}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{6 b^{2} c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{3}}-\frac{2 b a \,d^{3} e^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{4}}-\frac{3 i b \,e^{4} a \,d^{3}}{f^{4}}-\frac{6 i b^{2} c \,d^{2} x^{2}}{f}-\frac{6 i b^{2} c \,d^{2} e^{2}}{f^{3}}+\frac{6 i b^{2} d^{3} e^{2} x}{f^{3}}-\frac{6 b^{2} c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}"," ",0,"3/f^4*b^2*d^3*e^2*ln(exp(I*(f*x+e))-1)+a^2*c^3*x-b^2*c^3*x-2*I*a*b*c*d^2*x^3-3*I*a*b*c^2*d*x^2-12*I/f^2*b*a*c*d^2*polylog(2,exp(I*(f*x+e)))*x-12*I/f*b*a*c^2*d*e*x-12*I/f^2*b*a*c*d^2*polylog(2,-exp(I*(f*x+e)))*x+12*I/f^2*b*a*c*d^2*e^2*x+a^2*c*d^2*x^3-b^2*c*d^2*x^3+3/2*a^2*c^2*d*x^2-3/2*b^2*c^2*d*x^2+2/f*b*a*c^3*ln(exp(I*(f*x+e))+1)+3/f^2*b^2*c^2*d*ln(exp(I*(f*x+e))+1)+3/f^2*b^2*c^2*d*ln(exp(I*(f*x+e))-1)-6/f^2*b^2*c^2*d*ln(exp(I*(f*x+e)))-4/f*b*a*c^3*ln(exp(I*(f*x+e)))+2/f*b*a*c^3*ln(exp(I*(f*x+e))-1)-6/f^4*b^2*d^3*e^2*ln(exp(I*(f*x+e)))+3/f^2*b^2*d^3*ln(1-exp(I*(f*x+e)))*x^2-3/f^4*b^2*d^3*ln(1-exp(I*(f*x+e)))*e^2+3/f^2*b^2*d^3*ln(exp(I*(f*x+e))+1)*x^2-2*I/f*b^2*d^3*x^3+4*I/f^4*b^2*d^3*e^3+2*I*a*b*c^3*x-1/2*I*a*b*d^3*x^4+1/4*a^2*d^3*x^4-1/4*b^2*d^3*x^4+6/f^4*b^2*d^3*polylog(3,-exp(I*(f*x+e)))+6/f^4*b^2*d^3*polylog(3,exp(I*(f*x+e)))-2*I*b^2*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/(exp(2*I*(f*x+e))-1)+2/f*b*a*d^3*ln(exp(I*(f*x+e))+1)*x^3+2/f*b*a*d^3*ln(1-exp(I*(f*x+e)))*x^3+2/f^4*b*a*d^3*ln(1-exp(I*(f*x+e)))*e^3-6*I/f^2*b*a*c^2*d*e^2-6*I/f^2*b*a*c^2*d*polylog(2,-exp(I*(f*x+e)))-6*I/f^2*b*a*d^3*polylog(2,-exp(I*(f*x+e)))*x^2-6*I/f^2*b*a*d^3*polylog(2,exp(I*(f*x+e)))*x^2-6*I/f^2*b*a*c^2*d*polylog(2,exp(I*(f*x+e)))-4*I/f^3*b*a*d^3*e^3*x-12*I/f^2*b^2*c*d^2*e*x+8*I/f^3*b*a*c*d^2*e^3+6/f^3*b*a*c*d^2*e^2*ln(exp(I*(f*x+e))-1)-12/f^3*b*a*c*d^2*e^2*ln(exp(I*(f*x+e)))+12/f^2*b*a*c^2*d*e*ln(exp(I*(f*x+e)))-6/f^2*b*a*c^2*d*e*ln(exp(I*(f*x+e))-1)+6/f^2*b*ln(1-exp(I*(f*x+e)))*a*c^2*d*e+6/f^2*b^2*c*d^2*ln(1-exp(I*(f*x+e)))*x+6/f^3*b^2*c*d^2*ln(1-exp(I*(f*x+e)))*e-2/f^4*b*a*d^3*e^3*ln(exp(I*(f*x+e))-1)+12/f^3*b*a*c*d^2*polylog(3,exp(I*(f*x+e)))+12/f^3*b*a*c*d^2*polylog(3,-exp(I*(f*x+e)))-3*I/f^4*b*e^4*a*d^3+12*I/f^4*b*a*d^3*polylog(4,-exp(I*(f*x+e)))-6*I/f*b^2*c*d^2*x^2-6*I/f^3*b^2*c*d^2*e^2+6*I/f^3*b^2*d^3*e^2*x+6/f*b*ln(exp(I*(f*x+e))+1)*a*c^2*d*x+6/f*b*ln(1-exp(I*(f*x+e)))*a*c^2*d*x+6/f*b*a*c*d^2*ln(1-exp(I*(f*x+e)))*x^2-6/f^3*b*a*c*d^2*ln(1-exp(I*(f*x+e)))*e^2+6/f*b*a*c*d^2*ln(exp(I*(f*x+e))+1)*x^2-6/f^3*b^2*c*d^2*e*ln(exp(I*(f*x+e))-1)+4/f^4*b*a*d^3*e^3*ln(exp(I*(f*x+e)))+12/f^3*b^2*c*d^2*e*ln(exp(I*(f*x+e)))+12/f^3*b*a*d^3*polylog(3,exp(I*(f*x+e)))*x+12/f^3*b*a*d^3*polylog(3,-exp(I*(f*x+e)))*x+6/f^2*b^2*c*d^2*ln(exp(I*(f*x+e))+1)*x-6*I/f^3*b^2*c*d^2*polylog(2,-exp(I*(f*x+e)))-6*I/f^3*b^2*c*d^2*polylog(2,exp(I*(f*x+e)))-6*I/f^3*b^2*d^3*polylog(2,-exp(I*(f*x+e)))*x-6*I/f^3*b^2*d^3*polylog(2,exp(I*(f*x+e)))*x+12*I/f^4*b*a*d^3*polylog(4,exp(I*(f*x+e)))","B"
43,1,899,207,1.636000," ","int((d*x+c)^2*(a+b*cot(f*x+e))^2,x)","-\frac{8 i b a c d e x}{f}-\frac{4 i b a c d \,e^{2}}{f^{2}}-\frac{4 i b a c d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 i b a c d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-b^{2} c d \,x^{2}-\frac{2 i a b \,d^{2} x^{3}}{3}+\frac{4 b a \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 i b^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 i b^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{4 b a \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b^{2} d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f^{2}}+\frac{2 b a \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}-\frac{4 b a \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{2 b^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{2 b a \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}+\frac{2 b^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+a^{2} c d \,x^{2}+\frac{4 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a c d x}{f}-\frac{4 b a c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{8 b a c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{4 i b a \,d^{2} e^{2} x}{f^{2}}-\frac{4 i b a \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{4 i b a \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{4 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a c d e}{f^{2}}+\frac{4 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a c d x}{f}-\frac{2 i b^{2} d^{2} x^{2}}{f}-\frac{2 i b^{2} d^{2} e^{2}}{f^{3}}-\frac{2 i b^{2} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f \left({\mathrm e}^{2 i \left(f x +e \right)}-1\right)}-b^{2} c^{2} x +\frac{a^{2} d^{2} x^{3}}{3}-\frac{b^{2} d^{2} x^{3}}{3}+a^{2} c^{2} x +\frac{2 b^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{2 b^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{3}}+2 i a b \,c^{2} x +\frac{4 b^{2} d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 b^{2} d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}-\frac{4 b^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-2 i a b c d \,x^{2}+\frac{2 b a \,d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}+\frac{2 b a \,d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}-\frac{2 b a \,d^{2} e^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b a \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}-\frac{4 b a \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{4 i b^{2} d^{2} e x}{f^{2}}+\frac{8 i b a \,d^{2} e^{3}}{3 f^{3}}"," ",0,"-8*I/f*b*a*c*d*e*x-2*I*a*b*c*d*x^2-b^2*c*d*x^2+a^2*c*d*x^2+4/f*b*ln(exp(I*(f*x+e))+1)*a*c*d*x-4/f^2*b*a*c*d*e*ln(exp(I*(f*x+e))-1)+8/f^2*b*a*c*d*e*ln(exp(I*(f*x+e)))+4*I/f^2*b*a*d^2*e^2*x-4*I/f^2*b*a*c*d*polylog(2,exp(I*(f*x+e)))-4*I/f^2*b*a*c*d*polylog(2,-exp(I*(f*x+e)))-4*I/f^2*b*a*d^2*polylog(2,-exp(I*(f*x+e)))*x-4*I/f^2*b*a*d^2*polylog(2,exp(I*(f*x+e)))*x-4*I/f^2*b*a*c*d*e^2+4/f^2*b*ln(1-exp(I*(f*x+e)))*a*c*d*e+4/f*b*ln(1-exp(I*(f*x+e)))*a*c*d*x+2/f*b*a*d^2*ln(1-exp(I*(f*x+e)))*x^2+2/f*b*a*d^2*ln(exp(I*(f*x+e))+1)*x^2-2/f^3*b*a*d^2*e^2*ln(1-exp(I*(f*x+e)))+2/f^3*b*a*d^2*e^2*ln(exp(I*(f*x+e))-1)-4/f^3*b*a*d^2*e^2*ln(exp(I*(f*x+e)))-4*I/f^2*b^2*d^2*e*x+8/3*I/f^3*b*a*d^2*e^3-2/3*I*a*b*d^2*x^3+2/f^2*b^2*d^2*ln(exp(I*(f*x+e))+1)*x+4/f^3*b*a*d^2*polylog(3,-exp(I*(f*x+e)))+2/f*b*a*c^2*ln(exp(I*(f*x+e))+1)-4/f*b*a*c^2*ln(exp(I*(f*x+e)))+2/f^2*b^2*c*d*ln(exp(I*(f*x+e))+1)+2/f*b*a*c^2*ln(exp(I*(f*x+e))-1)+2/f^2*b^2*c*d*ln(exp(I*(f*x+e))-1)+2/f^2*b^2*d^2*ln(1-exp(I*(f*x+e)))*x+2/f^3*b^2*d^2*ln(1-exp(I*(f*x+e)))*e-b^2*c^2*x+1/3*a^2*d^2*x^3-1/3*b^2*d^2*x^3+a^2*c^2*x+2*I*a*b*c^2*x-2*I/f^3*b^2*d^2*polylog(2,-exp(I*(f*x+e)))-2*I/f^3*b^2*d^2*polylog(2,exp(I*(f*x+e)))+4/f^3*b^2*d^2*e*ln(exp(I*(f*x+e)))-2/f^3*b^2*d^2*e*ln(exp(I*(f*x+e))-1)+4/f^3*b*a*d^2*polylog(3,exp(I*(f*x+e)))-4/f^2*b^2*c*d*ln(exp(I*(f*x+e)))-2*I/f*b^2*d^2*x^2-2*I/f^3*b^2*d^2*e^2-2*I*b^2*(d^2*x^2+2*c*d*x+c^2)/f/(exp(2*I*(f*x+e))-1)","B"
44,1,365,127,1.348000," ","int((d*x+c)*(a+b*cot(f*x+e))^2,x)","-\frac{4 i b a d e x}{f}-\frac{2 i b a d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{a^{2} d \,x^{2}}{2}-\frac{b^{2} d \,x^{2}}{2}+a^{2} c x -b^{2} c x -\frac{2 i b^{2} \left(d x +c \right)}{f \left({\mathrm e}^{2 i \left(f x +e \right)}-1\right)}+\frac{b^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{b^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{2 b^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 b a c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{2 b a c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}+\frac{2 b a c \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}+\frac{4 b a d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 b a d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{2 i b a d \,e^{2}}{f^{2}}+\frac{2 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a d x}{f}+\frac{2 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a d e}{f^{2}}-i a b d \,x^{2}+\frac{2 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a d x}{f}-\frac{2 i b a d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+2 i a b c x"," ",0,"-4*I/f*b*a*d*e*x-2*I*b^2*(d*x+c)/f/(exp(2*I*(f*x+e))-1)+1/2*a^2*d*x^2-1/2*b^2*d*x^2+a^2*c*x-b^2*c*x-2*I/f^2*b*a*d*polylog(2,-exp(I*(f*x+e)))+1/f^2*b^2*d*ln(exp(I*(f*x+e))+1)+1/f^2*b^2*d*ln(exp(I*(f*x+e))-1)-2/f^2*b^2*d*ln(exp(I*(f*x+e)))-4/f*b*a*c*ln(exp(I*(f*x+e)))+2/f*b*a*c*ln(exp(I*(f*x+e))+1)+2/f*b*a*c*ln(exp(I*(f*x+e))-1)+4/f^2*b*a*d*e*ln(exp(I*(f*x+e)))-2/f^2*b*a*d*e*ln(exp(I*(f*x+e))-1)-2*I/f^2*b*a*d*e^2+2/f*b*ln(1-exp(I*(f*x+e)))*a*d*x+2/f^2*b*ln(1-exp(I*(f*x+e)))*a*d*e-I*a*b*d*x^2+2/f*b*ln(exp(I*(f*x+e))+1)*a*d*x+2*I*a*b*c*x-2*I/f^2*b*a*d*polylog(2,exp(I*(f*x+e)))","B"
45,0,0,22,5.793000," ","int((a+b*cot(f*x+e))^2/(d*x+c),x)","\int \frac{\left(a +b \cot \left(f x +e \right)\right)^{2}}{d x +c}\, dx"," ",0,"int((a+b*cot(f*x+e))^2/(d*x+c),x)","F"
46,0,0,22,7.245000," ","int((a+b*cot(f*x+e))^2/(d*x+c)^2,x)","\int \frac{\left(a +b \cot \left(f x +e \right)\right)^{2}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*cot(f*x+e))^2/(d*x+c)^2,x)","F"
47,1,3113,535,2.398000," ","int((d*x+c)^3*(a+b*cot(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-3*I*a^2*b*c*d^2*x^3-9/2*I*a^2*b*c^2*d*x^2-6/f^2*b^3*c^2*d*e*ln(exp(I*(f*x+e)))-18/f^2*b^2*a*c^2*d*ln(exp(I*(f*x+e)))+9/f^4*b^2*a*d^3*e^2*ln(exp(I*(f*x+e))-1)+9/f^2*b^2*a*c^2*d*ln(exp(I*(f*x+e))-1)-1/f*b^3*d^3*ln(exp(I*(f*x+e))+1)*x^3-18*I/f^2*b*polylog(2,exp(I*(f*x+e)))*a^2*c*d^2*x-18*I/f^2*b*polylog(2,-exp(I*(f*x+e)))*a^2*c*d^2*x-18*I/f*b*a^2*c^2*d*e*x+a^3*c*d^2*x^3+18*I/f^2*b*a^2*c*d^2*e^2*x-36*I/f^2*b^2*a*c*d^2*e*x-3/4*a*b^2*d^3*x^4+3/2*a^3*c^2*d*x^2-3*b^2*a*c^3*x+b^2*(3*I*d^3*x^2*b+3*I*b*c^2*d+2*b*d^3*f*x^3*exp(2*I*(f*x+e))-18*I*a*c^2*d*f*x*exp(2*I*(f*x+e))-6*I*b*c*d^2*x*exp(2*I*(f*x+e))-3*I*b*d^3*x^2*exp(2*I*(f*x+e))+6*b*c*d^2*f*x^2*exp(2*I*(f*x+e))+6*I*a*d^3*f*x^3+6*I*b*c*d^2*x-6*I*a*d^3*f*x^3*exp(2*I*(f*x+e))+6*b*c^2*d*f*x*exp(2*I*(f*x+e))+18*I*a*c*d^2*f*x^2-3*I*b*c^2*d*exp(2*I*(f*x+e))+6*I*a*c^3*f+2*b*c^3*f*exp(2*I*(f*x+e))+18*I*a*c^2*d*f*x-18*I*a*c*d^2*f*x^2*exp(2*I*(f*x+e))-6*I*a*c^3*f*exp(2*I*(f*x+e)))/f^2/(exp(2*I*(f*x+e))-1)^2-I*b^3*c^3*x+2/f*b^3*c^3*ln(exp(I*(f*x+e)))-1/f*b^3*c^3*ln(exp(I*(f*x+e))-1)-1/f*b^3*c^3*ln(exp(I*(f*x+e))+1)-9/f^4*b^2*a*d^3*e^2*ln(1-exp(I*(f*x+e)))-3/f*b^3*ln(exp(I*(f*x+e))+1)*c*d^2*x^2-3/f*b^3*ln(exp(I*(f*x+e))+1)*c^2*d*x-1/f*b^3*d^3*ln(1-exp(I*(f*x+e)))*x^3-1/f^4*b^3*d^3*ln(1-exp(I*(f*x+e)))*e^3+9/f^2*b^2*a*d^3*ln(1-exp(I*(f*x+e)))*x^2+9/f^2*b^2*a*d^3*ln(exp(I*(f*x+e))+1)*x^2-3/f*b^3*ln(1-exp(I*(f*x+e)))*c^2*d*x-3/f^2*b^3*ln(1-exp(I*(f*x+e)))*c^2*d*e+3/f*b*a^2*d^3*ln(exp(I*(f*x+e))+1)*x^3-6*I/f^3*b*a^2*d^3*e^3*x-6*I/f^2*b^3*c*d^2*e^2*x+12*I/f^3*b*a^2*c*d^2*e^3-9*I/f^2*b*a^2*c^2*d*polylog(2,exp(I*(f*x+e)))+6*I/f^2*b^3*polylog(2,-exp(I*(f*x+e)))*c*d^2*x-18*I/f^3*b^2*a*c*d^2*e^2-18*I/f^3*b^2*a*d^3*polylog(2,exp(I*(f*x+e)))*x-18*I/f^3*b^2*a*d^3*polylog(2,-exp(I*(f*x+e)))*x+1/4*a^3*d^3*x^4+a^3*c^3*x-3*a*b^2*c*d^2*x^3-9/2*a*b^2*c^2*d*x^2+1/4*I*b^3*d^3*x^4+I*b^3*c*d^2*x^3+9/f*b*ln(exp(I*(f*x+e))+1)*a^2*c*d^2*x^2+9/f*b*ln(1-exp(I*(f*x+e)))*a^2*c^2*d*x+9/f^2*b*ln(1-exp(I*(f*x+e)))*a^2*c^2*d*e-9/f^3*b*ln(1-exp(I*(f*x+e)))*a^2*c*d^2*e^2-18/f^3*b*a^2*c*d^2*e^2*ln(exp(I*(f*x+e)))-18/f^4*b^2*a*d^3*e^2*ln(exp(I*(f*x+e)))+18/f^3*b*a^2*c*d^2*polylog(3,exp(I*(f*x+e)))+18/f^3*b*a^2*c*d^2*polylog(3,-exp(I*(f*x+e)))-3/f^3*b^3*c*d^2*e^2*ln(exp(I*(f*x+e))-1)+9/f^2*b^2*a*c^2*d*ln(exp(I*(f*x+e))+1)-6/f^3*b^3*d^3*polylog(3,-exp(I*(f*x+e)))*x+6/f^4*b^3*d^3*e*ln(exp(I*(f*x+e)))+18/f^4*b^2*a*d^3*polylog(3,exp(I*(f*x+e)))+3/f*b*a^2*c^3*ln(exp(I*(f*x+e))-1)+3/f*b*a^2*c^3*ln(exp(I*(f*x+e))+1)+3/f^3*b^3*c*d^2*ln(exp(I*(f*x+e))-1)-6/f^3*b^3*c*d^2*polylog(3,-exp(I*(f*x+e)))-6/f*b*a^2*c^3*ln(exp(I*(f*x+e)))+3/f^3*b^3*c*d^2*ln(exp(I*(f*x+e))+1)-6/f^3*b^3*c*d^2*polylog(3,exp(I*(f*x+e)))-6/f^3*b^3*c*d^2*ln(exp(I*(f*x+e)))+18/f^4*b^2*a*d^3*polylog(3,-exp(I*(f*x+e)))-3/f^4*b^3*d^3*e*ln(exp(I*(f*x+e))-1)-2/f^4*b^3*d^3*e^3*ln(exp(I*(f*x+e)))+1/f^4*b^3*d^3*e^3*ln(exp(I*(f*x+e))-1)-3*I/f^4*b^3*d^3*polylog(2,-exp(I*(f*x+e)))-3*I/f^4*b^3*d^3*e^2-3*I/f^2*b^3*d^3*x^2+3/2*I/f^4*b^3*d^3*e^4+9/f^3*b*a^2*c*d^2*e^2*ln(exp(I*(f*x+e))-1)+18/f^2*b*a^2*c^2*d*e*ln(exp(I*(f*x+e)))+36/f^3*b^2*a*c*d^2*e*ln(exp(I*(f*x+e)))-18/f^3*b^2*a*c*d^2*e*ln(exp(I*(f*x+e))-1)-9/f^2*b*a^2*c^2*d*e*ln(exp(I*(f*x+e))-1)+3/f*b*a^2*d^3*ln(1-exp(I*(f*x+e)))*x^3+3/f^4*b*a^2*d^3*ln(1-exp(I*(f*x+e)))*e^3-3/4*I*a^2*b*d^3*x^4+3/2*I*b^3*c^2*d*x^2-3/f*b^3*ln(1-exp(I*(f*x+e)))*c*d^2*x^2-6*I/f^4*b^3*d^3*polylog(4,exp(I*(f*x+e)))-6*I/f^4*b^3*d^3*polylog(4,-exp(I*(f*x+e)))-3*I/f^4*b^3*d^3*polylog(2,exp(I*(f*x+e)))+6*I/f^2*b^3*polylog(2,exp(I*(f*x+e)))*c*d^2*x-18*I/f^3*b^2*a*c*d^2*polylog(2,exp(I*(f*x+e)))-18*I/f^3*b^2*a*c*d^2*polylog(2,-exp(I*(f*x+e)))+6*I/f*b^3*c^2*d*e*x+18*I/f^3*b^2*a*d^3*e^2*x-9*I/f^2*b*a^2*c^2*d*polylog(2,-exp(I*(f*x+e)))-18*I/f*b^2*a*c*d^2*x^2-9*I/f^2*b*a^2*d^3*polylog(2,exp(I*(f*x+e)))*x^2-9*I/f^2*b*a^2*c^2*d*e^2-9*I/f^2*b*a^2*d^3*polylog(2,-exp(I*(f*x+e)))*x^2+3*I*a^2*b*c^3*x+3/f^3*b^3*d^3*ln(1-exp(I*(f*x+e)))*x+3/f^4*b^3*d^3*ln(1-exp(I*(f*x+e)))*e+3/f^3*b^3*d^3*ln(exp(I*(f*x+e))+1)*x-6/f^3*b^3*d^3*polylog(3,exp(I*(f*x+e)))*x+18/f^3*b*a^2*d^3*polylog(3,exp(I*(f*x+e)))*x+18/f^3*b*a^2*d^3*polylog(3,-exp(I*(f*x+e)))*x+3/f^3*b^3*ln(1-exp(I*(f*x+e)))*c*d^2*e^2-3/f^4*b*a^2*d^3*e^3*ln(exp(I*(f*x+e))-1)+6/f^4*b*a^2*d^3*e^3*ln(exp(I*(f*x+e)))+6/f^3*b^3*c*d^2*e^2*ln(exp(I*(f*x+e)))+3/f^2*b^3*c^2*d*e*ln(exp(I*(f*x+e))-1)+12*I/f^4*b^2*a*d^3*e^3+3*I/f^2*b^3*c^2*d*e^2+3*I/f^2*b^3*c^2*d*polylog(2,exp(I*(f*x+e)))+3*I/f^2*b^3*c^2*d*polylog(2,-exp(I*(f*x+e)))-6*I/f^3*b^3*d^3*e*x-4*I/f^3*b^3*c*d^2*e^3-9/2*I/f^4*b*a^2*d^3*e^4+18*I/f^4*b*a^2*d^3*polylog(4,exp(I*(f*x+e)))+18*I/f^4*b*a^2*d^3*polylog(4,-exp(I*(f*x+e)))-6*I/f*b^2*a*d^3*x^3+3*I/f^2*b^3*d^3*polylog(2,-exp(I*(f*x+e)))*x^2+3*I/f^2*b^3*d^3*polylog(2,exp(I*(f*x+e)))*x^2+2*I/f^3*b^3*d^3*e^3*x+18/f^2*b^2*ln(1-exp(I*(f*x+e)))*a*c*d^2*x+18/f^2*b^2*ln(exp(I*(f*x+e))+1)*a*c*d^2*x+9/f*b*ln(exp(I*(f*x+e))+1)*a^2*c^2*d*x+18/f^3*b^2*ln(1-exp(I*(f*x+e)))*a*c*d^2*e+9/f*b*ln(1-exp(I*(f*x+e)))*a^2*c*d^2*x^2","B"
48,1,1740,399,2.066000," ","int((d*x+c)^2*(a+b*cot(f*x+e))^3,x)","-3 a \,b^{2} c d \,x^{2}+\frac{2 i b^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) d^{2} x}{f^{2}}+\frac{2 i b^{3} c d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 i b^{3} c d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 i b^{2} a \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{3 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d^{2} x^{2}}{f}+\frac{6 b^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a \,d^{2} e}{f^{3}}-\frac{3 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d^{2} e^{2}}{f^{3}}+\frac{6 b^{2} a c d \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{6 b^{2} a c d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{12 b^{2} a c d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 b^{3} c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 b^{2} a \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}-\frac{6 b \,a^{2} d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{3 b \,a^{2} d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}+\frac{12 b^{2} a \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) c d x}{f}-\frac{2 b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) c d e}{f^{2}}-\frac{2 b^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) c d x}{f}+\frac{6 b^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a \,d^{2} x}{f^{2}}+\frac{6 b^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a \,d^{2} x}{f^{2}}-\frac{12 i b \,a^{2} c d e x}{f}+a^{3} c d \,x^{2}-a \,b^{2} d^{2} x^{3}-3 b^{2} a \,c^{2} x +\frac{a^{3} d^{2} x^{3}}{3}+a^{3} c^{2} x -i a^{2} b \,d^{2} x^{3}+\frac{b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) d^{2} e^{2}}{f^{3}}-\frac{4 i b^{3} d^{2} e^{3}}{3 f^{3}}+3 i a^{2} b \,c^{2} x -\frac{b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) d^{2} x^{2}}{f}-\frac{b^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) d^{2} x^{2}}{f}+\frac{3 b \,a^{2} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}-\frac{b^{3} d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}+\frac{2 b^{3} d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 b \,a^{2} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{3 b \,a^{2} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}+\frac{i b^{3} d^{2} x^{3}}{3}-\frac{b^{3} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}-\frac{b^{3} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}+\frac{b^{3} d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}+\frac{b^{3} d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{3}}-\frac{2 b^{3} d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b^{2} \left(-3 i a \,d^{2} f \,x^{2} {\mathrm e}^{2 i \left(f x +e \right)}-6 i a c d f x \,{\mathrm e}^{2 i \left(f x +e \right)}+b \,d^{2} f \,x^{2} {\mathrm e}^{2 i \left(f x +e \right)}-3 i a \,c^{2} f \,{\mathrm e}^{2 i \left(f x +e \right)}+3 i a \,d^{2} f \,x^{2}-i b \,d^{2} x \,{\mathrm e}^{2 i \left(f x +e \right)}+2 b c d f x \,{\mathrm e}^{2 i \left(f x +e \right)}+6 i a c d f x -i b c d \,{\mathrm e}^{2 i \left(f x +e \right)}+b \,c^{2} f \,{\mathrm e}^{2 i \left(f x +e \right)}+3 i a \,c^{2} f +i d^{2} x b +i b c d \right)}{f^{2} \left({\mathrm e}^{2 i \left(f x +e \right)}-1\right)^{2}}+\frac{2 b^{3} c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{2 b^{3} d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 b^{3} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-i b^{3} c^{2} x +\frac{6 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a^{2} c d x}{f}+\frac{6 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} c d x}{f}+\frac{6 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} c d e}{f^{2}}-\frac{6 b \,a^{2} c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{12 b \,a^{2} c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{12 i b^{2} a \,d^{2} e x}{f^{2}}+\frac{4 i b^{3} c d e x}{f}+\frac{6 i b \,a^{2} d^{2} e^{2} x}{f^{2}}-\frac{6 i b \,a^{2} c d \,e^{2}}{f^{2}}-\frac{6 i b \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d^{2} x}{f^{2}}-\frac{6 i b \,a^{2} c d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 i b \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d^{2} x}{f^{2}}-\frac{6 i b \,a^{2} c d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a^{2} d^{2} x^{2}}{f}+\frac{2 b^{3} c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{6 i b^{2} a \,d^{2} e^{2}}{f^{3}}+\frac{4 i b \,a^{2} d^{2} e^{3}}{f^{3}}-\frac{6 i b^{2} a \,d^{2} x^{2}}{f}+\frac{2 i b^{3} c d \,e^{2}}{f^{2}}-\frac{2 i b^{3} d^{2} e^{2} x}{f^{2}}-\frac{6 i b^{2} a \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 i b^{3} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) d^{2} x}{f^{2}}+i b^{3} c d \,x^{2}+\frac{6 b \,a^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{6 b \,a^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-3 i a^{2} b c d \,x^{2}"," ",0,"-3*a*b^2*c*d*x^2-12*I/f*b*a^2*c*d*e*x+a^3*c*d*x^2+1/3*I*b^3*d^2*x^3+I*b^3*c*d*x^2-1/f*b^3*c^2*ln(exp(I*(f*x+e))-1)-1/f*b^3*c^2*ln(exp(I*(f*x+e))+1)+1/f^3*b^3*d^2*ln(exp(I*(f*x+e))+1)+1/f^3*b^3*d^2*ln(exp(I*(f*x+e))-1)-2/f^3*b^3*d^2*polylog(3,exp(I*(f*x+e)))-2/f^3*b^3*d^2*polylog(3,-exp(I*(f*x+e)))-2/f^3*b^3*d^2*ln(exp(I*(f*x+e)))-3*I*a^2*b*c*d*x^2-a*b^2*d^2*x^3-3*b^2*a*c^2*x+2*b^2*(-3*I*a*d^2*f*x^2*exp(2*I*(f*x+e))-6*I*a*c*d*f*x*exp(2*I*(f*x+e))+b*d^2*f*x^2*exp(2*I*(f*x+e))-3*I*a*c^2*f*exp(2*I*(f*x+e))+3*I*a*d^2*f*x^2-I*b*d^2*x*exp(2*I*(f*x+e))+2*b*c*d*f*x*exp(2*I*(f*x+e))+6*I*a*c*d*f*x-I*b*c*d*exp(2*I*(f*x+e))+b*c^2*f*exp(2*I*(f*x+e))+3*I*a*c^2*f+I*d^2*x*b+I*b*c*d)/f^2/(exp(2*I*(f*x+e))-1)^2+6/f*b*ln(exp(I*(f*x+e))+1)*a^2*c*d*x+6/f*b*ln(1-exp(I*(f*x+e)))*a^2*c*d*x+6/f^2*b*ln(1-exp(I*(f*x+e)))*a^2*c*d*e-6/f^2*b*a^2*c*d*e*ln(exp(I*(f*x+e))-1)+12/f^2*b*a^2*c*d*e*ln(exp(I*(f*x+e)))+2/f*b^3*c^2*ln(exp(I*(f*x+e)))+1/3*a^3*d^2*x^3+a^3*c^2*x-I*a^2*b*d^2*x^3-12*I/f^2*b^2*a*d^2*e*x+4*I/f*b^3*c*d*e*x+6*I/f^2*b*a^2*d^2*e^2*x-6*I/f^2*b*a^2*c*d*e^2-6*I/f^2*b*polylog(2,-exp(I*(f*x+e)))*a^2*d^2*x-6*I/f^2*b*a^2*c*d*polylog(2,-exp(I*(f*x+e)))-6*I/f^2*b*polylog(2,exp(I*(f*x+e)))*a^2*d^2*x-6*I/f^2*b*a^2*c*d*polylog(2,exp(I*(f*x+e)))+6/f^3*b*a^2*d^2*polylog(3,exp(I*(f*x+e)))+1/f^3*b^3*ln(1-exp(I*(f*x+e)))*d^2*e^2-4/3*I/f^3*b^3*d^2*e^3-I*b^3*c^2*x+3/f*b*ln(1-exp(I*(f*x+e)))*a^2*d^2*x^2+6/f^3*b^2*ln(1-exp(I*(f*x+e)))*a*d^2*e-3/f^3*b*ln(1-exp(I*(f*x+e)))*a^2*d^2*e^2+6/f^2*b^2*a*c*d*ln(exp(I*(f*x+e))-1)+6/f^2*b^2*a*c*d*ln(exp(I*(f*x+e))+1)-12/f^2*b^2*a*c*d*ln(exp(I*(f*x+e)))-4/f^2*b^3*c*d*e*ln(exp(I*(f*x+e)))-6/f^3*b^2*a*d^2*e*ln(exp(I*(f*x+e))-1)+3*I*a^2*b*c^2*x-1/f*b^3*ln(1-exp(I*(f*x+e)))*d^2*x^2-1/f*b^3*ln(exp(I*(f*x+e))+1)*d^2*x^2+3/f*b*a^2*c^2*ln(exp(I*(f*x+e))+1)-1/f^3*b^3*d^2*e^2*ln(exp(I*(f*x+e))-1)+2/f^3*b^3*d^2*e^2*ln(exp(I*(f*x+e)))-6/f*b*a^2*c^2*ln(exp(I*(f*x+e)))+3/f*b*a^2*c^2*ln(exp(I*(f*x+e))-1)+6/f^3*b*a^2*d^2*polylog(3,-exp(I*(f*x+e)))-6/f^3*b*a^2*d^2*e^2*ln(exp(I*(f*x+e)))+3/f^3*b*a^2*d^2*e^2*ln(exp(I*(f*x+e))-1)+12/f^3*b^2*a*d^2*e*ln(exp(I*(f*x+e)))-2/f*b^3*ln(1-exp(I*(f*x+e)))*c*d*x-2/f^2*b^3*ln(1-exp(I*(f*x+e)))*c*d*e-2/f*b^3*ln(exp(I*(f*x+e))+1)*c*d*x+6/f^2*b^2*ln(1-exp(I*(f*x+e)))*a*d^2*x+6/f^2*b^2*ln(exp(I*(f*x+e))+1)*a*d^2*x+3/f*b*ln(exp(I*(f*x+e))+1)*a^2*d^2*x^2+2/f^2*b^3*c*d*e*ln(exp(I*(f*x+e))-1)-6*I/f^3*b^2*a*d^2*polylog(2,exp(I*(f*x+e)))-6*I/f^3*b^2*a*d^2*e^2+4*I/f^3*b*a^2*d^2*e^3-6*I/f*b^2*a*d^2*x^2+2*I/f^2*b^3*polylog(2,exp(I*(f*x+e)))*d^2*x+2*I/f^2*b^3*polylog(2,-exp(I*(f*x+e)))*d^2*x+2*I/f^2*b^3*c*d*polylog(2,exp(I*(f*x+e)))+2*I/f^2*b^3*c*d*polylog(2,-exp(I*(f*x+e)))-6*I/f^3*b^2*a*d^2*polylog(2,-exp(I*(f*x+e)))+2*I/f^2*b^3*c*d*e^2-2*I/f^2*b^3*d^2*e^2*x","B"
49,1,745,248,1.809000," ","int((d*x+c)*(a+b*cot(f*x+e))^3,x)","\frac{b^{2} \left(-6 i a d f x \,{\mathrm e}^{2 i \left(f x +e \right)}-6 i a c f \,{\mathrm e}^{2 i \left(f x +e \right)}+2 b d f x \,{\mathrm e}^{2 i \left(f x +e \right)}+6 i a d f x -i b d \,{\mathrm e}^{2 i \left(f x +e \right)}+2 b c f \,{\mathrm e}^{2 i \left(f x +e \right)}+6 i a c f +i d b \right)}{f^{2} \left({\mathrm e}^{2 i \left(f x +e \right)}-1\right)^{2}}+\frac{i b^{3} d \,x^{2}}{2}-\frac{3 i a^{2} b d \,x^{2}}{2}+\frac{i b^{3} d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{b^{3} c \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}+\frac{2 b^{3} c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{b^{3} c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}-i b^{3} c x +\frac{i b^{3} d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 b \,a^{2} c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f}+\frac{3 b \,a^{2} c \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f}-\frac{6 b \,a^{2} c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{b^{3} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}+\frac{3 b^{2} a d \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{3 b^{2} a d \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{6 b^{2} a d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 b^{3} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) d e}{f^{2}}-\frac{b^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) d x}{f}-\frac{b^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) d x}{f}-\frac{6 i b \,a^{2} d e x}{f}+3 i a^{2} b c x +\frac{i b^{3} d \,e^{2}}{f^{2}}+\frac{a^{3} d \,x^{2}}{2}+a^{3} c x -3 a \,b^{2} c x -\frac{3 a \,b^{2} d \,x^{2}}{2}+\frac{3 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d e}{f^{2}}+\frac{3 b \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) a^{2} d x}{f}+\frac{3 b \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) a^{2} d x}{f}+\frac{6 b \,a^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{3 b \,a^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{f^{2}}-\frac{3 i b \,a^{2} d \,e^{2}}{f^{2}}+\frac{2 i b^{3} d e x}{f}-\frac{3 i b \,a^{2} d \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{3 i b \,a^{2} d \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}"," ",0,"-1/f*b^3*c*ln(exp(I*(f*x+e))-1)+2/f*b^3*c*ln(exp(I*(f*x+e)))-1/f*b^3*c*ln(exp(I*(f*x+e))+1)-6*I/f*b*a^2*d*e*x-I*b^3*c*x+b^2*(-6*I*a*d*f*x*exp(2*I*(f*x+e))-6*I*a*c*f*exp(2*I*(f*x+e))+2*b*d*f*x*exp(2*I*(f*x+e))+6*I*a*d*f*x-I*b*d*exp(2*I*(f*x+e))+2*b*c*f*exp(2*I*(f*x+e))+6*I*a*c*f+I*d*b)/f^2/(exp(2*I*(f*x+e))-1)^2-3/2*I*a^2*b*d*x^2+1/2*a^3*d*x^2+a^3*c*x-3*a*b^2*c*x-3/2*a*b^2*d*x^2+1/2*I*b^3*d*x^2+3/f*b*a^2*c*ln(exp(I*(f*x+e))+1)+3/f*b*a^2*c*ln(exp(I*(f*x+e))-1)-6/f*b*a^2*c*ln(exp(I*(f*x+e)))+I/f^2*b^3*d*polylog(2,exp(I*(f*x+e)))+1/f^2*b^3*d*e*ln(exp(I*(f*x+e))-1)+3/f^2*b^2*a*d*ln(exp(I*(f*x+e))+1)+3/f^2*b^2*a*d*ln(exp(I*(f*x+e))-1)-6/f^2*b^2*a*d*ln(exp(I*(f*x+e)))-2/f^2*b^3*d*e*ln(exp(I*(f*x+e)))-1/f^2*b^3*ln(1-exp(I*(f*x+e)))*d*e-1/f*b^3*ln(1-exp(I*(f*x+e)))*d*x-1/f*b^3*ln(exp(I*(f*x+e))+1)*d*x+3*I*a^2*b*c*x+I/f^2*b^3*d*e^2+I/f^2*b^3*d*polylog(2,-exp(I*(f*x+e)))+3/f^2*b*ln(1-exp(I*(f*x+e)))*a^2*d*e+3/f*b*ln(exp(I*(f*x+e))+1)*a^2*d*x+3/f*b*ln(1-exp(I*(f*x+e)))*a^2*d*x+6/f^2*b*a^2*d*e*ln(exp(I*(f*x+e)))-3/f^2*b*a^2*d*e*ln(exp(I*(f*x+e))-1)-3*I/f^2*b*a^2*d*polylog(2,-exp(I*(f*x+e)))-3*I/f^2*b*a^2*d*e^2-3*I/f^2*b*a^2*d*polylog(2,exp(I*(f*x+e)))+2*I/f*b^3*d*e*x","B"
50,0,0,22,8.519000," ","int((a+b*cot(f*x+e))^3/(d*x+c),x)","\int \frac{\left(a +b \cot \left(f x +e \right)\right)^{3}}{d x +c}\, dx"," ",0,"int((a+b*cot(f*x+e))^3/(d*x+c),x)","F"
51,0,0,22,11.166000," ","int((a+b*cot(f*x+e))^3/(d*x+c)^2,x)","\int \frac{\left(a +b \cot \left(f x +e \right)\right)^{3}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*cot(f*x+e))^3/(d*x+c)^2,x)","F"
52,1,1386,215,2.556000," ","int((d*x+c)^3/(a+b*cot(f*x+e)),x)","\frac{6 i b c \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3} \left(-i a +b \right) \left(i b -a \right)}+\frac{3 i b \,d^{3} \polylog \left(3, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{2 f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{i b \,d^{3} e^{3} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{f^{4} \left(-i a +b \right) \left(-i b +a \right)}+\frac{6 b \,c^{2} d e x}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{i b \,d^{3} e^{3} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{4} \left(-i a +b \right) \left(i b -a \right)}-\frac{6 b c \,d^{2} e^{2} x}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}-\frac{2 i b \,d^{3} e^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4} \left(-i a +b \right) \left(i b -a \right)}+\frac{3 i b c \,d^{2} \polylog \left(3, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{2 f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b c \,d^{2} \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{i b \,d^{3} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x^{3}}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b \,d^{3} \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x^{2}}{2 f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b \,c^{2} d \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{2 f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{c \,d^{2} x^{3}}{i b +a}+\frac{3 c^{2} d \,x^{2}}{2 \left(i b +a \right)}+\frac{c^{3} x}{i b +a}+\frac{b \,d^{3} x^{4}}{2 \left(-i a +b \right) \left(-i b +a \right)}+\frac{d^{3} x^{4}}{4 i b +4 a}-\frac{6 i b \,c^{2} d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2} \left(-i a +b \right) \left(i b -a \right)}+\frac{2 i b \,c^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f \left(-i a +b \right) \left(i b -a \right)}-\frac{i b \,c^{3} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f \left(-i a +b \right) \left(i b -a \right)}-\frac{4 b c \,d^{2} e^{3}}{f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b \,c^{2} d \,e^{2}}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 b \,d^{3} e^{3} x}{f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 i b c \,d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x^{2}}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 i b \,c^{2} d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{3 i b \,c^{2} d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{2} \left(-i a +b \right) \left(i b -a \right)}-\frac{3 i b c \,d^{2} e^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{f^{3} \left(-i a +b \right) \left(-i b +a \right)}-\frac{3 i b c \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{3} \left(-i a +b \right) \left(i b -a \right)}+\frac{3 i b \,c^{2} d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 b c \,d^{2} x^{3}}{\left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b \,c^{2} d \,x^{2}}{\left(-i a +b \right) \left(-i b +a \right)}+\frac{3 b \,d^{3} e^{4}}{2 f^{4} \left(-i a +b \right) \left(-i b +a \right)}-\frac{3 b \,d^{3} \polylog \left(4, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{4 f^{4} \left(-i a +b \right) \left(-i b +a \right)}"," ",0,"3/2*I/f^3/(b-I*a)*b*d^3/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+I/f^4/(b-I*a)*b*d^3*e^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+I/f/(b-I*a)*b*d^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^3+3/2*I/f^3/(b-I*a)*b*c*d^2/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-2*I/f^4/(b-I*a)*b*d^3*e^3/(I*b-a)*ln(exp(I*(f*x+e)))+3/f^2/(b-I*a)*b*c*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-6/f^2/(b-I*a)*b*c*d^2/(a-I*b)*e^2*x+6/f/(b-I*a)*b*c^2*d/(a-I*b)*e*x+I/f^4/(b-I*a)*b*d^3*e^3/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+3*I/f/(b-I*a)*b*c*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2+1/2/(b-I*a)*b*d^3/(a-I*b)*x^4+1/4/(a+I*b)*d^3*x^4+1/(a+I*b)*c^3*x+1/(a+I*b)*c*d^2*x^3+3/2/(a+I*b)*c^2*d*x^2+3/2/f^2/(b-I*a)*b*d^3/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2+3/2/f^2/(b-I*a)*b*c^2*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-4/f^3/(b-I*a)*b*c*d^2/(a-I*b)*e^3+3/f^2/(b-I*a)*b*c^2*d/(a-I*b)*e^2+2/f^3/(b-I*a)*b*d^3/(a-I*b)*e^3*x+2*I/f/(b-I*a)*b*c^3/(I*b-a)*ln(exp(I*(f*x+e)))-I/f/(b-I*a)*b*c^3/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+3*I/f^2/(b-I*a)*b*c^2*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+3*I/f^2/(b-I*a)*b*c^2*d*e/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-3*I/f^3/(b-I*a)*b*c*d^2*e^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-3*I/f^3/(b-I*a)*b*c*d^2*e^2/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+3*I/f/(b-I*a)*b*c^2*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+6*I/f^3/(b-I*a)*b*c*d^2*e^2/(I*b-a)*ln(exp(I*(f*x+e)))-6*I/f^2/(b-I*a)*b*c^2*d*e/(I*b-a)*ln(exp(I*(f*x+e)))+2/(b-I*a)*b*c*d^2/(a-I*b)*x^3+3/(b-I*a)*b*c^2*d/(a-I*b)*x^2-3/4/f^4/(b-I*a)*b*d^3/(a-I*b)*polylog(4,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+3/2/f^4/(b-I*a)*b*d^3/(a-I*b)*e^4","B"
53,1,881,163,2.273000," ","int((d*x+c)^2/(a+b*cot(f*x+e)),x)","\frac{d^{2} x^{3}}{3 i b +3 a}+\frac{c d \,x^{2}}{i b +a}+\frac{c^{2} x}{i b +a}-\frac{i b \,c^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f \left(-i a +b \right) \left(i b -a \right)}+\frac{i b \,d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x^{2}}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{i b \,d^{2} \polylog \left(3, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{2 f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 i b c d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{2} \left(-i a +b \right) \left(i b -a \right)}+\frac{2 b \,d^{2} x^{3}}{3 \left(-i a +b \right) \left(-i b +a \right)}-\frac{2 b \,d^{2} e^{2} x}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}-\frac{4 b \,d^{2} e^{3}}{3 f^{3} \left(-i a +b \right) \left(-i b +a \right)}-\frac{4 i b c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2} \left(-i a +b \right) \left(i b -a \right)}+\frac{2 i b c d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 i b \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3} \left(-i a +b \right) \left(i b -a \right)}+\frac{2 i b \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f \left(-i a +b \right) \left(i b -a \right)}-\frac{i b \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{3} \left(-i a +b \right) \left(i b -a \right)}+\frac{b \,d^{2} \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}-\frac{i b \,d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e^{2}}{f^{3} \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 i b c d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 b c d \,x^{2}}{\left(-i a +b \right) \left(-i b +a \right)}+\frac{4 b c d e x}{f \left(-i a +b \right) \left(-i b +a \right)}+\frac{2 b c d \,e^{2}}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}+\frac{b c d \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{f^{2} \left(-i a +b \right) \left(-i b +a \right)}"," ",0,"1/3/(a+I*b)*d^2*x^3+1/(a+I*b)*c*d*x^2+1/(a+I*b)*c^2*x-I/f/(b-I*a)*b*c^2/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+I/f/(b-I*a)*b*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2+2*I/f^2/(b-I*a)*b*c*d*e/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+1/2*I/f^3/(b-I*a)*b*d^2/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+2/3/(b-I*a)*b*d^2/(a-I*b)*x^3-2/f^2/(b-I*a)*b*d^2/(a-I*b)*e^2*x-4/3/f^3/(b-I*a)*b*d^2/(a-I*b)*e^3-4*I/f^2/(b-I*a)*b*c*d*e/(I*b-a)*ln(exp(I*(f*x+e)))+2*I/f/(b-I*a)*b*c*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+2*I/f^3/(b-I*a)*b*d^2*e^2/(I*b-a)*ln(exp(I*(f*x+e)))+2*I/f/(b-I*a)*b*c^2/(I*b-a)*ln(exp(I*(f*x+e)))-I/f^3/(b-I*a)*b*d^2*e^2/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+1/f^2/(b-I*a)*b*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-I/f^3/(b-I*a)*b*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e^2+2*I/f^2/(b-I*a)*b*c*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+2/(b-I*a)*b*c*d/(a-I*b)*x^2+4/f/(b-I*a)*b*c*d/(a-I*b)*e*x+2/f^2/(b-I*a)*b*c*d/(a-I*b)*e^2+1/f^2/(b-I*a)*b*c*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))","B"
54,1,445,112,2.251000," ","int((d*x+c)/(a+b*cot(f*x+e)),x)","\frac{d \,x^{2}}{2 i b +2 a}+\frac{c x}{i b +a}-\frac{2 b c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f \left(i b +a \right) \left(i b -a \right)}+\frac{b c \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f \left(i b +a \right) \left(i b -a \right)}-\frac{b d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{f \left(i b +a \right) \left(-i b +a \right)}-\frac{b d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{f^{2} \left(i b +a \right) \left(-i b +a \right)}+\frac{i b d \,x^{2}}{\left(i b +a \right) \left(-i b +a \right)}+\frac{2 i b d e x}{f \left(i b +a \right) \left(-i b +a \right)}+\frac{i b d \,e^{2}}{f^{2} \left(i b +a \right) \left(-i b +a \right)}+\frac{i b d \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{2 f^{2} \left(i b +a \right) \left(-i b +a \right)}+\frac{2 b d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2} \left(i b +a \right) \left(i b -a \right)}-\frac{b d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{f^{2} \left(i b +a \right) \left(i b -a \right)}"," ",0,"1/2/(a+I*b)*d*x^2+1/(a+I*b)*c*x-2/f*b/(a+I*b)*c/(I*b-a)*ln(exp(I*(f*x+e)))+1/f*b/(a+I*b)*c/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-1/f*b/(a+I*b)*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-1/f^2*b/(a+I*b)*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+I*b/(a+I*b)*d/(a-I*b)*x^2+2*I/f*b/(a+I*b)*d/(a-I*b)*e*x+I/f^2*b/(a+I*b)*d/(a-I*b)*e^2+1/2*I/f^2*b/(a+I*b)*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+2/f^2*b/(a+I*b)*d*e/(I*b-a)*ln(exp(I*(f*x+e)))-1/f^2*b/(a+I*b)*d*e/(I*b-a)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)","B"
55,0,0,22,3.290000," ","int(1/(d*x+c)/(a+b*cot(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +b \cot \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+b*cot(f*x+e)),x)","F"
56,0,0,22,5.052000," ","int(1/(d*x+c)^2/(a+b*cot(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \cot \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*cot(f*x+e)),x)","F"
57,1,3446,754,2.917000," ","int((d*x+c)^3/(a+b*cot(f*x+e))^2,x)","\text{output too large to display}"," ",0,"-8/(b-I*a)^2/f^3/(I*a+b)*b*a*c*d^2/(a-I*b)*e^3-12/(b-I*a)^2/f^2/(I*a+b)*b^2*c*d^2/(a-I*b)*e*x+4/(b-I*a)^2/f^3/(I*a+b)*b*a*d^3*e^3/(a-I*b)*x+3/(b-I*a)^2/f^2/(I*a+b)*b*a*c^2*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+3/(b-I*a)^2/f^2/(I*a+b)*b*a*d^3/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2+4*I/(b-I*a)^2/f/(I*a+b)*b*a*c^3/(I*b-a)*ln(exp(I*(f*x+e)))-6/(b-I*a)^2/f^3/(I*a+b)*b^2*c*d^2/(a-I*b)*e^2-6/(b-I*a)^2/f/(I*a+b)*b^2*c*d^2/(a-I*b)*x^2-3/2/(b-I*a)^2/f^4/(I*a+b)*b*a*d^3/(a-I*b)*polylog(4,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-3/(b-I*a)^2/f^3/(I*a+b)*b^2*c*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+3/(b-I*a)^2/f^4/(I*a+b)*b*a*d^3*e^4/(a-I*b)+6/(b-I*a)^2/f^3/(I*a+b)*b^2*d^3/(a-I*b)*e^2*x-3/(b-I*a)^2/f^3/(I*a+b)*b^2*d^3/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+4/(b-I*a)^2/(I*a+b)*b*a*c*d^2/(a-I*b)*x^3+6/(b-I*a)^2/(I*a+b)*b*a*c^2*d/(a-I*b)*x^2-3/2*I/(b-I*a)^2/f^4/(I*a+b)*b^2*d^3/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+2*I*b^2*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/(I*a+b)/f/(b-I*a)^2/(exp(2*I*(f*x+e))*b-I*exp(2*I*(f*x+e))*a+b+I*a)-6*I/(b-I*a)^2/f^2/(I*a+b)*b^2*c^2*d/(I*b-a)*ln(exp(I*(f*x+e)))-3*I/(b-I*a)^2/f^2/(I*a+b)*b^2*d^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2-6*I/(b-I*a)^2/f^4/(I*a+b)*b^2*d^3*e^2/(I*b-a)*ln(exp(I*(f*x+e)))+3*I/(b-I*a)^2/f^4/(I*a+b)*b^2*d^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e^2+6*I/(b-I*a)^2/f^2/(I*a+b)*b*a^2*c^2*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-6*I/(b-I*a)^2/f^3/(I*a+b)*b*a^2*c*d^2*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-6*I/(b-I*a)^2/f^3/(I*a+b)*b^2*c*d^2*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a+1/(2*I*a*b+a^2-b^2)*c*d^2*x^3+3/2/(2*I*a*b+a^2-b^2)*c^2*d*x^2+1/(b-I*a)^2/(I*a+b)*b*a*d^3/(a-I*b)*x^4-2/(b-I*a)^2/f/(I*a+b)*b^2*d^3/(a-I*b)*x^3+4/(b-I*a)^2/f^4/(I*a+b)*b^2*d^3/(a-I*b)*e^3+1/4/(2*I*a*b+a^2-b^2)*d^3*x^4+1/(2*I*a*b+a^2-b^2)*c^3*x-3/(b-I*a)^2/f^2/(I*a+b)*b^3*c^2*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+2/(b-I*a)^2/f/(I*a+b)*b^2*a*c^3/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+6/(b-I*a)^2/f^2/(I*a+b)*b*a*c^2*d/(a-I*b)*e^2-3/(b-I*a)^2/f^4/(I*a+b)*b^3*d^3*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-6/(b-I*a)^2/f^2/(I*a+b)*b^2*a*c^2*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+6/(b-I*a)^2/f^3/(I*a+b)*b^2*a*c*d^2*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+6*I/(b-I*a)^2/f/(I*a+b)*b*a*c*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2+2*I/(b-I*a)^2/f^4/(I*a+b)*b*a^2*d^3*e^3/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+12*I/(b-I*a)^2/f^3/(I*a+b)*b*a*c*d^2*e^2/(I*b-a)*ln(exp(I*(f*x+e)))+6*I/(b-I*a)^2/f/(I*a+b)*b*a*c^2*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+3*I/(b-I*a)^2/f^2/(I*a+b)*b^2*c^2*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a+6*I/(b-I*a)^2/f^2/(I*a+b)*b*a*c^2*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e-12*I/(b-I*a)^2/f^2/(I*a+b)*b*a*c^2*d*e/(I*b-a)*ln(exp(I*(f*x+e)))+3*I/(b-I*a)^2/f^4/(I*a+b)*b^2*d^3*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a-6*I/(b-I*a)^2/f^3/(I*a+b)*b*a*c*d^2*e^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-2/(b-I*a)^2/f^4/(I*a+b)*b^2*a*d^3*e^3/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+2*I/(b-I*a)^2/f^4/(I*a+b)*b*a*d^3*e^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+6/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-12/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d^2/(a-I*b)*e^2*x+12/(b-I*a)^2/f/(I*a+b)*b*a*c^2*d/(a-I*b)*e*x-6*I/(b-I*a)^2/f^2/(I*a+b)*b^2*c*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-6*I/(b-I*a)^2/f^3/(I*a+b)*b^2*c*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+3*I/(b-I*a)^2/f^3/(I*a+b)*b*a*d^3/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x+2*I/(b-I*a)^2/f/(I*a+b)*b*a*d^3/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^3+12*I/(b-I*a)^2/f^3/(I*a+b)*b^2*c*d^2*e/(I*b-a)*ln(exp(I*(f*x+e)))+3*I/(b-I*a)^2/f^3/(I*a+b)*b*a*c*d^2/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-4*I/(b-I*a)^2/f^4/(I*a+b)*b*a*d^3*e^3/(I*b-a)*ln(exp(I*(f*x+e)))-2*I/(b-I*a)^2/f/(I*a+b)*b*a^2*c^3/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+6/(b-I*a)^2/f^3/(I*a+b)*b^3*c*d^2*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)","B"
58,1,2137,584,2.717000," ","int((d*x+c)^2/(a+b*cot(f*x+e))^2,x)","\frac{d^{2} x^{3}}{6 i a b +3 a^{2}-3 b^{2}}+\frac{c d \,x^{2}}{2 i a b +a^{2}-b^{2}}-\frac{2 i b \,a^{2} c^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{4 i b a \,d^{2} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right)}+\frac{2 i b a \,d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x^{2}}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}-\frac{4 b^{2} d^{2} e x}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}-\frac{8 b a \,d^{2} e^{3}}{3 \left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}+\frac{4 b a c d \,x^{2}}{\left(-i a +b \right)^{2} \left(i a +b \right) \left(-i b +a \right)}-\frac{2 i b^{2} d^{2} e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right) a}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{2 i b^{2} c d \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right) a}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{2 i b \,a^{2} d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{4 i b a c d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}+\frac{4 b a \,d^{2} x^{3}}{3 \left(-i a +b \right)^{2} \left(i a +b \right) \left(-i b +a \right)}-\frac{2 b^{2} d^{2} x^{2}}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}-\frac{2 b^{2} d^{2} e^{2}}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}-\frac{b^{2} d^{2} \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}+\frac{2 i b^{2} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{\left(i a +b \right) f \left(-i a +b \right)^{2} \left({\mathrm e}^{2 i \left(f x +e \right)} b -i {\mathrm e}^{2 i \left(f x +e \right)} a +b +i a \right)}-\frac{4 b^{2} a c d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{8 i b a c d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right)}+\frac{4 i b a c d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{4 b a c d \,e^{2}}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}-\frac{4 i b^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right)}+\frac{4 i b a \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right)}+\frac{4 i b^{2} d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right)}-\frac{2 i b^{2} d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{4 i b \,a^{2} c d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{2 i b^{2} d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}-\frac{2 b^{3} c d \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{4 b a \,d^{2} e^{2} x}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{2 b^{2} a \,c^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{2 b^{3} d^{2} e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{2 b a \,d^{2} \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{i b a \,d^{2} \polylog \left(3, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}+\frac{2 b a c d \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{c^{2} x}{2 i a b +a^{2}-b^{2}}-\frac{2 i b a \,d^{2} \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e^{2}}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(-i b +a \right)}+\frac{2 b^{2} a \,d^{2} e^{2} \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{3} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{8 b a c d e x}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}"," ",0,"-4/(b-I*a)^2/f^2/(I*a+b)*b^2*a*c*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-8*I/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d*e/(I*b-a)*ln(exp(I*(f*x+e)))+4*I/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e-2*I/(b-I*a)^2/f^3/(I*a+b)*b^2*d^2*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a+1/(2*I*a*b+a^2-b^2)*c*d*x^2+4/(b-I*a)^2/(I*a+b)*b*a*c*d/(a-I*b)*x^2-4/(b-I*a)^2/f^2/(I*a+b)*b^2*d^2/(a-I*b)*e*x-8/3/(b-I*a)^2/f^3/(I*a+b)*b*a*d^2*e^3/(a-I*b)+4/3/(b-I*a)^2/(I*a+b)*b*a*d^2/(a-I*b)*x^3-1/(b-I*a)^2/f^3/(I*a+b)*b^2*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-2/(b-I*a)^2/f/(I*a+b)*b^2*d^2/(a-I*b)*x^2-2/(b-I*a)^2/f^3/(I*a+b)*b^2*d^2/(a-I*b)*e^2+2*I*b^2*(d^2*x^2+2*c*d*x+c^2)/(I*a+b)/f/(b-I*a)^2/(exp(2*I*(f*x+e))*b-I*exp(2*I*(f*x+e))*a+b+I*a)+4/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d/(a-I*b)*e^2+2/(b-I*a)^2/f^2/(I*a+b)*b*a*d^2/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-4*I/(b-I*a)^2/f^2/(I*a+b)*b^2*c*d/(I*b-a)*ln(exp(I*(f*x+e)))+4*I/(b-I*a)^2/f/(I*a+b)*b*a*c^2/(I*b-a)*ln(exp(I*(f*x+e)))+4*I/(b-I*a)^2/f^3/(I*a+b)*b^2*d^2*e/(I*b-a)*ln(exp(I*(f*x+e)))-2*I/(b-I*a)^2/f^2/(I*a+b)*b^2*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-2*I/(b-I*a)^2/f^3/(I*a+b)*b^2*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+2*I/(b-I*a)^2/f^2/(I*a+b)*b^2*c*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a-2*I/(b-I*a)^2/f^3/(I*a+b)*b*a^2*d^2*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+4*I/(b-I*a)^2/f/(I*a+b)*b*a*c*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-2/(b-I*a)^2/f^2/(I*a+b)*b^3*c*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+I/(b-I*a)^2/f^3/(I*a+b)*b*a*d^2/(a-I*b)*polylog(3,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))+2/(b-I*a)^2/f^2/(I*a+b)*b*a*c*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))-4/(b-I*a)^2/f^2/(I*a+b)*b*a*d^2*e^2/(a-I*b)*x+2/(b-I*a)^2/f/(I*a+b)*b^2*a*c^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+2/(b-I*a)^2/f^3/(I*a+b)*b^3*d^2*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+4*I/(b-I*a)^2/f^2/(I*a+b)*b*a^2*c*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+1/3/(2*I*a*b+a^2-b^2)*d^2*x^3+1/(2*I*a*b+a^2-b^2)*c^2*x-2*I/(b-I*a)^2/f^3/(I*a+b)*b*a*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e^2+2/(b-I*a)^2/f^3/(I*a+b)*b^2*a*d^2*e^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+8/(b-I*a)^2/f/(I*a+b)*b*a*c*d/(a-I*b)*e*x-2*I/(b-I*a)^2/f/(I*a+b)*b*a^2*c^2/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+4*I/(b-I*a)^2/f^3/(I*a+b)*b*a*d^2*e^2/(I*b-a)*ln(exp(I*(f*x+e)))+2*I/(b-I*a)^2/f/(I*a+b)*b*a*d^2/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x^2","B"
59,1,990,198,2.563000," ","int((d*x+c)/(a+b*cot(f*x+e))^2,x)","\frac{d \,x^{2}}{4 i a b +2 a^{2}-2 b^{2}}+\frac{c x}{2 i a b +a^{2}-b^{2}}+\frac{2 i b a d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) x}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}-\frac{2 i b \,a^{2} c \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{b^{3} d \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{2 i b \,a^{2} d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{4 i b a d e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right)}+\frac{2 b^{2} a c \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{4 i b a c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(i b -a \right)}+\frac{i b^{2} d \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right) a}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}-\frac{2 b^{2} a d e \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+i {\mathrm e}^{2 i \left(f x +e \right)} b -a +i b \right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right) \left(i b +a \right)}+\frac{2 i b^{2} \left(d x +c \right)}{\left(i a +b \right) f \left(-i a +b \right)^{2} \left({\mathrm e}^{2 i \left(f x +e \right)} b -i {\mathrm e}^{2 i \left(f x +e \right)} a +b +i a \right)}-\frac{2 i b^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(i b -a \right)}+\frac{2 i b a d \ln \left(1-\frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right) e}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{2 b a d \,x^{2}}{\left(-i a +b \right)^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{4 b a d e x}{\left(-i a +b \right)^{2} f \left(i a +b \right) \left(-i b +a \right)}+\frac{2 b a d \,e^{2}}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}+\frac{b a d \polylog \left(2, \frac{\left(i b +a \right) {\mathrm e}^{2 i \left(f x +e \right)}}{-i b +a}\right)}{\left(-i a +b \right)^{2} f^{2} \left(i a +b \right) \left(-i b +a \right)}"," ",0,"1/2/(2*I*a*b+a^2-b^2)*d*x^2+1/(2*I*a*b+a^2-b^2)*c*x+2*I/(b-I*a)^2/f/(I*a+b)*b*a*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*x-2*I/(b-I*a)^2/f/(I*a+b)*b*a^2*c/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-1/(b-I*a)^2/f^2/(I*a+b)*b^3*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+2*I/(b-I*a)^2/f^2/(I*a+b)*b*a^2*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)-4*I/(b-I*a)^2/f^2/(I*a+b)*b*a*d*e/(I*b-a)*ln(exp(I*(f*x+e)))+2/(b-I*a)^2/f/(I*a+b)*b^2*a*c/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+4*I/(b-I*a)^2/f/(I*a+b)*b*a*c/(I*b-a)*ln(exp(I*(f*x+e)))+I/(b-I*a)^2/f^2/(I*a+b)*b^2*d/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)*a-2/(b-I*a)^2/f^2/(I*a+b)*b^2*a*d*e/(I*b-a)/(a+I*b)*ln(a*exp(2*I*(f*x+e))+I*exp(2*I*(f*x+e))*b-a+I*b)+2*I*b^2*(d*x+c)/(I*a+b)/f/(b-I*a)^2/(exp(2*I*(f*x+e))*b-I*exp(2*I*(f*x+e))*a+b+I*a)-2*I/(b-I*a)^2/f^2/(I*a+b)*b^2*d/(I*b-a)*ln(exp(I*(f*x+e)))+2*I/(b-I*a)^2/f^2/(I*a+b)*b*a*d/(a-I*b)*ln(1-(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))*e+2/(b-I*a)^2/(I*a+b)*b*a*d/(a-I*b)*x^2+4/(b-I*a)^2/f/(I*a+b)*b*a*d/(a-I*b)*e*x+2/(b-I*a)^2/f^2/(I*a+b)*b*a*d/(a-I*b)*e^2+1/(b-I*a)^2/f^2/(I*a+b)*b*a*d/(a-I*b)*polylog(2,(a+I*b)*exp(2*I*(f*x+e))/(a-I*b))","B"
60,0,0,22,13.352000," ","int(1/(d*x+c)/(a+b*cot(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +b \cot \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+b*cot(f*x+e))^2,x)","F"
61,0,0,22,21.116000," ","int(1/(d*x+c)^2/(a+b*cot(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \cot \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*cot(f*x+e))^2,x)","F"