1,1,747,200,1.014000," ","int((d*x+c)^3*(a+a*sec(f*x+e)),x)","\frac{3 a \,c^{2} d \,x^{2}}{2}+a c \,d^{2} x^{3}+\frac{6 i a \,d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{6 i a \,d^{3} \polylog \left(4, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{a \,d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}+a \,c^{3} x +\frac{a \,d^{3} x^{4}}{4}+\frac{6 i a \,c^{2} d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 i a c \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 i a \,d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{3 i a \,c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 i a \,d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}+\frac{3 a \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{3 a \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{6 i a \,d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{3 a \,d^{2} c \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{3 a \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}-\frac{3 a c \,d^{2} e^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{3 a \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{3 a c \,d^{2} e^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{3 a \,d^{2} c \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{2 i a \,d^{3} e^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{3 i a \,d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{3 i a \,c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 a \,d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 a \,d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{6 a \,d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 i a \,c^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{a \,d^{3} e^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{4}}-\frac{a \,d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}+\frac{6 a \,d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{a \,d^{3} e^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}"," ",0,"3/2*a*c^2*d*x^2-6*I*a*d^3*polylog(4,-I*exp(I*(f*x+e)))/f^4+a*c*d^2*x^3+6*I/f^2*a*c^2*d*e*arctan(exp(I*(f*x+e)))-6*I/f^2*a*d^2*c*polylog(2,I*exp(I*(f*x+e)))*x+6*I/f^2*a*d^2*c*polylog(2,-I*exp(I*(f*x+e)))*x-6*I/f^3*a*c*d^2*e^2*arctan(exp(I*(f*x+e)))+6*I*a*d^3*polylog(4,I*exp(I*(f*x+e)))/f^4+a*c^3*x+1/4*a*d^3*x^4+3/f*a*c^2*d*ln(1-I*exp(I*(f*x+e)))*x+3/f^2*a*c^2*d*ln(1-I*exp(I*(f*x+e)))*e+3/f*a*d^2*c*ln(1-I*exp(I*(f*x+e)))*x^2-2*I/f*a*c^3*arctan(exp(I*(f*x+e)))-3/f^2*a*c^2*d*ln(I*exp(I*(f*x+e))+1)*e-3/f^3*a*c*d^2*e^2*ln(1-I*exp(I*(f*x+e)))-3/f*a*c^2*d*ln(I*exp(I*(f*x+e))+1)*x+3/f^3*a*c*d^2*e^2*ln(I*exp(I*(f*x+e))+1)-3/f*a*d^2*c*ln(I*exp(I*(f*x+e))+1)*x^2+3*I/f^2*a*c^2*d*polylog(2,-I*exp(I*(f*x+e)))+3*I/f^2*a*d^3*polylog(2,-I*exp(I*(f*x+e)))*x^2-3*I/f^2*a*d^3*polylog(2,I*exp(I*(f*x+e)))*x^2+2*I/f^4*a*d^3*e^3*arctan(exp(I*(f*x+e)))-3*I/f^2*a*c^2*d*polylog(2,I*exp(I*(f*x+e)))-1/f^4*a*d^3*e^3*ln(I*exp(I*(f*x+e))+1)-1/f*a*d^3*ln(I*exp(I*(f*x+e))+1)*x^3+1/f*a*d^3*ln(1-I*exp(I*(f*x+e)))*x^3+6/f^3*a*d^3*polylog(3,I*exp(I*(f*x+e)))*x+1/f^4*a*d^3*e^3*ln(1-I*exp(I*(f*x+e)))-6/f^3*a*d^2*c*polylog(3,-I*exp(I*(f*x+e)))-6/f^3*a*d^3*polylog(3,-I*exp(I*(f*x+e)))*x+6/f^3*a*d^2*c*polylog(3,I*exp(I*(f*x+e)))","B"
2,1,431,138,0.962000," ","int((d*x+c)^2*(a+a*sec(f*x+e)),x)","\frac{a \,d^{2} x^{3}}{3}+a c d \,x^{2}+a \,c^{2} x -\frac{a \,d^{2} e^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 i a \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{2 i a \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 i a c d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 a c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{a \,d^{2} e^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{2 i a c d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{a \,d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}-\frac{2 a \,d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 i a \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{2 a c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{2 a c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{2 a \,d^{2} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{a \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{2 i a \,c^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{2 a c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{4 i a c d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}"," ",0,"1/3*a*d^2*x^3+a*c*d*x^2+a*c^2*x-1/f^3*a*d^2*e^2*ln(1-I*exp(I*(f*x+e)))+2*I/f^2*a*c*d*polylog(2,-I*exp(I*(f*x+e)))-2*I/f^2*a*d^2*polylog(2,I*exp(I*(f*x+e)))*x-2*I/f^3*a*d^2*e^2*arctan(exp(I*(f*x+e)))-2/f^2*a*c*d*ln(I*exp(I*(f*x+e))+1)*e+1/f^3*a*d^2*e^2*ln(I*exp(I*(f*x+e))+1)+2*I/f^2*a*d^2*polylog(2,-I*exp(I*(f*x+e)))*x-1/f*a*d^2*ln(I*exp(I*(f*x+e))+1)*x^2-2*a*d^2*polylog(3,-I*exp(I*(f*x+e)))/f^3-2*I/f*a*c^2*arctan(exp(I*(f*x+e)))-2/f*a*c*d*ln(I*exp(I*(f*x+e))+1)*x+2/f^2*a*c*d*ln(1-I*exp(I*(f*x+e)))*e+2*a*d^2*polylog(3,I*exp(I*(f*x+e)))/f^3+1/f*a*d^2*ln(1-I*exp(I*(f*x+e)))*x^2-2*I/f^2*a*c*d*polylog(2,I*exp(I*(f*x+e)))+2/f*a*c*d*ln(1-I*exp(I*(f*x+e)))*x+4*I/f^2*a*c*d*e*arctan(exp(I*(f*x+e)))","B"
3,1,208,80,0.266000," ","int((d*x+c)*(a+a*sec(f*x+e)),x)","\frac{a d \,x^{2}}{2}-\frac{a d \,e^{2}}{2 f^{2}}+c a x +\frac{a c e}{f}-\frac{a d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{a d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{i a d \dilog \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{i a d \dilog \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{a d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{a d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{c a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}-\frac{a d e \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f^{2}}"," ",0,"1/2*a*d*x^2-1/2/f^2*a*d*e^2+c*a*x+1/f*a*c*e-1/f*a*d*ln(I*exp(I*(f*x+e))+1)*x+1/f*a*d*ln(1-I*exp(I*(f*x+e)))*x+I/f^2*a*d*dilog(I*exp(I*(f*x+e))+1)-I/f^2*a*d*dilog(1-I*exp(I*(f*x+e)))-1/f^2*a*d*ln(I*exp(I*(f*x+e))+1)*e+1/f^2*a*d*ln(1-I*exp(I*(f*x+e)))*e+1/f*c*a*ln(sec(f*x+e)+tan(f*x+e))-1/f^2*a*d*e*ln(sec(f*x+e)+tan(f*x+e))","B"
4,0,0,20,1.232000," ","int((a+a*sec(f*x+e))/(d*x+c),x)","\int \frac{a +a \sec \left(f x +e \right)}{d x +c}\, dx"," ",0,"int((a+a*sec(f*x+e))/(d*x+c),x)","F"
5,0,0,20,1.227000," ","int((a+a*sec(f*x+e))/(d*x+c)^2,x)","\int \frac{a +a \sec \left(f x +e \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+a*sec(f*x+e))/(d*x+c)^2,x)","F"
6,1,1506,334,1.731000," ","int((d*x+c)^3*(a+a*sec(f*x+e))^2,x)","-\frac{12 i a^{2} c \,d^{2} e x}{f^{2}}-\frac{12 i a^{2} c \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{12 i a^{2} c^{2} d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{12 i a^{2} d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{12 i a^{2} d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+a^{2} c^{3} x +a^{2} c \,d^{2} x^{3}+\frac{3 a^{2} c^{2} d \,x^{2}}{2}-\frac{6 i a^{2} d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i a^{2} d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{4}}-\frac{6 i a^{2} d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i a^{2} d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{4}}+\frac{6 i a^{2} d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{6 i a^{2} d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}+\frac{6 i a^{2} c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{a^{2} d^{3} x^{4}}{4}+\frac{4 i a^{2} d^{3} e^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{6 i a^{2} e^{2} c \,d^{2}}{f^{3}}+\frac{6 a^{2} d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{6 a^{2} d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{3 a^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e^{2}}{f^{4}}+\frac{3 a^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{4}}-\frac{2 a^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}-\frac{6 a^{2} d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{3 a^{2} d^{3} e^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{4}}+\frac{12 i a^{2} d^{3} \polylog \left(4, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{12 i a^{2} d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{12 a^{2} d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{12 a^{2} d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{12 a^{2} d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{12 a^{2} d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 i a^{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{2 a^{2} e^{3} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{2 a^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}+\frac{3 a^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f^{2}}+\frac{3 a^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{4 i a^{2} c^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{4 i a^{2} e^{3} d^{3}}{f^{4}}-\frac{2 i a^{2} d^{3} x^{3}}{f}-\frac{6 a^{2} c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 a^{2} c^{2} d \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{2 a^{2} e^{3} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{4}}+\frac{6 i a^{2} d^{3} e^{2} x}{f^{3}}-\frac{6 i a^{2} c \,d^{2} x^{2}}{f}+\frac{6 a^{2} c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{6 a^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e x}{f^{3}}+\frac{6 a^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e x}{f^{3}}-\frac{6 a^{2} d^{2} c \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{6 a^{2} d^{2} c \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}+\frac{6 a^{2} c \,d^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{2}}-\frac{6 a^{2} c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{12 a^{2} c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{6 a^{2} e^{2} c \,d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{6 a^{2} e \,d^{3} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{3}}+\frac{6 a^{2} c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{6 a^{2} e^{2} c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 a^{2} c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}-\frac{6 i a^{2} c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{3 i a^{2} c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{3}}+\frac{3 i a^{2} e \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{4}}"," ",0,"-12*I/f^2*a^2*c*d^2*e*x-12*I/f^3*a^2*c*d^2*e^2*arctan(exp(I*(f*x+e)))+12*I/f^2*a^2*c^2*d*e*arctan(exp(I*(f*x+e)))+12*I/f^2*a^2*d^2*c*polylog(2,-I*exp(I*(f*x+e)))*x-12*I/f^2*a^2*d^2*c*polylog(2,I*exp(I*(f*x+e)))*x+a^2*c^3*x+12*I*a^2*d^3*polylog(4,I*exp(I*(f*x+e)))/f^4+a^2*c*d^2*x^3+3/2*a^2*c^2*d*x^2-12*I*a^2*d^3*polylog(4,-I*exp(I*(f*x+e)))/f^4+6/f^4*a^2*d^3*polylog(3,-I*exp(I*(f*x+e)))+6/f^4*a^2*d^3*polylog(3,I*exp(I*(f*x+e)))+2*I*a^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)+1/4*a^2*d^3*x^4-6*I/f^2*a^2*c^2*d*polylog(2,I*exp(I*(f*x+e)))+4*I/f^4*a^2*d^3*e^3*arctan(exp(I*(f*x+e)))-6*I/f^3*a^2*e^2*c*d^2-3*I/f^3*a^2*c*d^2*polylog(2,-exp(2*I*(f*x+e)))+3*I/f^4*a^2*e*d^3*polylog(2,-exp(2*I*(f*x+e)))-6*I/f^3*a^2*d^3*polylog(2,-I*exp(I*(f*x+e)))*x-6*I/f^4*a^2*d^3*polylog(2,-I*exp(I*(f*x+e)))*e-6*I/f^3*a^2*d^3*polylog(2,I*exp(I*(f*x+e)))*x-6*I/f^4*a^2*d^3*polylog(2,I*exp(I*(f*x+e)))*e+6*I/f^3*a^2*d^3*e^2*x-6*I/f*a^2*c*d^2*x^2+6*I/f^2*a^2*d^3*polylog(2,-I*exp(I*(f*x+e)))*x^2-6*I/f^2*a^2*d^3*polylog(2,I*exp(I*(f*x+e)))*x^2+6*I/f^2*a^2*c^2*d*polylog(2,-I*exp(I*(f*x+e)))+2/f^4*a^2*e^3*d^3*ln(1-I*exp(I*(f*x+e)))+2/f*a^2*d^3*ln(1-I*exp(I*(f*x+e)))*x^3-12/f^3*a^2*d^2*c*polylog(3,-I*exp(I*(f*x+e)))-12/f^3*a^2*d^3*polylog(3,-I*exp(I*(f*x+e)))*x+3/f^2*a^2*d^3*ln(I*exp(I*(f*x+e))+1)*x^2+3/f^2*a^2*d^3*ln(1-I*exp(I*(f*x+e)))*x^2+12/f^3*a^2*d^3*polylog(3,I*exp(I*(f*x+e)))*x-4*I/f*a^2*c^3*arctan(exp(I*(f*x+e)))+4*I/f^4*a^2*e^3*d^3-2*I/f*a^2*d^3*x^3-6/f^2*a^2*c^2*d*ln(exp(I*(f*x+e)))+3/f^2*a^2*c^2*d*ln(exp(2*I*(f*x+e))+1)+12/f^3*a^2*d^2*c*polylog(3,I*exp(I*(f*x+e)))-2/f^4*a^2*e^3*d^3*ln(I*exp(I*(f*x+e))+1)+3/f^4*a^2*d^3*ln(I*exp(I*(f*x+e))+1)*e^2+3/f^4*a^2*d^3*ln(1-I*exp(I*(f*x+e)))*e^2-2/f*a^2*d^3*ln(I*exp(I*(f*x+e))+1)*x^3-6/f^4*a^2*d^3*e^2*ln(exp(I*(f*x+e)))-3/f^4*a^2*d^3*e^2*ln(exp(2*I*(f*x+e))+1)+6/f^2*a^2*c^2*d*ln(1-I*exp(I*(f*x+e)))*e+6/f^3*a^2*d^3*ln(I*exp(I*(f*x+e))+1)*e*x+6/f^3*a^2*d^3*ln(1-I*exp(I*(f*x+e)))*e*x-6/f*a^2*d^2*c*ln(I*exp(I*(f*x+e))+1)*x^2+6/f*a^2*d^2*c*ln(1-I*exp(I*(f*x+e)))*x^2+6/f^2*a^2*c*d^2*ln(exp(2*I*(f*x+e))+1)*x-6/f*a^2*c^2*d*ln(I*exp(I*(f*x+e))+1)*x+12/f^3*a^2*c*d^2*e*ln(exp(I*(f*x+e)))+6/f^3*a^2*e^2*c*d^2*ln(I*exp(I*(f*x+e))+1)-6/f^3*a^2*e*d^3*ln(exp(2*I*(f*x+e))+1)*x+6/f*a^2*c^2*d*ln(1-I*exp(I*(f*x+e)))*x-6/f^3*a^2*e^2*c*d^2*ln(1-I*exp(I*(f*x+e)))-6/f^2*a^2*c^2*d*ln(I*exp(I*(f*x+e))+1)*e","B"
7,1,668,237,1.447000," ","int((d*x+c)^2*(a+a*sec(f*x+e))^2,x)","-\frac{4 a^{2} c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{4 a^{2} c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{4 a^{2} c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{2 a^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{2 a^{2} d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}-\frac{4 a^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 a^{2} c d \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{2 a^{2} d^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{2}}+\frac{4 a^{2} d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 a^{2} e^{2} d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{2 a^{2} e^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 i a^{2} d^{2} x^{2}}{f}-\frac{4 i a^{2} c^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{2 i a^{2} e^{2} d^{2}}{f^{3}}-\frac{i a^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{3}}+a^{2} c d \,x^{2}-\frac{4 i a^{2} d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{4 i a^{2} d^{2} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{4 i a^{2} d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{4 i a^{2} c d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 a^{2} d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{4 a^{2} d^{2} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{4 i a^{2} c d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 i a^{2} d^{2} e x}{f^{2}}+\frac{8 i a^{2} c d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 i a^{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)}+\frac{4 a^{2} c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{a^{2} d^{2} x^{3}}{3}+a^{2} c^{2} x"," ",0,"2/f*a^2*d^2*ln(1-I*exp(I*(f*x+e)))*x^2-2/f*a^2*d^2*ln(I*exp(I*(f*x+e))+1)*x^2-4/f^2*a^2*c*d*ln(exp(I*(f*x+e)))+2/f^2*a^2*c*d*ln(exp(2*I*(f*x+e))+1)+2/f^2*a^2*d^2*ln(exp(2*I*(f*x+e))+1)*x+4/f^3*a^2*d^2*e*ln(exp(I*(f*x+e)))+2/f^3*a^2*e^2*d^2*ln(I*exp(I*(f*x+e))+1)-2/f^3*a^2*e^2*d^2*ln(1-I*exp(I*(f*x+e)))-2*I/f*a^2*d^2*x^2-4*I/f*a^2*c^2*arctan(exp(I*(f*x+e)))-4*a^2*d^2*polylog(3,-I*exp(I*(f*x+e)))/f^3+4*a^2*d^2*polylog(3,I*exp(I*(f*x+e)))/f^3+a^2*c*d*x^2-2*I/f^3*a^2*e^2*d^2-I*a^2*d^2*polylog(2,-exp(2*I*(f*x+e)))/f^3+8*I/f^2*a^2*c*d*e*arctan(exp(I*(f*x+e)))+4/f*a^2*c*d*ln(1-I*exp(I*(f*x+e)))*x-4*I/f^2*a^2*d^2*polylog(2,I*exp(I*(f*x+e)))*x+2*I*a^2*(d^2*x^2+2*c*d*x+c^2)/f/(exp(2*I*(f*x+e))+1)-4/f*a^2*c*d*ln(I*exp(I*(f*x+e))+1)*x+4/f^2*a^2*c*d*ln(1-I*exp(I*(f*x+e)))*e-4/f^2*a^2*c*d*ln(I*exp(I*(f*x+e))+1)*e+1/3*a^2*d^2*x^3+a^2*c^2*x+4*I/f^2*a^2*d^2*polylog(2,-I*exp(I*(f*x+e)))*x+4*I/f^2*a^2*c*d*polylog(2,-I*exp(I*(f*x+e)))-4*I/f^2*a^2*d^2*e*x-4*I/f^3*a^2*d^2*e^2*arctan(exp(I*(f*x+e)))-4*I/f^2*a^2*c*d*polylog(2,I*exp(I*(f*x+e)))","B"
8,1,279,121,0.528000," ","int((d*x+c)*(a+a*sec(f*x+e))^2,x)","\frac{a^{2} d \,x^{2}}{2}-\frac{a^{2} d \,e^{2}}{2 f^{2}}+a^{2} c x +\frac{a^{2} c e}{f}-\frac{2 a^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{2 a^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{2 i a^{2} d \dilog \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 i a^{2} d \dilog \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{2 a^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{2 a^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{2 a^{2} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}-\frac{2 a^{2} d e \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f^{2}}+\frac{a^{2} d \tan \left(f x +e \right) x}{f}+\frac{a^{2} d \ln \left(\cos \left(f x +e \right)\right)}{f^{2}}+\frac{a^{2} c \tan \left(f x +e \right)}{f}"," ",0,"1/2*a^2*d*x^2-1/2/f^2*a^2*d*e^2+a^2*c*x+1/f*a^2*c*e-2/f*a^2*d*ln(I*exp(I*(f*x+e))+1)*x+2/f*a^2*d*ln(1-I*exp(I*(f*x+e)))*x-2*I/f^2*a^2*d*dilog(1-I*exp(I*(f*x+e)))+2*I/f^2*a^2*d*dilog(I*exp(I*(f*x+e))+1)-2/f^2*a^2*d*ln(I*exp(I*(f*x+e))+1)*e+2/f^2*a^2*d*ln(1-I*exp(I*(f*x+e)))*e+2/f*a^2*c*ln(sec(f*x+e)+tan(f*x+e))-2/f^2*a^2*d*e*ln(sec(f*x+e)+tan(f*x+e))+1/f*a^2*d*tan(f*x+e)*x+a^2*d*ln(cos(f*x+e))/f^2+a^2*c*tan(f*x+e)/f","B"
9,0,0,22,4.233000," ","int((a+a*sec(f*x+e))^2/(d*x+c),x)","\int \frac{\left(a +a \sec \left(f x +e \right)\right)^{2}}{d x +c}\, dx"," ",0,"int((a+a*sec(f*x+e))^2/(d*x+c),x)","F"
10,0,0,22,5.145000," ","int((a+a*sec(f*x+e))^2/(d*x+c)^2,x)","\int \frac{\left(a +a \sec \left(f x +e \right)\right)^{2}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+a*sec(f*x+e))^2/(d*x+c)^2,x)","F"
11,1,406,138,0.897000," ","int((d*x+c)^3/(a+a*sec(f*x+e)),x)","\frac{d^{3} x^{4}}{4 a}+\frac{c \,d^{2} x^{3}}{a}+\frac{3 c^{2} d \,x^{2}}{2 a}+\frac{c^{3} x}{a}+\frac{12 i d^{2} c e x}{a \,f^{2}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a \,f^{2}}+\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}+\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}-\frac{6 i d^{3} e^{2} x}{a \,f^{3}}+\frac{2 i d^{3} x^{3}}{a f}-\frac{12 d^{2} c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{a \,f^{2}}-\frac{6 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{a \,f^{2}}+\frac{6 i d^{2} c \,x^{2}}{a f}-\frac{12 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}-\frac{12 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}+\frac{12 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{3}}-\frac{4 i d^{3} e^{3}}{a \,f^{4}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}+\frac{12 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}+\frac{6 i d^{2} c \,e^{2}}{a \,f^{3}}"," ",0,"1/4/a*d^3*x^4+1/a*c*d^2*x^3+3/2/a*c^2*d*x^2+c^3*x/a+12*I/a/f^2*d^2*c*e*x-6/a/f^2*d*c^2*ln(exp(I*(f*x+e))+1)+6/a/f^2*d*c^2*ln(exp(I*(f*x+e)))+6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e)))-6*I/a/f^3*d^3*e^2*x+12*I/a/f^3*d^2*c*polylog(2,-exp(I*(f*x+e)))-12/a/f^2*d^2*c*ln(exp(I*(f*x+e))+1)*x-6/a/f^2*d^3*ln(exp(I*(f*x+e))+1)*x^2+2*I/a/f*d^3*x^3-12*d^3*polylog(3,-exp(I*(f*x+e)))/a/f^4-12/a/f^3*d^2*c*e*ln(exp(I*(f*x+e)))+6*I/a/f*d^2*c*x^2-4*I/a/f^4*d^3*e^3-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/a/(exp(I*(f*x+e))+1)+12*I/a/f^3*d^3*polylog(2,-exp(I*(f*x+e)))*x+6*I/a/f^3*d^2*c*e^2","B"
12,1,225,107,0.818000," ","int((d*x+c)^2/(a+a*sec(f*x+e)),x)","\frac{d^{2} x^{3}}{3 a}+\frac{c d \,x^{2}}{a}+\frac{c^{2} x}{a}-\frac{2 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}-\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a \,f^{2}}+\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}+\frac{2 i d^{2} x^{2}}{a f}+\frac{4 i d^{2} e x}{a \,f^{2}}+\frac{2 i d^{2} e^{2}}{a \,f^{3}}-\frac{4 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{a \,f^{2}}+\frac{4 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{4 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}"," ",0,"1/3/a*d^2*x^3+1/a*c*d*x^2+c^2*x/a-2*I*(d^2*x^2+2*c*d*x+c^2)/f/a/(exp(I*(f*x+e))+1)-4/a/f^2*d*c*ln(exp(I*(f*x+e))+1)+4/a/f^2*d*c*ln(exp(I*(f*x+e)))+2*I/a/f*d^2*x^2+4*I/a/f^2*d^2*e*x+2*I/a/f^3*d^2*e^2-4/a/f^2*d^2*ln(exp(I*(f*x+e))+1)*x+4*I*d^2*polylog(2,-exp(I*(f*x+e)))/a/f^3-4/a/f^3*d^2*e*ln(exp(I*(f*x+e)))","B"
13,1,76,57,0.526000," ","int((d*x+c)/(a+a*sec(f*x+e)),x)","\frac{c x}{a}+\frac{d \,x^{2}}{2 a}-\frac{c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{x d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}+\frac{d \ln \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a \,f^{2}}"," ",0,"1/a*c*x+1/2*d/a*x^2-c/a/f*tan(1/2*e+1/2*f*x)-1/f/a*x*d*tan(1/2*e+1/2*f*x)+d/a/f^2*ln(1+tan(1/2*e+1/2*f*x)^2)","A"
14,0,0,22,1.000000," ","int(1/(d*x+c)/(a+a*sec(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +a \sec \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+a*sec(f*x+e)),x)","F"
15,0,0,22,1.115000," ","int(1/(d*x+c)^2/(a+a*sec(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \sec \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*sec(f*x+e)),x)","F"
16,1,799,246,1.186000," ","int((d*x+c)^3/(a+a*sec(f*x+e))^2,x)","\frac{d^{3} x^{4}}{4 a^{2}}+\frac{c \,d^{2} x^{3}}{a^{2}}+\frac{3 c^{2} d \,x^{2}}{2 a^{2}}+\frac{c^{3} x}{a^{2}}-\frac{20 i d^{3} e^{3}}{3 a^{2} f^{4}}-\frac{10 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a^{2} f^{2}}+\frac{10 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{2}}+\frac{10 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}-\frac{20 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) c x}{a^{2} f^{2}}+\frac{20 i d^{2} c e x}{a^{2} f^{2}}-\frac{10 i d^{3} e^{2} x}{a^{2} f^{3}}+\frac{4 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a^{2} f^{4}}-\frac{4 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}-\frac{20 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}-\frac{20 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{3}}-\frac{2 i \left(6 d^{3} f^{2} x^{3} {\mathrm e}^{2 i \left(f x +e \right)}-3 i c^{2} d f \,{\mathrm e}^{i \left(f x +e \right)}+18 c \,d^{2} f^{2} x^{2} {\mathrm e}^{2 i \left(f x +e \right)}+9 d^{3} f^{2} x^{3} {\mathrm e}^{i \left(f x +e \right)}-3 i d^{3} f \,x^{2} {\mathrm e}^{i \left(f x +e \right)}-6 i c \,d^{2} f x \,{\mathrm e}^{i \left(f x +e \right)}+18 c^{2} d \,f^{2} x \,{\mathrm e}^{2 i \left(f x +e \right)}+27 c \,d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}+5 d^{3} f^{2} x^{3}-3 i d^{3} f \,x^{2} {\mathrm e}^{2 i \left(f x +e \right)}-3 i c^{2} d f \,{\mathrm e}^{2 i \left(f x +e \right)}+6 c^{3} f^{2} {\mathrm e}^{2 i \left(f x +e \right)}+27 c^{2} d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+15 c \,d^{2} f^{2} x^{2}-6 i c \,d^{2} f x \,{\mathrm e}^{2 i \left(f x +e \right)}+9 c^{3} f^{2} {\mathrm e}^{i \left(f x +e \right)}+15 c^{2} d \,f^{2} x -6 d^{3} x \,{\mathrm e}^{2 i \left(f x +e \right)}+5 c^{3} f^{2}-6 c \,d^{2} {\mathrm e}^{2 i \left(f x +e \right)}-12 d^{3} x \,{\mathrm e}^{i \left(f x +e \right)}-12 c \,d^{2} {\mathrm e}^{i \left(f x +e \right)}-6 d^{3} x -6 c \,d^{2}\right)}{3 f^{3} a^{2} \left({\mathrm e}^{i \left(f x +e \right)}+1\right)^{3}}+\frac{10 i d^{3} x^{3}}{3 a^{2} f}+\frac{10 i d^{2} c \,x^{2}}{a^{2} f}+\frac{10 i d^{2} c \,e^{2}}{a^{2} f^{3}}+\frac{20 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{3}}+\frac{20 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{a^{2} f^{3}}-\frac{10 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{a^{2} f^{2}}"," ",0,"1/4/a^2*d^3*x^4+1/a^2*c*d^2*x^3+3/2/a^2*c^2*d*x^2+c^3*x/a^2+20*I/a^2/f^3*d^2*c*polylog(2,-exp(I*(f*x+e)))-10/a^2/f^2*d*c^2*ln(exp(I*(f*x+e))+1)+10/a^2/f^2*d*c^2*ln(exp(I*(f*x+e)))+10/a^2/f^4*d^3*e^2*ln(exp(I*(f*x+e)))-20/a^2/f^2*d^2*ln(exp(I*(f*x+e))+1)*c*x-20/3*I/a^2/f^4*d^3*e^3+20*I/a^2/f^2*d^2*c*e*x+4/a^2/f^4*d^3*ln(exp(I*(f*x+e))+1)-4/a^2/f^4*d^3*ln(exp(I*(f*x+e)))-20*d^3*polylog(3,-exp(I*(f*x+e)))/a^2/f^4-20/a^2/f^3*d^2*c*e*ln(exp(I*(f*x+e)))+20*I/a^2/f^3*d^3*polylog(2,-exp(I*(f*x+e)))*x-10*I/a^2/f^3*d^3*e^2*x-2/3*I*(6*d^3*f^2*x^3*exp(2*I*(f*x+e))-3*I*c^2*d*f*exp(I*(f*x+e))+18*c*d^2*f^2*x^2*exp(2*I*(f*x+e))+9*d^3*f^2*x^3*exp(I*(f*x+e))-3*I*d^3*f*x^2*exp(I*(f*x+e))-6*I*c*d^2*f*x*exp(I*(f*x+e))+18*c^2*d*f^2*x*exp(2*I*(f*x+e))+27*c*d^2*f^2*x^2*exp(I*(f*x+e))+5*d^3*f^2*x^3-3*I*d^3*f*x^2*exp(2*I*(f*x+e))-3*I*c^2*d*f*exp(2*I*(f*x+e))+6*c^3*f^2*exp(2*I*(f*x+e))+27*c^2*d*f^2*x*exp(I*(f*x+e))+15*c*d^2*f^2*x^2-6*I*c*d^2*f*x*exp(2*I*(f*x+e))+9*c^3*f^2*exp(I*(f*x+e))+15*c^2*d*f^2*x-6*d^3*x*exp(2*I*(f*x+e))+5*c^3*f^2-6*c*d^2*exp(2*I*(f*x+e))-12*d^3*x*exp(I*(f*x+e))-12*c*d^2*exp(I*(f*x+e))-6*d^3*x-6*c*d^2)/f^3/a^2/(exp(I*(f*x+e))+1)^3+10/3*I/a^2/f*d^3*x^3+10*I/a^2/f*d^2*c*x^2+10*I/a^2/f^3*d^2*c*e^2-10/a^2/f^2*d^3*ln(exp(I*(f*x+e))+1)*x^2","B"
17,1,442,187,0.966000," ","int((d*x+c)^2/(a+a*sec(f*x+e))^2,x)","\frac{d^{2} x^{3}}{3 a^{2}}+\frac{c d \,x^{2}}{a^{2}}+\frac{c^{2} x}{a^{2}}-\frac{2 i \left(6 d^{2} f^{2} x^{2} {\mathrm e}^{2 i \left(f x +e \right)}-2 i d^{2} f x \,{\mathrm e}^{2 i \left(f x +e \right)}+12 c d \,f^{2} x \,{\mathrm e}^{2 i \left(f x +e \right)}+9 d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}-2 i c d f \,{\mathrm e}^{2 i \left(f x +e \right)}-2 i d^{2} f x \,{\mathrm e}^{i \left(f x +e \right)}+6 c^{2} f^{2} {\mathrm e}^{2 i \left(f x +e \right)}+18 c d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+5 d^{2} f^{2} x^{2}-2 i c d f \,{\mathrm e}^{i \left(f x +e \right)}+9 c^{2} f^{2} {\mathrm e}^{i \left(f x +e \right)}+10 c d \,f^{2} x +5 c^{2} f^{2}-2 d^{2} {\mathrm e}^{2 i \left(f x +e \right)}-4 d^{2} {\mathrm e}^{i \left(f x +e \right)}-2 d^{2}\right)}{3 f^{3} a^{2} \left({\mathrm e}^{i \left(f x +e \right)}+1\right)^{3}}-\frac{20 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{3 a^{2} f^{2}}+\frac{20 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{2}}+\frac{10 i d^{2} x^{2}}{3 a^{2} f}+\frac{20 i d^{2} e x}{3 a^{2} f^{2}}+\frac{10 i d^{2} e^{2}}{3 a^{2} f^{3}}-\frac{20 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{3 a^{2} f^{2}}+\frac{20 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{3}}-\frac{20 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{3}}"," ",0,"1/3/a^2*d^2*x^3+1/a^2*c*d*x^2+1/a^2*c^2*x-2/3*I*(6*d^2*f^2*x^2*exp(2*I*(f*x+e))-2*I*d^2*f*x*exp(2*I*(f*x+e))+12*c*d*f^2*x*exp(2*I*(f*x+e))+9*d^2*f^2*x^2*exp(I*(f*x+e))-2*I*c*d*f*exp(2*I*(f*x+e))-2*I*d^2*f*x*exp(I*(f*x+e))+6*c^2*f^2*exp(2*I*(f*x+e))+18*c*d*f^2*x*exp(I*(f*x+e))+5*d^2*f^2*x^2-2*I*c*d*f*exp(I*(f*x+e))+9*c^2*f^2*exp(I*(f*x+e))+10*c*d*f^2*x+5*c^2*f^2-2*d^2*exp(2*I*(f*x+e))-4*d^2*exp(I*(f*x+e))-2*d^2)/f^3/a^2/(exp(I*(f*x+e))+1)^3-20/3/a^2*d/f^2*c*ln(exp(I*(f*x+e))+1)+20/3/a^2*d/f^2*c*ln(exp(I*(f*x+e)))+10/3*I/a^2*d^2/f*x^2+20/3*I/a^2*d^2/f^2*e*x+10/3*I/a^2*d^2/f^3*e^2-20/3/a^2*d^2/f^2*ln(exp(I*(f*x+e))+1)*x+20/3*I*d^2*polylog(2,-exp(I*(f*x+e)))/a^2/f^3-20/3/a^2*d^2/f^3*e*ln(exp(I*(f*x+e)))","B"
18,1,138,110,0.637000," ","int((d*x+c)/(a+a*sec(f*x+e))^2,x)","\frac{c x}{a^{2}}+\frac{d \,x^{2}}{2 a^{2}}-\frac{3 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^{2} f}+\frac{c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f}-\frac{d \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f^{2}}+\frac{d x \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f}-\frac{3 x d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^{2} f}+\frac{5 d \ln \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^{2} f^{2}}"," ",0,"1/a^2*c*x+1/2*d*x^2/a^2-3/2/a^2*c/f*tan(1/2*e+1/2*f*x)+1/6/a^2*c/f*tan(1/2*e+1/2*f*x)^3-1/6/a^2*d/f^2*tan(1/2*e+1/2*f*x)^2+1/6/a^2*d/f*x*tan(1/2*e+1/2*f*x)^3-3/2/a^2/f*x*d*tan(1/2*e+1/2*f*x)+5/3*d/a^2/f^2*ln(1+tan(1/2*e+1/2*f*x)^2)","A"
19,0,0,22,5.734000," ","int(1/(d*x+c)/(a+a*sec(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+a*sec(f*x+e))^2,x)","F"
20,0,0,22,6.844000," ","int(1/(d*x+c)^2/(a+a*sec(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*sec(f*x+e))^2,x)","F"
21,0,0,22,0.874000," ","int((d*x+c)^m*(a+a*sec(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(a +a \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(a+a*sec(f*x+e))^n,x)","F"
22,0,0,20,0.755000," ","int((d*x+c)^m*(a+a*sec(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +a \sec \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+a*sec(f*x+e)),x)","F"
23,0,0,22,0.713000," ","int((d*x+c)^m/(a+a*sec(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+a*sec(f*x+e)),x)","F"
24,1,747,200,1.216000," ","int((d*x+c)^3*(a+b*sec(f*x+e)),x)","\frac{3 a \,c^{2} d \,x^{2}}{2}+a c \,d^{2} x^{3}-\frac{6 i b \,d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{6 i b \,c^{2} d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{6 i b \,d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+a \,c^{3} x +\frac{a \,d^{3} x^{4}}{4}-\frac{6 i b c \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{6 b \,d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{b \,d^{3} e^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{4}}+\frac{b \,d^{3} e^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{b \,d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}+\frac{b \,d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}-\frac{2 i b \,c^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{6 i b \,d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{6 i b \,d^{3} \polylog \left(4, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{6 b \,d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 b \,d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{6 b \,d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{3 i b \,c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 i b \,c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 i b \,d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{3 i b \,d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{3 b c \,d^{2} e^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{3 b \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{3 b \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{3 b \,d^{2} c \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{3 b \,d^{2} c \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}+\frac{3 b c \,d^{2} e^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{3 b \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}-\frac{3 b \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{2 i b \,d^{3} e^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}"," ",0,"3/2*a*c^2*d*x^2+a*c*d^2*x^3-6*I*b*d^3*polylog(4,-I*exp(I*(f*x+e)))/f^4+6*I/f^2*b*d^2*c*polylog(2,-I*exp(I*(f*x+e)))*x+6*I/f^2*b*c^2*d*e*arctan(exp(I*(f*x+e)))-6*I/f^2*b*d^2*c*polylog(2,I*exp(I*(f*x+e)))*x-6*I/f^3*b*c*d^2*e^2*arctan(exp(I*(f*x+e)))+a*c^3*x+1/4*a*d^3*x^4+6*I*b*d^3*polylog(4,I*exp(I*(f*x+e)))/f^4-3/f^3*b*c*d^2*e^2*ln(1-I*exp(I*(f*x+e)))+3/f^2*b*c^2*d*ln(1-I*exp(I*(f*x+e)))*e+3/f*b*c^2*d*ln(1-I*exp(I*(f*x+e)))*x-3/f*b*d^2*c*ln(I*exp(I*(f*x+e))+1)*x^2+3/f*b*d^2*c*ln(1-I*exp(I*(f*x+e)))*x^2+3/f^3*b*c*d^2*e^2*ln(I*exp(I*(f*x+e))+1)-3/f*b*c^2*d*ln(I*exp(I*(f*x+e))+1)*x-3/f^2*b*c^2*d*ln(I*exp(I*(f*x+e))+1)*e-6/f^3*b*d^2*c*polylog(3,-I*exp(I*(f*x+e)))-1/f^4*b*d^3*e^3*ln(I*exp(I*(f*x+e))+1)+1/f^4*b*d^3*e^3*ln(1-I*exp(I*(f*x+e)))-6/f^3*b*d^3*polylog(3,-I*exp(I*(f*x+e)))*x+6/f^3*b*d^2*c*polylog(3,I*exp(I*(f*x+e)))+6/f^3*b*d^3*polylog(3,I*exp(I*(f*x+e)))*x-1/f*b*d^3*ln(I*exp(I*(f*x+e))+1)*x^3+1/f*b*d^3*ln(1-I*exp(I*(f*x+e)))*x^3-2*I/f*b*c^3*arctan(exp(I*(f*x+e)))-3*I/f^2*b*c^2*d*polylog(2,I*exp(I*(f*x+e)))+3*I/f^2*b*c^2*d*polylog(2,-I*exp(I*(f*x+e)))+2*I/f^4*b*d^3*e^3*arctan(exp(I*(f*x+e)))+3*I/f^2*b*d^3*polylog(2,-I*exp(I*(f*x+e)))*x^2-3*I/f^2*b*d^3*polylog(2,I*exp(I*(f*x+e)))*x^2","B"
25,1,431,138,0.936000," ","int((d*x+c)^2*(a+b*sec(f*x+e)),x)","\frac{a \,d^{2} x^{3}}{3}+a c d \,x^{2}+a \,c^{2} x -\frac{b \,d^{2} e^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{2 i b \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{2 b c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{2 i b \,c^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}-\frac{2 i b \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{2 b c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{4 i b c d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 b c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{2 b \,d^{2} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{b \,d^{2} e^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{2 b \,d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{b \,d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{2 i b \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{b \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}+\frac{2 i b c d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{2 i b c d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}"," ",0,"1/3*a*d^2*x^3+a*c*d*x^2+a*c^2*x-1/f^3*b*d^2*e^2*ln(1-I*exp(I*(f*x+e)))+2/f*b*c*d*ln(1-I*exp(I*(f*x+e)))*x+2*I/f^2*b*d^2*polylog(2,-I*exp(I*(f*x+e)))*x+2/f^2*b*c*d*ln(1-I*exp(I*(f*x+e)))*e+2*I/f^2*b*c*d*polylog(2,-I*exp(I*(f*x+e)))-2*I/f*b*c^2*arctan(exp(I*(f*x+e)))-2/f*b*c*d*ln(I*exp(I*(f*x+e))+1)*x-2*I/f^3*b*d^2*e^2*arctan(exp(I*(f*x+e)))-2/f^2*b*c*d*ln(I*exp(I*(f*x+e))+1)*e+2*b*d^2*polylog(3,I*exp(I*(f*x+e)))/f^3+1/f^3*b*d^2*e^2*ln(I*exp(I*(f*x+e))+1)-2*b*d^2*polylog(3,-I*exp(I*(f*x+e)))/f^3-1/f*b*d^2*ln(I*exp(I*(f*x+e))+1)*x^2+4*I/f^2*b*c*d*e*arctan(exp(I*(f*x+e)))+1/f*b*d^2*ln(1-I*exp(I*(f*x+e)))*x^2-2*I/f^2*b*d^2*polylog(2,I*exp(I*(f*x+e)))*x-2*I/f^2*b*c*d*polylog(2,I*exp(I*(f*x+e)))","B"
26,1,208,80,0.267000," ","int((d*x+c)*(a+b*sec(f*x+e)),x)","\frac{a d \,x^{2}}{2}-\frac{a d \,e^{2}}{2 f^{2}}+c a x +\frac{a c e}{f}-\frac{b d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{b d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}+\frac{i b d \dilog \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{i b d \dilog \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{b d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{b d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{c b \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}-\frac{b d e \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f^{2}}"," ",0,"1/2*a*d*x^2-1/2/f^2*a*d*e^2+c*a*x+1/f*a*c*e-1/f*b*d*ln(I*exp(I*(f*x+e))+1)*x+1/f*b*d*ln(1-I*exp(I*(f*x+e)))*x+I/f^2*b*d*dilog(I*exp(I*(f*x+e))+1)-I/f^2*b*d*dilog(1-I*exp(I*(f*x+e)))-1/f^2*b*d*ln(I*exp(I*(f*x+e))+1)*e+1/f^2*b*d*ln(1-I*exp(I*(f*x+e)))*e+1/f*c*b*ln(sec(f*x+e)+tan(f*x+e))-1/f^2*b*d*e*ln(sec(f*x+e)+tan(f*x+e))","B"
27,0,0,20,1.247000," ","int((a+b*sec(f*x+e))/(d*x+c),x)","\int \frac{a +b \sec \left(f x +e \right)}{d x +c}\, dx"," ",0,"int((a+b*sec(f*x+e))/(d*x+c),x)","F"
28,0,0,20,1.309000," ","int((a+b*sec(f*x+e))/(d*x+c)^2,x)","\int \frac{a +b \sec \left(f x +e \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*sec(f*x+e))/(d*x+c)^2,x)","F"
29,1,1478,327,1.736000," ","int((d*x+c)^3*(a+b*sec(f*x+e))^2,x)","\frac{3 b^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\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} e^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{4}}-\frac{6 b^{2} c^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{3 b^{2} c^{2} d \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{3 b^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e^{2}}{f^{4}}+\frac{3 b^{2} d^{3} \ln \left(i {\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 i b^{2} d^{3} e^{3}}{f^{4}}+\frac{6 b^{2} d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{6 b^{2} d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+a^{2} c^{3} x +\frac{12 i b a \,c^{2} d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{12 i b \,d^{2} c a \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{12 i b \,d^{2} c a \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}-\frac{12 i b a c \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+a^{2} c \,d^{2} x^{3}+\frac{3 a^{2} c^{2} d \,x^{2}}{2}+\frac{6 b a \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}+\frac{6 b \,d^{2} c a \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{6 b \,d^{2} c a \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}-\frac{6 b a \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{6 b \,e^{2} a c \,d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{6 b a \,c^{2} d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{6 b a \,c^{2} d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{6 b \,e^{2} a c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{12 i b^{2} c \,d^{2} e x}{f^{2}}-\frac{6 i b^{2} d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i b^{2} d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{4}}-\frac{12 i a b \,d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{12 i a b \,d^{3} \polylog \left(4, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}-\frac{4 i b a \,c^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{4 i b a \,d^{3} e^{3} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{4}}+\frac{6 i b a \,c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{6 i b a \,c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{6 i b a \,d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}-\frac{6 i b a \,d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f^{2}}+\frac{a^{2} d^{3} x^{4}}{4}+\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{2 b \,e^{3} a \,d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{4}}+\frac{2 b a \,d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{3}}{f}+\frac{6 b^{2} d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e x}{f^{3}}+\frac{6 b^{2} d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e x}{f^{3}}+\frac{6 b^{2} c \,d^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{2}}-\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{3 i b^{2} c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 i b^{2} d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{6 i b^{2} d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{4}}+\frac{3 i b^{2} e \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{4}}-\frac{12 b a \,d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}-\frac{12 b \,d^{2} c a \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{12 b a \,d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{3}}+\frac{12 b \,d^{2} c a \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{6 b^{2} e \,d^{3} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{3}}+\frac{2 b \,e^{3} a \,d^{3} \ln \left(1-i {\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{2 b a \,d^{3} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{3}}{f}"," ",0,"a^2*c^3*x-12*I/f^2*b*d^2*c*a*polylog(2,I*exp(I*(f*x+e)))*x-12*I/f^3*b*a*c*d^2*e^2*arctan(exp(I*(f*x+e)))+12*I/f^2*b*a*c^2*d*e*arctan(exp(I*(f*x+e)))+12*I/f^2*b*d^2*c*a*polylog(2,-I*exp(I*(f*x+e)))*x+6/f^4*b^2*d^3*polylog(3,I*exp(I*(f*x+e)))+6/f^4*b^2*d^3*polylog(3,-I*exp(I*(f*x+e)))+a^2*c*d^2*x^3+3/2*a^2*c^2*d*x^2+6/f^2*b*a*c^2*d*ln(1-I*exp(I*(f*x+e)))*e+6/f*b*d^2*c*a*ln(1-I*exp(I*(f*x+e)))*x^2-6/f*b*d^2*c*a*ln(I*exp(I*(f*x+e))+1)*x^2-6/f*b*a*c^2*d*ln(I*exp(I*(f*x+e))+1)*x+6/f^3*b*e^2*a*c*d^2*ln(I*exp(I*(f*x+e))+1)-6/f^2*b*a*c^2*d*ln(I*exp(I*(f*x+e))+1)*e+6/f*b*a*c^2*d*ln(1-I*exp(I*(f*x+e)))*x-6/f^3*b*e^2*a*c*d^2*ln(1-I*exp(I*(f*x+e)))-12*I/f^2*b^2*c*d^2*e*x+6*I/f^2*b*a*c^2*d*polylog(2,-I*exp(I*(f*x+e)))+4*I/f^4*b*a*d^3*e^3*arctan(exp(I*(f*x+e)))-6*I/f^2*b*a*c^2*d*polylog(2,I*exp(I*(f*x+e)))+6*I/f^2*b*a*d^3*polylog(2,-I*exp(I*(f*x+e)))*x^2-6*I/f^2*b*a*d^3*polylog(2,I*exp(I*(f*x+e)))*x^2+1/4*a^2*d^3*x^4-6*I/f^3*b^2*d^3*polylog(2,-I*exp(I*(f*x+e)))*x-6*I/f^4*b^2*d^3*polylog(2,-I*exp(I*(f*x+e)))*e-4*I/f*b*a*c^3*arctan(exp(I*(f*x+e)))-12*I*a*b*d^3*polylog(4,-I*exp(I*(f*x+e)))/f^4+12*I*a*b*d^3*polylog(4,I*exp(I*(f*x+e)))/f^4+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)-6*I/f*b^2*c*d^2*x^2-6*I/f^3*b^2*c*d^2*e^2-3*I/f^3*b^2*c*d^2*polylog(2,-exp(2*I*(f*x+e)))-6*I/f^3*b^2*d^3*polylog(2,I*exp(I*(f*x+e)))*x-6*I/f^4*b^2*d^3*polylog(2,I*exp(I*(f*x+e)))*e+3*I/f^4*b^2*e*d^3*polylog(2,-exp(2*I*(f*x+e)))+6*I/f^3*b^2*d^3*e^2*x-12/f^3*b*a*d^3*polylog(3,-I*exp(I*(f*x+e)))*x-12/f^3*b*d^2*c*a*polylog(3,-I*exp(I*(f*x+e)))-6/f^3*b^2*e*d^3*ln(exp(2*I*(f*x+e))+1)*x+2/f^4*b*e^3*a*d^3*ln(1-I*exp(I*(f*x+e)))+12/f^3*b^2*c*d^2*e*ln(exp(I*(f*x+e)))-2/f*b*a*d^3*ln(I*exp(I*(f*x+e))+1)*x^3+12/f^3*b*a*d^3*polylog(3,I*exp(I*(f*x+e)))*x-2/f^4*b*e^3*a*d^3*ln(I*exp(I*(f*x+e))+1)+12/f^3*b*d^2*c*a*polylog(3,I*exp(I*(f*x+e)))+2/f*b*a*d^3*ln(1-I*exp(I*(f*x+e)))*x^3+6/f^3*b^2*d^3*ln(I*exp(I*(f*x+e))+1)*e*x+6/f^3*b^2*d^3*ln(1-I*exp(I*(f*x+e)))*e*x+6/f^2*b^2*c*d^2*ln(exp(2*I*(f*x+e))+1)*x+3/f^2*b^2*d^3*ln(1-I*exp(I*(f*x+e)))*x^2-6/f^4*b^2*d^3*e^2*ln(exp(I*(f*x+e)))-3/f^4*b^2*d^3*e^2*ln(exp(2*I*(f*x+e))+1)-6/f^2*b^2*c^2*d*ln(exp(I*(f*x+e)))+3/f^2*b^2*c^2*d*ln(exp(2*I*(f*x+e))+1)+3/f^4*b^2*d^3*ln(1-I*exp(I*(f*x+e)))*e^2+3/f^4*b^2*d^3*ln(I*exp(I*(f*x+e))+1)*e^2+3/f^2*b^2*d^3*ln(I*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","B"
30,1,651,232,1.357000," ","int((d*x+c)^2*(a+b*sec(f*x+e))^2,x)","-\frac{i b^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b^{2} d^{2} \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right) x}{f^{2}}+\frac{4 b^{2} d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{8 i b a c d e \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+a^{2} c d \,x^{2}-\frac{4 b^{2} c d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 b^{2} c d \ln \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}{f^{2}}-\frac{2 i b^{2} d^{2} x^{2}}{f}-\frac{2 i b^{2} d^{2} e^{2}}{f^{3}}-\frac{4 a b \,d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{4 a b \,d^{2} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{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)}-\frac{4 b a c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{4 b a c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{4 b a c d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{4 b a c d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{4 i b a \,d^{2} e^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}-\frac{4 i b \,d^{2} a \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{4 i b \,d^{2} a \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f^{2}}+\frac{4 i b a c d \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 i b a c d \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}-\frac{4 i b^{2} d^{2} e x}{f^{2}}-\frac{4 i b a \,c^{2} \arctan \left({\mathrm e}^{i \left(f x +e \right)}\right)}{f}+\frac{2 b \,e^{2} a \,d^{2} \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{3}}-\frac{2 b \,e^{2} a \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{3}}+\frac{2 b \,d^{2} a \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{f}-\frac{2 b \,d^{2} a \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{f}+\frac{a^{2} d^{2} x^{3}}{3}+a^{2} c^{2} x"," ",0,"8*I/f^2*b*a*c*d*e*arctan(exp(I*(f*x+e)))+a^2*c*d*x^2-4/f*b*a*c*d*ln(I*exp(I*(f*x+e))+1)*x+4/f*b*a*c*d*ln(1-I*exp(I*(f*x+e)))*x-4/f^2*b*a*c*d*ln(I*exp(I*(f*x+e))+1)*e+4/f^2*b*a*c*d*ln(1-I*exp(I*(f*x+e)))*e-4*I/f^2*b*d^2*a*polylog(2,I*exp(I*(f*x+e)))*x+4*I/f^2*b*d^2*a*polylog(2,-I*exp(I*(f*x+e)))*x+4*I/f^2*b*a*c*d*polylog(2,-I*exp(I*(f*x+e)))-4*I/f^2*b*a*c*d*polylog(2,I*exp(I*(f*x+e)))-4*I/f^3*b*a*d^2*e^2*arctan(exp(I*(f*x+e)))+2/f^2*b^2*d^2*ln(exp(2*I*(f*x+e))+1)*x-4*a*b*d^2*polylog(3,-I*exp(I*(f*x+e)))/f^3+4*a*b*d^2*polylog(3,I*exp(I*(f*x+e)))/f^3+4/f^3*b^2*d^2*e*ln(exp(I*(f*x+e)))-4/f^2*b^2*c*d*ln(exp(I*(f*x+e)))+2/f^2*b^2*c*d*ln(exp(2*I*(f*x+e))+1)-2*I/f*b^2*d^2*x^2-2*I/f^3*b^2*d^2*e^2-I*b^2*d^2*polylog(2,-exp(2*I*(f*x+e)))/f^3+1/3*a^2*d^2*x^3+a^2*c^2*x+2*I*b^2*(d^2*x^2+2*c*d*x+c^2)/f/(exp(2*I*(f*x+e))+1)-4*I/f^2*b^2*d^2*e*x-4*I/f*b*a*c^2*arctan(exp(I*(f*x+e)))+2/f^3*b*e^2*a*d^2*ln(I*exp(I*(f*x+e))+1)-2/f^3*b*e^2*a*d^2*ln(1-I*exp(I*(f*x+e)))+2/f*b*d^2*a*ln(1-I*exp(I*(f*x+e)))*x^2-2/f*b*d^2*a*ln(I*exp(I*(f*x+e))+1)*x^2","B"
31,1,271,118,0.518000," ","int((d*x+c)*(a+b*sec(f*x+e))^2,x)","\frac{a^{2} d \,x^{2}}{2}-\frac{a^{2} d \,e^{2}}{2 f^{2}}+a^{2} c x +\frac{a^{2} c e}{f}-\frac{2 a b d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) x}{f}+\frac{2 a b d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{f}-\frac{2 a b d \ln \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right) e}{f^{2}}+\frac{2 a b d \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{f^{2}}-\frac{2 i a b d \dilog \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right)}{f^{2}}+\frac{2 i a b d \dilog \left(i {\mathrm e}^{i \left(f x +e \right)}+1\right)}{f^{2}}+\frac{2 a b c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}-\frac{2 a b d e \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f^{2}}+\frac{b^{2} d \tan \left(f x +e \right) x}{f}+\frac{b^{2} d \ln \left(\cos \left(f x +e \right)\right)}{f^{2}}+\frac{c \,b^{2} \tan \left(f x +e \right)}{f}"," ",0,"1/2*a^2*d*x^2-1/2/f^2*a^2*d*e^2+a^2*c*x+1/f*a^2*c*e-2/f*a*b*d*ln(I*exp(I*(f*x+e))+1)*x+2/f*a*b*d*ln(1-I*exp(I*(f*x+e)))*x-2/f^2*a*b*d*ln(I*exp(I*(f*x+e))+1)*e+2/f^2*a*b*d*ln(1-I*exp(I*(f*x+e)))*e-2*I/f^2*a*b*d*dilog(1-I*exp(I*(f*x+e)))+2*I/f^2*a*b*d*dilog(I*exp(I*(f*x+e))+1)+2/f*a*b*c*ln(sec(f*x+e)+tan(f*x+e))-2/f^2*a*b*d*e*ln(sec(f*x+e)+tan(f*x+e))+1/f*b^2*d*tan(f*x+e)*x+b^2*d*ln(cos(f*x+e))/f^2+1/f*c*b^2*tan(f*x+e)","B"
32,0,0,22,4.184000," ","int((a+b*sec(f*x+e))^2/(d*x+c),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{2}}{d x +c}\, dx"," ",0,"int((a+b*sec(f*x+e))^2/(d*x+c),x)","F"
33,0,0,22,5.034000," ","int((a+b*sec(f*x+e))^2/(d*x+c)^2,x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{2}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b*sec(f*x+e))^2/(d*x+c)^2,x)","F"
34,0,0,472,2.567000," ","int((d*x+c)^3/(a+b*sec(f*x+e)),x)","\int \frac{\left(d x +c \right)^{3}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^3/(a+b*sec(f*x+e)),x)","F"
35,0,0,352,2.158000," ","int((d*x+c)^2/(a+b*sec(f*x+e)),x)","\int \frac{\left(d x +c \right)^{2}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^2/(a+b*sec(f*x+e)),x)","F"
36,1,516,229,0.953000," ","int((d*x+c)/(a+b*sec(f*x+e)),x)","\frac{d \,x^{2}}{2 a}+\frac{c x}{a}+\frac{2 i b c \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a f \sqrt{a^{2}-b^{2}}}+\frac{i b d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) x}{a f \sqrt{-a^{2}+b^{2}}}+\frac{i b d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) e}{a \,f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) x}{a f \sqrt{-a^{2}+b^{2}}}-\frac{i b d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) e}{a \,f^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b d \dilog \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right)}{a \,f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{b d \dilog \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right)}{a \,f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i b d e \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \,f^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2*d/a*x^2+1/a*c*x+2*I/a*b/f*c/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))+I/a*b/f*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*x+I/a*b/f^2*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*e-I/a*b/f*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*x-I/a*b/f^2*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*e+1/a*b/f^2*d/(-a^2+b^2)^(1/2)*dilog((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))-1/a*b/f^2*d/(-a^2+b^2)^(1/2)*dilog((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))-2*I/a*b/f^2*d*e/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))","B"
37,0,0,22,1.088000," ","int(1/(d*x+c)/(a+b*sec(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +b \sec \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+b*sec(f*x+e)),x)","F"
38,0,0,22,1.170000," ","int(1/(d*x+c)^2/(a+b*sec(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \sec \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*sec(f*x+e)),x)","F"
39,0,0,1384,3.475000," ","int((d*x+c)^3/(a+b*sec(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{3}}{\left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^3/(a+b*sec(f*x+e))^2,x)","F"
40,0,0,1012,2.862000," ","int((d*x+c)^2/(a+b*sec(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{2}}{\left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^2/(a+b*sec(f*x+e))^2,x)","F"
41,1,1289,528,1.072000," ","int((d*x+c)/(a+b*sec(f*x+e))^2,x)","\frac{d \,x^{2}}{2 a^{2}}+\frac{c x}{a^{2}}+\frac{2 i b^{2} \left(d x +c \right) \left(b \,{\mathrm e}^{i \left(f x +e \right)}+a \right)}{a^{2} \left(a^{2}-b^{2}\right) f \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+2 b \,{\mathrm e}^{i \left(f x +e \right)}+a \right)}+\frac{2 i b^{3} d e \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} f^{2}}-\frac{2 b^{2} d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} \left(a^{2}-b^{2}\right) f^{2}}+\frac{b^{2} d \ln \left(a \,{\mathrm e}^{2 i \left(f x +e \right)}+2 b \,{\mathrm e}^{i \left(f x +e \right)}+a \right)}{a^{2} \left(a^{2}-b^{2}\right) f^{2}}+\frac{4 i b c \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} f}-\frac{i b^{3} d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) x}{a^{2} \left(a^{2}-b^{2}\right) f \sqrt{-a^{2}+b^{2}}}+\frac{i b^{3} d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} \left(a^{2}-b^{2}\right) f \sqrt{-a^{2}+b^{2}}}-\frac{2 i b d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) e}{\left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{4 i b d e \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} f^{2}}+\frac{2 i b d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) e}{\left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b^{3} d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) e}{a^{2} \left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 b d \dilog \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right)}{\left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 b d \dilog \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right)}{\left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i b^{3} c \arctan \left(\frac{2 a \,{\mathrm e}^{i \left(f x +e \right)}+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}} f}+\frac{i b^{3} d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) e}{a^{2} \left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i b d \ln \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right) x}{\left(a^{2}-b^{2}\right) f \sqrt{-a^{2}+b^{2}}}-\frac{2 i b d \ln \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right) x}{\left(a^{2}-b^{2}\right) f \sqrt{-a^{2}+b^{2}}}-\frac{b^{3} d \dilog \left(\frac{-a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}-b}{\sqrt{-a^{2}+b^{2}}-b}\right)}{a^{2} \left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b^{3} d \dilog \left(\frac{a \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}+b}{b +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} \left(a^{2}-b^{2}\right) f^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"1/2*d*x^2/a^2+1/a^2*c*x+2*I*b^2*(d*x+c)*(b*exp(I*(f*x+e))+a)/a^2/(a^2-b^2)/f/(a*exp(2*I*(f*x+e))+2*b*exp(I*(f*x+e))+a)+2*I*b^3/a^2/(a^2-b^2)^(3/2)/f^2*d*e*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))-2*b^2/a^2/(a^2-b^2)/f^2*d*ln(exp(I*(f*x+e)))+b^2/a^2/(a^2-b^2)/f^2*d*ln(a*exp(2*I*(f*x+e))+2*b*exp(I*(f*x+e))+a)+4*I*b/(a^2-b^2)^(3/2)/f*c*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))-I*b^3/a^2/(a^2-b^2)/f*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*x+I*b^3/a^2/(a^2-b^2)/f*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*x-2*I*b/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*e-4*I*b/(a^2-b^2)^(3/2)/f^2*d*e*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))+2*I*b/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*e-I*b^3/a^2/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*e+2*b/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*dilog((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))-2*b/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*dilog((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))-2*I*b^3/a^2/(a^2-b^2)^(3/2)/f*c*arctan(1/2*(2*a*exp(I*(f*x+e))+2*b)/(a^2-b^2)^(1/2))+I*b^3/a^2/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*e+2*I*b/(a^2-b^2)/f*d/(-a^2+b^2)^(1/2)*ln((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))*x-2*I*b/(a^2-b^2)/f*d/(-a^2+b^2)^(1/2)*ln((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))*x-b^3/a^2/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*dilog((-a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)-b)/((-a^2+b^2)^(1/2)-b))+b^3/a^2/(a^2-b^2)/f^2*d/(-a^2+b^2)^(1/2)*dilog((a*exp(I*(f*x+e))+(-a^2+b^2)^(1/2)+b)/(b+(-a^2+b^2)^(1/2)))","B"
42,0,0,22,4.730000," ","int(1/(d*x+c)/(a+b*sec(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+b*sec(f*x+e))^2,x)","F"
43,0,0,22,6.086000," ","int(1/(d*x+c)^2/(a+b*sec(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*sec(f*x+e))^2,x)","F"
44,0,0,22,0.907000," ","int((d*x+c)^m*(a+b*sec(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(a +b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(a+b*sec(f*x+e))^n,x)","F"
45,0,0,20,0.728000," ","int((d*x+c)^m*(a+b*sec(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +b \sec \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+b*sec(f*x+e)),x)","F"
46,0,0,22,0.553000," ","int((d*x+c)^m/(a+b*sec(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+b*sec(f*x+e)),x)","F"