1,1,1081,0,1.253524," ","integrate((d*x+c)^3*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x + 12 i \, a d^{3} {\rm polylog}\left(4, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 i \, a d^{3} {\rm polylog}\left(4, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 i \, a d^{3} {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 12 i \, a d^{3} {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-6 i \, a d^{3} f^{2} x^{2} - 12 i \, a c d^{2} f^{2} x - 6 i \, a c^{2} d f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-6 i \, a d^{3} f^{2} x^{2} - 12 i \, a c d^{2} f^{2} x - 6 i \, a c^{2} d f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(6 i \, a d^{3} f^{2} x^{2} + 12 i \, a c d^{2} f^{2} x + 6 i \, a c^{2} d f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(6 i \, a d^{3} f^{2} x^{2} + 12 i \, a c d^{2} f^{2} x + 6 i \, a c^{2} d f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 2 \, {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + 3 \, a c^{2} d f^{3} x + a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2}\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + 3 \, a c^{2} d f^{3} x + a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2}\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + 3 \, a c^{2} d f^{3} x + a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2}\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + 3 \, a c^{2} d f^{3} x + a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2}\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 12 \, {\left(a d^{3} f x + a c d^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(a d^{3} f x + a c d^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 \, {\left(a d^{3} f x + a c d^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(a d^{3} f x + a c d^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x + 12*I*a*d^3*polylog(4, I*cos(f*x + e) + sin(f*x + e)) + 12*I*a*d^3*polylog(4, I*cos(f*x + e) - sin(f*x + e)) - 12*I*a*d^3*polylog(4, -I*cos(f*x + e) + sin(f*x + e)) - 12*I*a*d^3*polylog(4, -I*cos(f*x + e) - sin(f*x + e)) + (-6*I*a*d^3*f^2*x^2 - 12*I*a*c*d^2*f^2*x - 6*I*a*c^2*d*f^2)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-6*I*a*d^3*f^2*x^2 - 12*I*a*c*d^2*f^2*x - 6*I*a*c^2*d*f^2)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (6*I*a*d^3*f^2*x^2 + 12*I*a*c*d^2*f^2*x + 6*I*a*c^2*d*f^2)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (6*I*a*d^3*f^2*x^2 + 12*I*a*c*d^2*f^2*x + 6*I*a*c^2*d*f^2)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 2*(a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 2*(a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + 3*a*c^2*d*f^3*x + a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + 3*a*c^2*d*f^3*x + a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + 3*a*c^2*d*f^3*x + a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + 3*a*c^2*d*f^3*x + a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 2*(a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 2*(a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - 12*(a*d^3*f*x + a*c*d^2*f)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 12*(a*d^3*f*x + a*c*d^2*f)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 12*(a*d^3*f*x + a*c*d^2*f)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 12*(a*d^3*f*x + a*c*d^2*f)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)))/f^4","C",0
2,1,671,0,0.639089," ","integrate((d*x+c)^2*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d^{2} f^{3} x^{3} + 6 \, a c d f^{3} x^{2} + 6 \, a c^{2} f^{3} x - 6 \, a d^{2} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 6 \, a d^{2} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 6 \, a d^{2} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 6 \, a d^{2} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-6 i \, a d^{2} f x - 6 i \, a c d f\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-6 i \, a d^{2} f x - 6 i \, a c d f\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(6 i \, a d^{2} f x + 6 i \, a c d f\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(6 i \, a d^{2} f x + 6 i \, a c d f\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x - a d^{2} e^{2} + 2 \, a c d e f\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x - a d^{2} e^{2} + 2 \, a c d e f\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x - a d^{2} e^{2} + 2 \, a c d e f\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x - a d^{2} e^{2} + 2 \, a c d e f\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right)}{6 \, f^{3}}"," ",0,"1/6*(2*a*d^2*f^3*x^3 + 6*a*c*d*f^3*x^2 + 6*a*c^2*f^3*x - 6*a*d^2*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 6*a*d^2*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 6*a*d^2*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 6*a*d^2*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) + (-6*I*a*d^2*f*x - 6*I*a*c*d*f)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-6*I*a*d^2*f*x - 6*I*a*c*d*f)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (6*I*a*d^2*f*x + 6*I*a*c*d*f)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (6*I*a*d^2*f*x + 6*I*a*c*d*f)*dilog(-I*cos(f*x + e) - sin(f*x + e)) + 3*(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(cos(f*x + e) + I*sin(f*x + e) + I) - 3*(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x - a*d^2*e^2 + 2*a*c*d*e*f)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x - a*d^2*e^2 + 2*a*c*d*e*f)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x - a*d^2*e^2 + 2*a*c*d*e*f)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x - a*d^2*e^2 + 2*a*c*d*e*f)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(-cos(f*x + e) + I*sin(f*x + e) + I) - 3*(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(-cos(f*x + e) - I*sin(f*x + e) + I))/f^3","C",0
3,1,343,0,0.645705," ","integrate((d*x+c)*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x - i \, a d {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - i \, a d {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + i \, a d {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + i \, a d {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(a d e - a c f\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(a d e - a c f\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + {\left(a d f x + a d e\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - {\left(a d f x + a d e\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + {\left(a d f x + a d e\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - {\left(a d f x + a d e\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - {\left(a d e - a c f\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(a d e - a c f\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x - I*a*d*dilog(I*cos(f*x + e) + sin(f*x + e)) - I*a*d*dilog(I*cos(f*x + e) - sin(f*x + e)) + I*a*d*dilog(-I*cos(f*x + e) + sin(f*x + e)) + I*a*d*dilog(-I*cos(f*x + e) - sin(f*x + e)) - (a*d*e - a*c*f)*log(cos(f*x + e) + I*sin(f*x + e) + I) + (a*d*e - a*c*f)*log(cos(f*x + e) - I*sin(f*x + e) + I) + (a*d*f*x + a*d*e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - (a*d*f*x + a*d*e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + (a*d*f*x + a*d*e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - (a*d*f*x + a*d*e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - (a*d*e - a*c*f)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + (a*d*e - a*c*f)*log(-cos(f*x + e) - I*sin(f*x + e) + I))/f^2","B",0
4,0,0,0,0.617695," ","integrate((a+a*sec(f*x+e))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(f x + e\right) + a}{d x + c}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)/(d*x + c), x)","F",0
5,0,0,0,0.774168," ","integrate((a+a*sec(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(f x + e\right) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
6,1,1883,0,1.055095," ","integrate((d*x+c)^3*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{24 i \, a^{2} d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 24 i \, a^{2} d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 24 i \, a^{2} d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 24 i \, a^{2} d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-12 i \, a^{2} d^{3} f^{2} x^{2} - 12 i \, a^{2} c^{2} d f^{2} + 12 i \, a^{2} c d^{2} f - 12 i \, {\left(2 \, a^{2} c d^{2} f^{2} - a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-12 i \, a^{2} d^{3} f^{2} x^{2} - 12 i \, a^{2} c^{2} d f^{2} - 12 i \, a^{2} c d^{2} f - 12 i \, {\left(2 \, a^{2} c d^{2} f^{2} + a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(12 i \, a^{2} d^{3} f^{2} x^{2} + 12 i \, a^{2} c^{2} d f^{2} - 12 i \, a^{2} c d^{2} f + 12 i \, {\left(2 \, a^{2} c d^{2} f^{2} - a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(12 i \, a^{2} d^{3} f^{2} x^{2} + 12 i \, a^{2} c^{2} d f^{2} + 12 i \, a^{2} c d^{2} f + 12 i \, {\left(2 \, a^{2} c d^{2} f^{2} + a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 2 \, {\left(2 \, a^{2} d^{3} e^{3} - 2 \, a^{2} c^{3} f^{3} - 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c^{2} d e - a^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} - a^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a^{2} d^{3} e^{3} - 2 \, a^{2} c^{3} f^{3} + 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c^{2} d e + a^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} + a^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 6 \, a^{2} c^{2} d e f^{2} - 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c d^{2} f^{3} + a^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} - a^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} c^{2} d f^{3} + a^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 6 \, a^{2} c^{2} d e f^{2} + 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c d^{2} f^{3} - a^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} + a^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} c^{2} d f^{3} - a^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 6 \, a^{2} c^{2} d e f^{2} - 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c d^{2} f^{3} + a^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} - a^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} c^{2} d f^{3} + a^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 6 \, a^{2} c^{2} d e f^{2} + 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c d^{2} f^{3} - a^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} + a^{2} c d^{2} e\right)} f + 6 \, {\left(a^{2} c^{2} d f^{3} - a^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a^{2} d^{3} e^{3} - 2 \, a^{2} c^{3} f^{3} - 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c^{2} d e - a^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} - a^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a^{2} d^{3} e^{3} - 2 \, a^{2} c^{3} f^{3} + 3 \, a^{2} d^{3} e^{2} + 3 \, {\left(2 \, a^{2} c^{2} d e + a^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a^{2} c d^{2} e^{2} + a^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 12 \, {\left(2 \, a^{2} d^{3} f x + 2 \, a^{2} c d^{2} f - a^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(2 \, a^{2} d^{3} f x + 2 \, a^{2} c d^{2} f + a^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 \, {\left(2 \, a^{2} d^{3} f x + 2 \, a^{2} c d^{2} f - a^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(2 \, a^{2} d^{3} f x + 2 \, a^{2} c d^{2} f + a^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(a^{2} d^{3} f^{4} x^{4} + 4 \, a^{2} c d^{2} f^{4} x^{3} + 6 \, a^{2} c^{2} d f^{4} x^{2} + 4 \, a^{2} c^{3} f^{4} x\right)} \cos\left(f x + e\right) + 4 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)}{4 \, f^{4} \cos\left(f x + e\right)}"," ",0,"1/4*(24*I*a^2*d^3*cos(f*x + e)*polylog(4, I*cos(f*x + e) + sin(f*x + e)) + 24*I*a^2*d^3*cos(f*x + e)*polylog(4, I*cos(f*x + e) - sin(f*x + e)) - 24*I*a^2*d^3*cos(f*x + e)*polylog(4, -I*cos(f*x + e) + sin(f*x + e)) - 24*I*a^2*d^3*cos(f*x + e)*polylog(4, -I*cos(f*x + e) - sin(f*x + e)) + (-12*I*a^2*d^3*f^2*x^2 - 12*I*a^2*c^2*d*f^2 + 12*I*a^2*c*d^2*f - 12*I*(2*a^2*c*d^2*f^2 - a^2*d^3*f)*x)*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-12*I*a^2*d^3*f^2*x^2 - 12*I*a^2*c^2*d*f^2 - 12*I*a^2*c*d^2*f - 12*I*(2*a^2*c*d^2*f^2 + a^2*d^3*f)*x)*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (12*I*a^2*d^3*f^2*x^2 + 12*I*a^2*c^2*d*f^2 - 12*I*a^2*c*d^2*f + 12*I*(2*a^2*c*d^2*f^2 - a^2*d^3*f)*x)*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (12*I*a^2*d^3*f^2*x^2 + 12*I*a^2*c^2*d*f^2 + 12*I*a^2*c*d^2*f + 12*I*(2*a^2*c*d^2*f^2 + a^2*d^3*f)*x)*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 2*(2*a^2*d^3*e^3 - 2*a^2*c^3*f^3 - 3*a^2*d^3*e^2 + 3*(2*a^2*c^2*d*e - a^2*c^2*d)*f^2 - 6*(a^2*c*d^2*e^2 - a^2*c*d^2*e)*f)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 2*(2*a^2*d^3*e^3 - 2*a^2*c^3*f^3 + 3*a^2*d^3*e^2 + 3*(2*a^2*c^2*d*e + a^2*c^2*d)*f^2 - 6*(a^2*c*d^2*e^2 + a^2*c*d^2*e)*f)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 6*a^2*c^2*d*e*f^2 - 3*a^2*d^3*e^2 + 3*(2*a^2*c*d^2*f^3 + a^2*d^3*f^2)*x^2 - 6*(a^2*c*d^2*e^2 - a^2*c*d^2*e)*f + 6*(a^2*c^2*d*f^3 + a^2*c*d^2*f^2)*x)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 6*a^2*c^2*d*e*f^2 + 3*a^2*d^3*e^2 + 3*(2*a^2*c*d^2*f^3 - a^2*d^3*f^2)*x^2 - 6*(a^2*c*d^2*e^2 + a^2*c*d^2*e)*f + 6*(a^2*c^2*d*f^3 - a^2*c*d^2*f^2)*x)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 6*a^2*c^2*d*e*f^2 - 3*a^2*d^3*e^2 + 3*(2*a^2*c*d^2*f^3 + a^2*d^3*f^2)*x^2 - 6*(a^2*c*d^2*e^2 - a^2*c*d^2*e)*f + 6*(a^2*c^2*d*f^3 + a^2*c*d^2*f^2)*x)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 6*a^2*c^2*d*e*f^2 + 3*a^2*d^3*e^2 + 3*(2*a^2*c*d^2*f^3 - a^2*d^3*f^2)*x^2 - 6*(a^2*c*d^2*e^2 + a^2*c*d^2*e)*f + 6*(a^2*c^2*d*f^3 - a^2*c*d^2*f^2)*x)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 2*(2*a^2*d^3*e^3 - 2*a^2*c^3*f^3 - 3*a^2*d^3*e^2 + 3*(2*a^2*c^2*d*e - a^2*c^2*d)*f^2 - 6*(a^2*c*d^2*e^2 - a^2*c*d^2*e)*f)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 2*(2*a^2*d^3*e^3 - 2*a^2*c^3*f^3 + 3*a^2*d^3*e^2 + 3*(2*a^2*c^2*d*e + a^2*c^2*d)*f^2 - 6*(a^2*c*d^2*e^2 + a^2*c*d^2*e)*f)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - 12*(2*a^2*d^3*f*x + 2*a^2*c*d^2*f - a^2*d^3)*cos(f*x + e)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 12*(2*a^2*d^3*f*x + 2*a^2*c*d^2*f + a^2*d^3)*cos(f*x + e)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 12*(2*a^2*d^3*f*x + 2*a^2*c*d^2*f - a^2*d^3)*cos(f*x + e)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 12*(2*a^2*d^3*f*x + 2*a^2*c*d^2*f + a^2*d^3)*cos(f*x + e)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) + (a^2*d^3*f^4*x^4 + 4*a^2*c*d^2*f^4*x^3 + 6*a^2*c^2*d*f^4*x^2 + 4*a^2*c^3*f^4*x)*cos(f*x + e) + 4*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))/(f^4*cos(f*x + e))","C",0
7,1,1096,0,0.761704," ","integrate((d*x+c)^2*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 6 \, a^{2} d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 6 \, a^{2} d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 6 \, a^{2} d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(-6 i \, a^{2} d^{2} f x - 6 i \, a^{2} c d f + 3 i \, a^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(-6 i \, a^{2} d^{2} f x - 6 i \, a^{2} c d f - 3 i \, a^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(6 i \, a^{2} d^{2} f x + 6 i \, a^{2} c d f - 3 i \, a^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(6 i \, a^{2} d^{2} f x + 6 i \, a^{2} c d f + 3 i \, a^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 3 \, {\left(a^{2} d^{2} e^{2} + a^{2} c^{2} f^{2} - a^{2} d^{2} e - {\left(2 \, a^{2} c d e - a^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(a^{2} d^{2} e^{2} + a^{2} c^{2} f^{2} + a^{2} d^{2} e - {\left(2 \, a^{2} c d e + a^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(a^{2} d^{2} f^{2} x^{2} - a^{2} d^{2} e^{2} + 2 \, a^{2} c d e f + a^{2} d^{2} e + {\left(2 \, a^{2} c d f^{2} + a^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a^{2} d^{2} f^{2} x^{2} - a^{2} d^{2} e^{2} + 2 \, a^{2} c d e f - a^{2} d^{2} e + {\left(2 \, a^{2} c d f^{2} - a^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a^{2} d^{2} f^{2} x^{2} - a^{2} d^{2} e^{2} + 2 \, a^{2} c d e f + a^{2} d^{2} e + {\left(2 \, a^{2} c d f^{2} + a^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a^{2} d^{2} f^{2} x^{2} - a^{2} d^{2} e^{2} + 2 \, a^{2} c d e f - a^{2} d^{2} e + {\left(2 \, a^{2} c d f^{2} - a^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a^{2} d^{2} e^{2} + a^{2} c^{2} f^{2} - a^{2} d^{2} e - {\left(2 \, a^{2} c d e - a^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(a^{2} d^{2} e^{2} + a^{2} c^{2} f^{2} + a^{2} d^{2} e - {\left(2 \, a^{2} c d e + a^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - {\left(a^{2} d^{2} f^{3} x^{3} + 3 \, a^{2} c d f^{3} x^{2} + 3 \, a^{2} c^{2} f^{3} x\right)} \cos\left(f x + e\right) - 3 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)}{3 \, f^{3} \cos\left(f x + e\right)}"," ",0,"-1/3*(6*a^2*d^2*cos(f*x + e)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) - 6*a^2*d^2*cos(f*x + e)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) + 6*a^2*d^2*cos(f*x + e)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) - 6*a^2*d^2*cos(f*x + e)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) - (-6*I*a^2*d^2*f*x - 6*I*a^2*c*d*f + 3*I*a^2*d^2)*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) - (-6*I*a^2*d^2*f*x - 6*I*a^2*c*d*f - 3*I*a^2*d^2)*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) - (6*I*a^2*d^2*f*x + 6*I*a^2*c*d*f - 3*I*a^2*d^2)*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) - (6*I*a^2*d^2*f*x + 6*I*a^2*c*d*f + 3*I*a^2*d^2)*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 3*(a^2*d^2*e^2 + a^2*c^2*f^2 - a^2*d^2*e - (2*a^2*c*d*e - a^2*c*d)*f)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 3*(a^2*d^2*e^2 + a^2*c^2*f^2 + a^2*d^2*e - (2*a^2*c*d*e + a^2*c*d)*f)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) - 3*(a^2*d^2*f^2*x^2 - a^2*d^2*e^2 + 2*a^2*c*d*e*f + a^2*d^2*e + (2*a^2*c*d*f^2 + a^2*d^2*f)*x)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) + 3*(a^2*d^2*f^2*x^2 - a^2*d^2*e^2 + 2*a^2*c*d*e*f - a^2*d^2*e + (2*a^2*c*d*f^2 - a^2*d^2*f)*x)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) - 3*(a^2*d^2*f^2*x^2 - a^2*d^2*e^2 + 2*a^2*c*d*e*f + a^2*d^2*e + (2*a^2*c*d*f^2 + a^2*d^2*f)*x)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) + 3*(a^2*d^2*f^2*x^2 - a^2*d^2*e^2 + 2*a^2*c*d*e*f - a^2*d^2*e + (2*a^2*c*d*f^2 - a^2*d^2*f)*x)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 3*(a^2*d^2*e^2 + a^2*c^2*f^2 - a^2*d^2*e - (2*a^2*c*d*e - a^2*c*d)*f)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 3*(a^2*d^2*e^2 + a^2*c^2*f^2 + a^2*d^2*e - (2*a^2*c*d*e + a^2*c*d)*f)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - (a^2*d^2*f^3*x^3 + 3*a^2*c*d*f^3*x^2 + 3*a^2*c^2*f^3*x)*cos(f*x + e) - 3*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*sin(f*x + e))/(f^3*cos(f*x + e))","C",0
8,1,525,0,0.853134," ","integrate((d*x+c)*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} d \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 2 i \, a^{2} d \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 2 i \, a^{2} d \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 2 i \, a^{2} d \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(2 \, a^{2} d e - 2 \, a^{2} c f - a^{2} d\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(2 \, a^{2} d e - 2 \, a^{2} c f + a^{2} d\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - {\left(2 \, a^{2} d e - 2 \, a^{2} c f - a^{2} d\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(2 \, a^{2} d e - 2 \, a^{2} c f + a^{2} d\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + {\left(a^{2} d f^{2} x^{2} + 2 \, a^{2} c f^{2} x\right)} \cos\left(f x + e\right) + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)}{2 \, f^{2} \cos\left(f x + e\right)}"," ",0,"1/2*(-2*I*a^2*d*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) - 2*I*a^2*d*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) + 2*I*a^2*d*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + 2*I*a^2*d*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - (2*a^2*d*e - 2*a^2*c*f - a^2*d)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + (2*a^2*d*e - 2*a^2*c*f + a^2*d)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(a^2*d*f*x + a^2*d*e)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a^2*d*f*x + a^2*d*e)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(a^2*d*f*x + a^2*d*e)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a^2*d*f*x + a^2*d*e)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - (2*a^2*d*e - 2*a^2*c*f - a^2*d)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + (2*a^2*d*e - 2*a^2*c*f + a^2*d)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) + (a^2*d*f^2*x^2 + 2*a^2*c*f^2*x)*cos(f*x + e) + 2*(a^2*d*f*x + a^2*c*f)*sin(f*x + e))/(f^2*cos(f*x + e))","B",0
9,0,0,0,1.562296," ","integrate((a+a*sec(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}{d x + c}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)/(d*x + c), x)","F",0
10,0,0,0,0.680233," ","integrate((a+a*sec(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
11,1,514,0,0.925360," ","integrate((d*x+c)^3/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x + {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x\right)} \cos\left(f x + e\right) + {\left(-24 i \, d^{3} f x - 24 i \, c d^{2} f + {\left(-24 i \, d^{3} f x - 24 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + {\left(24 i \, d^{3} f x + 24 i \, c d^{2} f + {\left(24 i \, d^{3} f x + 24 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 12 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 12 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - 24 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) - 24 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3}\right)} \sin\left(f x + e\right)}{4 \, {\left(a f^{4} \cos\left(f x + e\right) + a f^{4}\right)}}"," ",0,"1/4*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x + (d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x)*cos(f*x + e) + (-24*I*d^3*f*x - 24*I*c*d^2*f + (-24*I*d^3*f*x - 24*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) + I*sin(f*x + e)) + (24*I*d^3*f*x + 24*I*c*d^2*f + (24*I*d^3*f*x + 24*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 12*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 12*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - 24*(d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) + I*sin(f*x + e)) - 24*(d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) - I*sin(f*x + e)) - 4*(d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3)*sin(f*x + e))/(a*f^4*cos(f*x + e) + a*f^4)","C",0
12,1,290,0,1.450457," ","integrate((d*x+c)^2/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x + {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x\right)} \cos\left(f x + e\right) + {\left(-6 i \, d^{2} \cos\left(f x + e\right) - 6 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + {\left(6 i \, d^{2} \cos\left(f x + e\right) + 6 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 6 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 6 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \sin\left(f x + e\right)}{3 \, {\left(a f^{3} \cos\left(f x + e\right) + a f^{3}\right)}}"," ",0,"1/3*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x + (d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x)*cos(f*x + e) + (-6*I*d^2*cos(f*x + e) - 6*I*d^2)*dilog(-cos(f*x + e) + I*sin(f*x + e)) + (6*I*d^2*cos(f*x + e) + 6*I*d^2)*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 6*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 6*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*sin(f*x + e))/(a*f^3*cos(f*x + e) + a*f^3)","B",0
13,1,99,0,0.792496," ","integrate((d*x+c)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","\frac{d f^{2} x^{2} + 2 \, c f^{2} x + {\left(d f^{2} x^{2} + 2 \, c f^{2} x\right)} \cos\left(f x + e\right) - 2 \, {\left(d \cos\left(f x + e\right) + d\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) - 2 \, {\left(d f x + c f\right)} \sin\left(f x + e\right)}{2 \, {\left(a f^{2} \cos\left(f x + e\right) + a f^{2}\right)}}"," ",0,"1/2*(d*f^2*x^2 + 2*c*f^2*x + (d*f^2*x^2 + 2*c*f^2*x)*cos(f*x + e) - 2*(d*cos(f*x + e) + d)*log(1/2*cos(f*x + e) + 1/2) - 2*(d*f*x + c*f)*sin(f*x + e))/(a*f^2*cos(f*x + e) + a*f^2)","A",0
14,0,0,0,0.641144," ","integrate(1/(d*x+c)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(a d x + a c\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (a*d*x + a*c)*sec(f*x + e)), x)","F",0
15,0,0,0,1.263445," ","integrate(1/(d*x+c)^2/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (a*d^2*x^2 + 2*a*c*d*x + a*c^2)*sec(f*x + e)), x)","F",0
16,1,929,0,1.576798," ","integrate((d*x+c)^3/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, d^{3} f^{4} x^{4} + 12 \, c d^{2} f^{4} x^{3} - 12 \, c^{2} d f^{2} + 6 \, {\left(3 \, c^{2} d f^{4} - 2 \, d^{3} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} + 6 \, c^{2} d f^{4} x^{2} + 4 \, c^{3} f^{4} x\right)} \cos\left(f x + e\right)^{2} + 12 \, {\left(c^{3} f^{4} - 2 \, c d^{2} f^{2}\right)} x + 6 \, {\left(d^{3} f^{4} x^{4} + 4 \, c d^{2} f^{4} x^{3} - 2 \, c^{2} d f^{2} + 2 \, {\left(3 \, c^{2} d f^{4} - d^{3} f^{2}\right)} x^{2} + 4 \, {\left(c^{3} f^{4} - c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) + {\left(-120 i \, d^{3} f x - 120 i \, c d^{2} f + {\left(-120 i \, d^{3} f x - 120 i \, c d^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left(-240 i \, d^{3} f x - 240 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + {\left(120 i \, d^{3} f x + 120 i \, c d^{2} f + {\left(120 i \, d^{3} f x + 120 i \, c d^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left(240 i \, d^{3} f x + 240 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 12 \, {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3} + {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 12 \, {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3} + {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - 120 \, {\left(d^{3} \cos\left(f x + e\right)^{2} + 2 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) - 120 \, {\left(d^{3} \cos\left(f x + e\right)^{2} + 2 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 4 \, {\left(4 \, d^{3} f^{3} x^{3} + 12 \, c d^{2} f^{3} x^{2} + 4 \, c^{3} f^{3} - 6 \, c d^{2} f + 6 \, {\left(2 \, c^{2} d f^{3} - d^{3} f\right)} x + {\left(5 \, d^{3} f^{3} x^{3} + 15 \, c d^{2} f^{3} x^{2} + 5 \, c^{3} f^{3} - 6 \, c d^{2} f + 3 \, {\left(5 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f^{4} \cos\left(f x + e\right)^{2} + 2 \, a^{2} f^{4} \cos\left(f x + e\right) + a^{2} f^{4}\right)}}"," ",0,"1/12*(3*d^3*f^4*x^4 + 12*c*d^2*f^4*x^3 - 12*c^2*d*f^2 + 6*(3*c^2*d*f^4 - 2*d^3*f^2)*x^2 + 3*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 + 6*c^2*d*f^4*x^2 + 4*c^3*f^4*x)*cos(f*x + e)^2 + 12*(c^3*f^4 - 2*c*d^2*f^2)*x + 6*(d^3*f^4*x^4 + 4*c*d^2*f^4*x^3 - 2*c^2*d*f^2 + 2*(3*c^2*d*f^4 - d^3*f^2)*x^2 + 4*(c^3*f^4 - c*d^2*f^2)*x)*cos(f*x + e) + (-120*I*d^3*f*x - 120*I*c*d^2*f + (-120*I*d^3*f*x - 120*I*c*d^2*f)*cos(f*x + e)^2 + (-240*I*d^3*f*x - 240*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) + I*sin(f*x + e)) + (120*I*d^3*f*x + 120*I*c*d^2*f + (120*I*d^3*f*x + 120*I*c*d^2*f)*cos(f*x + e)^2 + (240*I*d^3*f*x + 240*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 12*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3 + (5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3)*cos(f*x + e)^2 + 2*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 12*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3 + (5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3)*cos(f*x + e)^2 + 2*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - 120*(d^3*cos(f*x + e)^2 + 2*d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) + I*sin(f*x + e)) - 120*(d^3*cos(f*x + e)^2 + 2*d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) - I*sin(f*x + e)) - 4*(4*d^3*f^3*x^3 + 12*c*d^2*f^3*x^2 + 4*c^3*f^3 - 6*c*d^2*f + 6*(2*c^2*d*f^3 - d^3*f)*x + (5*d^3*f^3*x^3 + 15*c*d^2*f^3*x^2 + 5*c^3*f^3 - 6*c*d^2*f + 3*(5*c^2*d*f^3 - 2*d^3*f)*x)*cos(f*x + e))*sin(f*x + e))/(a^2*f^4*cos(f*x + e)^2 + 2*a^2*f^4*cos(f*x + e) + a^2*f^4)","C",0
17,1,491,0,0.838318," ","integrate((d*x+c)^2/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} - 2 \, c d f + {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} + 3 \, c^{2} f^{3} x\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, c^{2} f^{3} - 2 \, d^{2} f\right)} x + 2 \, {\left(d^{2} f^{3} x^{3} + 3 \, c d f^{3} x^{2} - c d f + {\left(3 \, c^{2} f^{3} - d^{2} f\right)} x\right)} \cos\left(f x + e\right) + {\left(-10 i \, d^{2} \cos\left(f x + e\right)^{2} - 20 i \, d^{2} \cos\left(f x + e\right) - 10 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + {\left(10 i \, d^{2} \cos\left(f x + e\right)^{2} + 20 i \, d^{2} \cos\left(f x + e\right) + 10 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 10 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 10 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - {\left(4 \, d^{2} f^{2} x^{2} + 8 \, c d f^{2} x + 4 \, c^{2} f^{2} - 2 \, d^{2} + {\left(5 \, d^{2} f^{2} x^{2} + 10 \, c d f^{2} x + 5 \, c^{2} f^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f^{3} \cos\left(f x + e\right)^{2} + 2 \, a^{2} f^{3} \cos\left(f x + e\right) + a^{2} f^{3}\right)}}"," ",0,"1/3*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 - 2*c*d*f + (d^2*f^3*x^3 + 3*c*d*f^3*x^2 + 3*c^2*f^3*x)*cos(f*x + e)^2 + (3*c^2*f^3 - 2*d^2*f)*x + 2*(d^2*f^3*x^3 + 3*c*d*f^3*x^2 - c*d*f + (3*c^2*f^3 - d^2*f)*x)*cos(f*x + e) + (-10*I*d^2*cos(f*x + e)^2 - 20*I*d^2*cos(f*x + e) - 10*I*d^2)*dilog(-cos(f*x + e) + I*sin(f*x + e)) + (10*I*d^2*cos(f*x + e)^2 + 20*I*d^2*cos(f*x + e) + 10*I*d^2)*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 10*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e)^2 + 2*(d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 10*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e)^2 + 2*(d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - (4*d^2*f^2*x^2 + 8*c*d*f^2*x + 4*c^2*f^2 - 2*d^2 + (5*d^2*f^2*x^2 + 10*c*d*f^2*x + 5*c^2*f^2 - 2*d^2)*cos(f*x + e))*sin(f*x + e))/(a^2*f^3*cos(f*x + e)^2 + 2*a^2*f^3*cos(f*x + e) + a^2*f^3)","B",0
18,1,183,0,1.349135," ","integrate((d*x+c)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, d f^{2} x^{2} + 6 \, c f^{2} x + 3 \, {\left(d f^{2} x^{2} + 2 \, c f^{2} x\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, d f^{2} x^{2} + 6 \, c f^{2} x - d\right)} \cos\left(f x + e\right) - 10 \, {\left(d \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right) + d\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, d f x + 4 \, c f + 5 \, {\left(d f x + c f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 2 \, d}{6 \, {\left(a^{2} f^{2} \cos\left(f x + e\right)^{2} + 2 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)}}"," ",0,"1/6*(3*d*f^2*x^2 + 6*c*f^2*x + 3*(d*f^2*x^2 + 2*c*f^2*x)*cos(f*x + e)^2 + 2*(3*d*f^2*x^2 + 6*c*f^2*x - d)*cos(f*x + e) - 10*(d*cos(f*x + e)^2 + 2*d*cos(f*x + e) + d)*log(1/2*cos(f*x + e) + 1/2) - 2*(4*d*f*x + 4*c*f + 5*(d*f*x + c*f)*cos(f*x + e))*sin(f*x + e) - 2*d)/(a^2*f^2*cos(f*x + e)^2 + 2*a^2*f^2*cos(f*x + e) + a^2*f^2)","A",0
19,0,0,0,0.537062," ","integrate(1/(d*x+c)/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(a^{2} d x + a^{2} c\right)} \sec\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d x + a^{2} c\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (a^2*d*x + a^2*c)*sec(f*x + e)^2 + 2*(a^2*d*x + a^2*c)*sec(f*x + e)), x)","F",0
20,0,0,0,0.823572," ","integrate(1/(d*x+c)^2/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \sec\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*sec(f*x + e)^2 + 2*(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*sec(f*x + e)), x)","F",0
21,0,0,0,0.689412," ","integrate((d*x+c)^m*(a+a*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(a \sec\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(a*sec(f*x + e) + a)^n, x)","F",0
22,0,0,0,0.781861," ","integrate((d*x+c)^m*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)} {\left(d x + c\right)}^{m}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)*(d*x + c)^m, x)","F",0
23,0,0,0,1.063362," ","integrate((d*x+c)^m/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(a*sec(f*x + e) + a), x)","F",0
24,1,1081,0,1.070005," ","integrate((d*x+c)^3*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x + 12 i \, b d^{3} {\rm polylog}\left(4, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 i \, b d^{3} {\rm polylog}\left(4, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 i \, b d^{3} {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 12 i \, b d^{3} {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-6 i \, b d^{3} f^{2} x^{2} - 12 i \, b c d^{2} f^{2} x - 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-6 i \, b d^{3} f^{2} x^{2} - 12 i \, b c d^{2} f^{2} x - 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(6 i \, b d^{3} f^{2} x^{2} + 12 i \, b c d^{2} f^{2} x + 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(6 i \, b d^{3} f^{2} x^{2} + 12 i \, b c d^{2} f^{2} x + 6 i \, b c^{2} d f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x + 12*I*b*d^3*polylog(4, I*cos(f*x + e) + sin(f*x + e)) + 12*I*b*d^3*polylog(4, I*cos(f*x + e) - sin(f*x + e)) - 12*I*b*d^3*polylog(4, -I*cos(f*x + e) + sin(f*x + e)) - 12*I*b*d^3*polylog(4, -I*cos(f*x + e) - sin(f*x + e)) + (-6*I*b*d^3*f^2*x^2 - 12*I*b*c*d^2*f^2*x - 6*I*b*c^2*d*f^2)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-6*I*b*d^3*f^2*x^2 - 12*I*b*c*d^2*f^2*x - 6*I*b*c^2*d*f^2)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (6*I*b*d^3*f^2*x^2 + 12*I*b*c*d^2*f^2*x + 6*I*b*c^2*d*f^2)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (6*I*b*d^3*f^2*x^2 + 12*I*b*c*d^2*f^2*x + 6*I*b*c^2*d*f^2)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - 12*(b*d^3*f*x + b*c*d^2*f)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 12*(b*d^3*f*x + b*c*d^2*f)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 12*(b*d^3*f*x + b*c*d^2*f)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 12*(b*d^3*f*x + b*c*d^2*f)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)))/f^4","C",0
25,1,671,0,0.799321," ","integrate((d*x+c)^2*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a d^{2} f^{3} x^{3} + 6 \, a c d f^{3} x^{2} + 6 \, a c^{2} f^{3} x - 6 \, b d^{2} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 6 \, b d^{2} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 6 \, b d^{2} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 6 \, b d^{2} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-6 i \, b d^{2} f x - 6 i \, b c d f\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-6 i \, b d^{2} f x - 6 i \, b c d f\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(6 i \, b d^{2} f x + 6 i \, b c d f\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(6 i \, b d^{2} f x + 6 i \, b c d f\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right)}{6 \, f^{3}}"," ",0,"1/6*(2*a*d^2*f^3*x^3 + 6*a*c*d*f^3*x^2 + 6*a*c^2*f^3*x - 6*b*d^2*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 6*b*d^2*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 6*b*d^2*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 6*b*d^2*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-6*I*b*d^2*f*x - 6*I*b*c*d*f)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (6*I*b*d^2*f*x + 6*I*b*c*d*f)*dilog(-I*cos(f*x + e) - sin(f*x + e)) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(cos(f*x + e) + I*sin(f*x + e) + I) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-cos(f*x + e) + I*sin(f*x + e) + I) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-cos(f*x + e) - I*sin(f*x + e) + I))/f^3","C",0
26,1,343,0,0.913158," ","integrate((d*x+c)*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x - i \, b d {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - i \, b d {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + i \, b d {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + i \, b d {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(b d e - b c f\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(b d e - b c f\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + {\left(b d f x + b d e\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - {\left(b d f x + b d e\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + {\left(b d f x + b d e\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - {\left(b d f x + b d e\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - {\left(b d e - b c f\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(b d e - b c f\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x - I*b*d*dilog(I*cos(f*x + e) + sin(f*x + e)) - I*b*d*dilog(I*cos(f*x + e) - sin(f*x + e)) + I*b*d*dilog(-I*cos(f*x + e) + sin(f*x + e)) + I*b*d*dilog(-I*cos(f*x + e) - sin(f*x + e)) - (b*d*e - b*c*f)*log(cos(f*x + e) + I*sin(f*x + e) + I) + (b*d*e - b*c*f)*log(cos(f*x + e) - I*sin(f*x + e) + I) + (b*d*f*x + b*d*e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - (b*d*f*x + b*d*e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + (b*d*f*x + b*d*e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - (b*d*f*x + b*d*e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - (b*d*e - b*c*f)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + (b*d*e - b*c*f)*log(-cos(f*x + e) - I*sin(f*x + e) + I))/f^2","B",0
27,0,0,0,0.750870," ","integrate((a+b*sec(f*x+e))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(f x + e\right) + a}{d x + c}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)/(d*x + c), x)","F",0
28,0,0,0,0.795207," ","integrate((a+b*sec(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(f x + e\right) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
29,1,1819,0,0.975095," ","integrate((d*x+c)^3*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{24 i \, a b d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 24 i \, a b d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 24 i \, a b d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 24 i \, a b d^{3} \cos\left(f x + e\right) {\rm polylog}\left(4, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(-12 i \, a b d^{3} f^{2} x^{2} - 12 i \, a b c^{2} d f^{2} + 12 i \, b^{2} c d^{2} f - 12 i \, {\left(2 \, a b c d^{2} f^{2} - b^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(-12 i \, a b d^{3} f^{2} x^{2} - 12 i \, a b c^{2} d f^{2} - 12 i \, b^{2} c d^{2} f - 12 i \, {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(12 i \, a b d^{3} f^{2} x^{2} + 12 i \, a b c^{2} d f^{2} - 12 i \, b^{2} c d^{2} f + 12 i \, {\left(2 \, a b c d^{2} f^{2} - b^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(12 i \, a b d^{3} f^{2} x^{2} + 12 i \, a b c^{2} d f^{2} + 12 i \, b^{2} c d^{2} f + 12 i \, {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} + 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e + b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} + b^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} + 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} - b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} + b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} - b^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} + 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} - b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} + b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} - b^{2} c d^{2} f^{2}\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} + 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e + b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} + b^{2} c d^{2} e\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 12 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f - b^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 12 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f - b^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 12 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + {\left(a^{2} d^{3} f^{4} x^{4} + 4 \, a^{2} c d^{2} f^{4} x^{3} + 6 \, a^{2} c^{2} d f^{4} x^{2} + 4 \, a^{2} c^{3} f^{4} x\right)} \cos\left(f x + e\right) + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} f^{3} x^{2} + 3 \, b^{2} c^{2} d f^{3} x + b^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)}{4 \, f^{4} \cos\left(f x + e\right)}"," ",0,"1/4*(24*I*a*b*d^3*cos(f*x + e)*polylog(4, I*cos(f*x + e) + sin(f*x + e)) + 24*I*a*b*d^3*cos(f*x + e)*polylog(4, I*cos(f*x + e) - sin(f*x + e)) - 24*I*a*b*d^3*cos(f*x + e)*polylog(4, -I*cos(f*x + e) + sin(f*x + e)) - 24*I*a*b*d^3*cos(f*x + e)*polylog(4, -I*cos(f*x + e) - sin(f*x + e)) + (-12*I*a*b*d^3*f^2*x^2 - 12*I*a*b*c^2*d*f^2 + 12*I*b^2*c*d^2*f - 12*I*(2*a*b*c*d^2*f^2 - b^2*d^3*f)*x)*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) + (-12*I*a*b*d^3*f^2*x^2 - 12*I*a*b*c^2*d*f^2 - 12*I*b^2*c*d^2*f - 12*I*(2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) + (12*I*a*b*d^3*f^2*x^2 + 12*I*a*b*c^2*d*f^2 - 12*I*b^2*c*d^2*f + 12*I*(2*a*b*c*d^2*f^2 - b^2*d^3*f)*x)*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + (12*I*a*b*d^3*f^2*x^2 + 12*I*a*b*c^2*d*f^2 + 12*I*b^2*c*d^2*f + 12*I*(2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 + 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e + b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 + b^2*c*d^2*e)*f)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 + 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 - b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 + b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 - b^2*c*d^2*f^2)*x)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 + 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 - b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 + b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 - b^2*c*d^2*f^2)*x)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 + 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e + b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 + b^2*c*d^2*e)*f)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - 12*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f - b^2*d^3)*cos(f*x + e)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 12*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cos(f*x + e)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 12*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f - b^2*d^3)*cos(f*x + e)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + 12*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cos(f*x + e)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) + (a^2*d^3*f^4*x^4 + 4*a^2*c*d^2*f^4*x^3 + 6*a^2*c^2*d*f^4*x^2 + 4*a^2*c^3*f^4*x)*cos(f*x + e) + 4*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*f^3*x^2 + 3*b^2*c^2*d*f^3*x + b^2*c^3*f^3)*sin(f*x + e))/(f^4*cos(f*x + e))","C",0
30,1,1056,0,0.794373," ","integrate((d*x+c)^2*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, a b d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 6 \, a b d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 6 \, a b d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 6 \, a b d^{2} \cos\left(f x + e\right) {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(-6 i \, a b d^{2} f x - 6 i \, a b c d f + 3 i \, b^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(-6 i \, a b d^{2} f x - 6 i \, a b c d f - 3 i \, b^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(6 i \, a b d^{2} f x + 6 i \, a b c d f - 3 i \, b^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(6 i \, a b d^{2} f x + 6 i \, a b c d f + 3 i \, b^{2} d^{2}\right)} \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 3 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} + b^{2} d^{2} e - {\left(2 \, a b c d e + b^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f - b^{2} d^{2} e + {\left(2 \, a b c d f^{2} - b^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 3 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f - b^{2} d^{2} e + {\left(2 \, a b c d f^{2} - b^{2} d^{2} f\right)} x\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 3 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} + b^{2} d^{2} e - {\left(2 \, a b c d e + b^{2} c d\right)} f\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) - {\left(a^{2} d^{2} f^{3} x^{3} + 3 \, a^{2} c d f^{3} x^{2} + 3 \, a^{2} c^{2} f^{3} x\right)} \cos\left(f x + e\right) - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)}{3 \, f^{3} \cos\left(f x + e\right)}"," ",0,"-1/3*(6*a*b*d^2*cos(f*x + e)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) - 6*a*b*d^2*cos(f*x + e)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) + 6*a*b*d^2*cos(f*x + e)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) - 6*a*b*d^2*cos(f*x + e)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) - (-6*I*a*b*d^2*f*x - 6*I*a*b*c*d*f + 3*I*b^2*d^2)*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) - (-6*I*a*b*d^2*f*x - 6*I*a*b*c*d*f - 3*I*b^2*d^2)*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) - (6*I*a*b*d^2*f*x + 6*I*a*b*c*d*f - 3*I*b^2*d^2)*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) - (6*I*a*b*d^2*f*x + 6*I*a*b*c*d*f + 3*I*b^2*d^2)*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 3*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + 3*(a*b*d^2*e^2 + a*b*c^2*f^2 + b^2*d^2*e - (2*a*b*c*d*e + b^2*c*d)*f)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) - 3*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) + 3*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f - b^2*d^2*e + (2*a*b*c*d*f^2 - b^2*d^2*f)*x)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) - 3*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) + 3*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f - b^2*d^2*e + (2*a*b*c*d*f^2 - b^2*d^2*f)*x)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 3*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 3*(a*b*d^2*e^2 + a*b*c^2*f^2 + b^2*d^2*e - (2*a*b*c*d*e + b^2*c*d)*f)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) - (a^2*d^2*f^3*x^3 + 3*a^2*c*d*f^3*x^2 + 3*a^2*c^2*f^3*x)*cos(f*x + e) - 3*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*sin(f*x + e))/(f^3*cos(f*x + e))","C",0
31,1,505,0,0.651857," ","integrate((d*x+c)*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, a b d \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 2 i \, a b d \cos\left(f x + e\right) {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 2 i \, a b d \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 2 i \, a b d \cos\left(f x + e\right) {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(2 \, a b d e - 2 \, a b c f + b^{2} d\right)} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(a b d f x + a b d e\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a b d f x + a b d e\right)} \cos\left(f x + e\right) \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(a b d f x + a b d e\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(a b d f x + a b d e\right)} \cos\left(f x + e\right) \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + {\left(2 \, a b d e - 2 \, a b c f + b^{2} d\right)} \cos\left(f x + e\right) \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + {\left(a^{2} d f^{2} x^{2} + 2 \, a^{2} c f^{2} x\right)} \cos\left(f x + e\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \sin\left(f x + e\right)}{2 \, f^{2} \cos\left(f x + e\right)}"," ",0,"1/2*(-2*I*a*b*d*cos(f*x + e)*dilog(I*cos(f*x + e) + sin(f*x + e)) - 2*I*a*b*d*cos(f*x + e)*dilog(I*cos(f*x + e) - sin(f*x + e)) + 2*I*a*b*d*cos(f*x + e)*dilog(-I*cos(f*x + e) + sin(f*x + e)) + 2*I*a*b*d*cos(f*x + e)*dilog(-I*cos(f*x + e) - sin(f*x + e)) - (2*a*b*d*e - 2*a*b*c*f - b^2*d)*cos(f*x + e)*log(cos(f*x + e) + I*sin(f*x + e) + I) + (2*a*b*d*e - 2*a*b*c*f + b^2*d)*cos(f*x + e)*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(a*b*d*f*x + a*b*d*e)*cos(f*x + e)*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a*b*d*f*x + a*b*d*e)*cos(f*x + e)*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(a*b*d*f*x + a*b*d*e)*cos(f*x + e)*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(a*b*d*f*x + a*b*d*e)*cos(f*x + e)*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - (2*a*b*d*e - 2*a*b*c*f - b^2*d)*cos(f*x + e)*log(-cos(f*x + e) + I*sin(f*x + e) + I) + (2*a*b*d*e - 2*a*b*c*f + b^2*d)*cos(f*x + e)*log(-cos(f*x + e) - I*sin(f*x + e) + I) + (a^2*d*f^2*x^2 + 2*a^2*c*f^2*x)*cos(f*x + e) + 2*(b^2*d*f*x + b^2*c*f)*sin(f*x + e))/(f^2*cos(f*x + e))","B",0
32,0,0,0,0.647246," ","integrate((a+b*sec(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}{d x + c}, x\right)"," ",0,"integral((b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2)/(d*x + c), x)","F",0
33,0,0,0,0.734635," ","integrate((a+b*sec(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
34,1,2353,0,0.911550," ","integrate((d*x+c)^3/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{2} - b^{2}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{2} - b^{2}\right)} c^{3} f^{4} x + 12 \, a b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 \, a b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 12 \, a b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 \, a b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 6 \, {\left(a b d^{3} f^{2} x^{2} + 2 \, a b c d^{2} f^{2} x + a b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + 6 \, {\left(a b d^{3} f^{2} x^{2} + 2 \, a b c d^{2} f^{2} x + a b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - 6 \, {\left(a b d^{3} f^{2} x^{2} + 2 \, a b c d^{2} f^{2} x + a b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + 6 \, {\left(a b d^{3} f^{2} x^{2} + 2 \, a b c d^{2} f^{2} x + a b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - 2 \, {\left(i \, a b d^{3} e^{3} - 3 i \, a b c d^{2} e^{2} f + 3 i \, a b c^{2} d e f^{2} - i \, a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(-i \, a b d^{3} e^{3} + 3 i \, a b c d^{2} e^{2} f - 3 i \, a b c^{2} d e f^{2} + i \, a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(i \, a b d^{3} e^{3} - 3 i \, a b c d^{2} e^{2} f + 3 i \, a b c^{2} d e f^{2} - i \, a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - 2 \, {\left(-i \, a b d^{3} e^{3} + 3 i \, a b c d^{2} e^{2} f - 3 i \, a b c^{2} d e f^{2} + i \, a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - 2 \, {\left(i \, a b d^{3} f^{3} x^{3} + 3 i \, a b c d^{2} f^{3} x^{2} + 3 i \, a b c^{2} d f^{3} x + i \, a b d^{3} e^{3} - 3 i \, a b c d^{2} e^{2} f + 3 i \, a b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(-i \, a b d^{3} f^{3} x^{3} - 3 i \, a b c d^{2} f^{3} x^{2} - 3 i \, a b c^{2} d f^{3} x - i \, a b d^{3} e^{3} + 3 i \, a b c d^{2} e^{2} f - 3 i \, a b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(-i \, a b d^{3} f^{3} x^{3} - 3 i \, a b c d^{2} f^{3} x^{2} - 3 i \, a b c^{2} d f^{3} x - i \, a b d^{3} e^{3} + 3 i \, a b c d^{2} e^{2} f - 3 i \, a b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(i \, a b d^{3} f^{3} x^{3} + 3 i \, a b c d^{2} f^{3} x^{2} + 3 i \, a b c^{2} d f^{3} x + i \, a b d^{3} e^{3} - 3 i \, a b c d^{2} e^{2} f + 3 i \, a b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(6 i \, a b d^{3} f x + 6 i \, a b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 2 \, {\left(-6 i \, a b d^{3} f x - 6 i \, a b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 2 \, {\left(-6 i \, a b d^{3} f x - 6 i \, a b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 2 \, {\left(6 i \, a b d^{3} f x + 6 i \, a b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} f^{4}}"," ",0,"1/4*((a^2 - b^2)*d^3*f^4*x^4 + 4*(a^2 - b^2)*c*d^2*f^4*x^3 + 6*(a^2 - b^2)*c^2*d*f^4*x^2 + 4*(a^2 - b^2)*c^3*f^4*x + 12*a*b*d^3*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*a*b*d^3*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 12*a*b*d^3*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*a*b*d^3*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 6*(a*b*d^3*f^2*x^2 + 2*a*b*c*d^2*f^2*x + a*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + 6*(a*b*d^3*f^2*x^2 + 2*a*b*c*d^2*f^2*x + a*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - 6*(a*b*d^3*f^2*x^2 + 2*a*b*c*d^2*f^2*x + a*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + 6*(a*b*d^3*f^2*x^2 + 2*a*b*c*d^2*f^2*x + a*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - 2*(I*a*b*d^3*e^3 - 3*I*a*b*c*d^2*e^2*f + 3*I*a*b*c^2*d*e*f^2 - I*a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(-I*a*b*d^3*e^3 + 3*I*a*b*c*d^2*e^2*f - 3*I*a*b*c^2*d*e*f^2 + I*a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(I*a*b*d^3*e^3 - 3*I*a*b*c*d^2*e^2*f + 3*I*a*b*c^2*d*e*f^2 - I*a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - 2*(-I*a*b*d^3*e^3 + 3*I*a*b*c*d^2*e^2*f - 3*I*a*b*c^2*d*e*f^2 + I*a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - 2*(I*a*b*d^3*f^3*x^3 + 3*I*a*b*c*d^2*f^3*x^2 + 3*I*a*b*c^2*d*f^3*x + I*a*b*d^3*e^3 - 3*I*a*b*c*d^2*e^2*f + 3*I*a*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(-I*a*b*d^3*f^3*x^3 - 3*I*a*b*c*d^2*f^3*x^2 - 3*I*a*b*c^2*d*f^3*x - I*a*b*d^3*e^3 + 3*I*a*b*c*d^2*e^2*f - 3*I*a*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(-I*a*b*d^3*f^3*x^3 - 3*I*a*b*c*d^2*f^3*x^2 - 3*I*a*b*c^2*d*f^3*x - I*a*b*d^3*e^3 + 3*I*a*b*c*d^2*e^2*f - 3*I*a*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(I*a*b*d^3*f^3*x^3 + 3*I*a*b*c*d^2*f^3*x^2 + 3*I*a*b*c^2*d*f^3*x + I*a*b*d^3*e^3 - 3*I*a*b*c*d^2*e^2*f + 3*I*a*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(6*I*a*b*d^3*f*x + 6*I*a*b*c*d^2*f)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 2*(-6*I*a*b*d^3*f*x - 6*I*a*b*c*d^2*f)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 2*(-6*I*a*b*d^3*f*x - 6*I*a*b*c*d^2*f)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 2*(6*I*a*b*d^3*f*x + 6*I*a*b*c*d^2*f)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a))/((a^3 - a*b^2)*f^4)","C",0
35,1,1663,0,1.060204," ","integrate((d*x+c)^2/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{3} + 12 \, {\left(a^{2} - b^{2}\right)} c d f^{3} x^{2} + 12 \, {\left(a^{2} - b^{2}\right)} c^{2} f^{3} x - 12 i \, a b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 12 i \, a b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 12 i \, a b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 i \, a b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 \, {\left(a b d^{2} f x + a b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + 12 \, {\left(a b d^{2} f x + a b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - 12 \, {\left(a b d^{2} f x + a b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + 12 \, {\left(a b d^{2} f x + a b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - 2 \, {\left(-3 i \, a b d^{2} e^{2} + 6 i \, a b c d e f - 3 i \, a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(3 i \, a b d^{2} e^{2} - 6 i \, a b c d e f + 3 i \, a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(-3 i \, a b d^{2} e^{2} + 6 i \, a b c d e f - 3 i \, a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - 2 \, {\left(3 i \, a b d^{2} e^{2} - 6 i \, a b c d e f + 3 i \, a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - 2 \, {\left(3 i \, a b d^{2} f^{2} x^{2} + 6 i \, a b c d f^{2} x - 3 i \, a b d^{2} e^{2} + 6 i \, a b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(-3 i \, a b d^{2} f^{2} x^{2} - 6 i \, a b c d f^{2} x + 3 i \, a b d^{2} e^{2} - 6 i \, a b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(-3 i \, a b d^{2} f^{2} x^{2} - 6 i \, a b c d f^{2} x + 3 i \, a b d^{2} e^{2} - 6 i \, a b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - 2 \, {\left(3 i \, a b d^{2} f^{2} x^{2} + 6 i \, a b c d f^{2} x - 3 i \, a b d^{2} e^{2} + 6 i \, a b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right)}{12 \, {\left(a^{3} - a b^{2}\right)} f^{3}}"," ",0,"1/12*(4*(a^2 - b^2)*d^2*f^3*x^3 + 12*(a^2 - b^2)*c*d*f^3*x^2 + 12*(a^2 - b^2)*c^2*f^3*x - 12*I*a*b*d^2*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 12*I*a*b*d^2*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 12*I*a*b*d^2*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*I*a*b*d^2*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*(a*b*d^2*f*x + a*b*c*d*f)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + 12*(a*b*d^2*f*x + a*b*c*d*f)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - 12*(a*b*d^2*f*x + a*b*c*d*f)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + 12*(a*b*d^2*f*x + a*b*c*d*f)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - 2*(-3*I*a*b*d^2*e^2 + 6*I*a*b*c*d*e*f - 3*I*a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(3*I*a*b*d^2*e^2 - 6*I*a*b*c*d*e*f + 3*I*a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(-3*I*a*b*d^2*e^2 + 6*I*a*b*c*d*e*f - 3*I*a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - 2*(3*I*a*b*d^2*e^2 - 6*I*a*b*c*d*e*f + 3*I*a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - 2*(3*I*a*b*d^2*f^2*x^2 + 6*I*a*b*c*d*f^2*x - 3*I*a*b*d^2*e^2 + 6*I*a*b*c*d*e*f)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(-3*I*a*b*d^2*f^2*x^2 - 6*I*a*b*c*d*f^2*x + 3*I*a*b*d^2*e^2 - 6*I*a*b*c*d*e*f)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(-3*I*a*b*d^2*f^2*x^2 - 6*I*a*b*c*d*f^2*x + 3*I*a*b*d^2*e^2 - 6*I*a*b*c*d*e*f)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - 2*(3*I*a*b*d^2*f^2*x^2 + 6*I*a*b*c*d*f^2*x - 3*I*a*b*d^2*e^2 + 6*I*a*b*c*d*e*f)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a))/((a^3 - a*b^2)*f^3)","C",0
36,1,1073,0,0.889691," ","integrate((d*x+c)/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} c f^{2} x - a b d \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + a b d \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - a b d \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + a b d \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - {\left(i \, a b d e - i \, a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - {\left(-i \, a b d e + i \, a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - {\left(i \, a b d e - i \, a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - {\left(-i \, a b d e + i \, a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - {\left(i \, a b d f x + i \, a b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - {\left(-i \, a b d f x - i \, a b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - {\left(-i \, a b d f x - i \, a b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) - {\left(i \, a b d f x + i \, a b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} f^{2}}"," ",0,"1/2*((a^2 - b^2)*d*f^2*x^2 + 2*(a^2 - b^2)*c*f^2*x - a*b*d*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + a*b*d*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - a*b*d*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + a*b*d*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - (I*a*b*d*e - I*a*b*c*f)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - (-I*a*b*d*e + I*a*b*c*f)*sqrt(-(a^2 - b^2)/a^2)*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - (I*a*b*d*e - I*a*b*c*f)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - (-I*a*b*d*e + I*a*b*c*f)*sqrt(-(a^2 - b^2)/a^2)*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - (I*a*b*d*f*x + I*a*b*d*e)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - (-I*a*b*d*f*x - I*a*b*d*e)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - (-I*a*b*d*f*x - I*a*b*d*e)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) - (I*a*b*d*f*x + I*a*b*d*e)*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a))/((a^3 - a*b^2)*f^2)","B",0
37,0,0,0,0.733286," ","integrate(1/(d*x+c)/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*sec(f*x + e)), x)","F",0
38,0,0,0,1.042110," ","integrate(1/(d*x+c)^2/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sec(f*x + e)), x)","F",0
39,1,7050,0,1.765176," ","integrate((d*x+c)^3/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c^{3} f^{4} x + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) - 12 \, {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(4, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} f^{4} x\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f x - 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f + {\left(-12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f x - 12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f\right)} \cos\left(f x + e\right) - 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{2} x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(-12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f x - 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f + {\left(-12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f x - 12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{2} x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f x + 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f + {\left(12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f x + 12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f\right)} \cos\left(f x + e\right) - 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{2} x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f x + 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f + {\left(12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f x + 12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2} + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{2} x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f + {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{3} f^{3} + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f + {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{3} f^{3} + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f + {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{3} f^{3} + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2} + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f + {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{3} f^{3} + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2} - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x - {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{3} x^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{3} x^{2} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{3} x - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{3} x^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{3} x^{2} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{3} x - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x - {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{3} x^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{3} x^{2} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{3} x + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{3} x^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{3} x^{2} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{3} x + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x - {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{3} x^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{3} x^{2} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{3} x + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{3} x^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{3} x^{2} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{3} x + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2} e f + 3 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{2} x - {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f^{3} x^{3} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{3} x^{2} - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{3} x - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d e f^{2} + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f^{3} x^{3} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f^{3} x^{2} - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d f^{3} x - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} e^{3} + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} e^{2} f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d e f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} \cos\left(f x + e\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f x - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f + {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f x - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} \cos\left(f x + e\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f x + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f + {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f x + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} \cos\left(f x + e\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} + {\left(6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f x + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f + {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f x + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{3} \cos\left(f x + e\right) + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3} + {\left(-6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{3} f x - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} f + {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{3} f x - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 4 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d f^{3} x + {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} f^{3}\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} f^{4} \cos\left(f x + e\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} f^{4}\right)}}"," ",0,"1/4*((a^4*b - 2*a^2*b^3 + b^5)*d^3*f^4*x^4 + 4*(a^4*b - 2*a^2*b^3 + b^5)*c*d^2*f^4*x^3 + 6*(a^4*b - 2*a^2*b^3 + b^5)*c^2*d*f^4*x^2 + 4*(a^4*b - 2*a^2*b^3 + b^5)*c^3*f^4*x + 12*((2*a^4*b - a^2*b^3)*d^3*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d^3)*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*((2*a^4*b - a^2*b^3)*d^3*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d^3)*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 12*((2*a^4*b - a^2*b^3)*d^3*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d^3)*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) - 12*((2*a^4*b - a^2*b^3)*d^3*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d^3)*sqrt(-(a^2 - b^2)/a^2)*polylog(4, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + ((a^5 - 2*a^3*b^2 + a*b^4)*d^3*f^4*x^4 + 4*(a^5 - 2*a^3*b^2 + a*b^4)*c*d^2*f^4*x^3 + 6*(a^5 - 2*a^3*b^2 + a*b^4)*c^2*d*f^4*x^2 + 4*(a^5 - 2*a^3*b^2 + a*b^4)*c^3*f^4*x)*cos(f*x + e) + (-12*I*(a^2*b^3 - b^5)*d^3*f*x - 12*I*(a^2*b^3 - b^5)*c*d^2*f + (-12*I*(a^3*b^2 - a*b^4)*d^3*f*x - 12*I*(a^3*b^2 - a*b^4)*c*d^2*f)*cos(f*x + e) - 6*((2*a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(2*a^3*b^2 - a*b^4)*c*d^2*f^2*x + (2*a^3*b^2 - a*b^4)*c^2*d*f^2 + ((2*a^4*b - a^2*b^3)*d^3*f^2*x^2 + 2*(2*a^4*b - a^2*b^3)*c*d^2*f^2*x + (2*a^4*b - a^2*b^3)*c^2*d*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (-12*I*(a^2*b^3 - b^5)*d^3*f*x - 12*I*(a^2*b^3 - b^5)*c*d^2*f + (-12*I*(a^3*b^2 - a*b^4)*d^3*f*x - 12*I*(a^3*b^2 - a*b^4)*c*d^2*f)*cos(f*x + e) + 6*((2*a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(2*a^3*b^2 - a*b^4)*c*d^2*f^2*x + (2*a^3*b^2 - a*b^4)*c^2*d*f^2 + ((2*a^4*b - a^2*b^3)*d^3*f^2*x^2 + 2*(2*a^4*b - a^2*b^3)*c*d^2*f^2*x + (2*a^4*b - a^2*b^3)*c^2*d*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (12*I*(a^2*b^3 - b^5)*d^3*f*x + 12*I*(a^2*b^3 - b^5)*c*d^2*f + (12*I*(a^3*b^2 - a*b^4)*d^3*f*x + 12*I*(a^3*b^2 - a*b^4)*c*d^2*f)*cos(f*x + e) - 6*((2*a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(2*a^3*b^2 - a*b^4)*c*d^2*f^2*x + (2*a^3*b^2 - a*b^4)*c^2*d*f^2 + ((2*a^4*b - a^2*b^3)*d^3*f^2*x^2 + 2*(2*a^4*b - a^2*b^3)*c*d^2*f^2*x + (2*a^4*b - a^2*b^3)*c^2*d*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (12*I*(a^2*b^3 - b^5)*d^3*f*x + 12*I*(a^2*b^3 - b^5)*c*d^2*f + (12*I*(a^3*b^2 - a*b^4)*d^3*f*x + 12*I*(a^3*b^2 - a*b^4)*c*d^2*f)*cos(f*x + e) + 6*((2*a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(2*a^3*b^2 - a*b^4)*c*d^2*f^2*x + (2*a^3*b^2 - a*b^4)*c^2*d*f^2 + ((2*a^4*b - a^2*b^3)*d^3*f^2*x^2 + 2*(2*a^4*b - a^2*b^3)*c*d^2*f^2*x + (2*a^4*b - a^2*b^3)*c^2*d*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + 2*(3*(a^2*b^3 - b^5)*d^3*e^2 - 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*(a^2*b^3 - b^5)*c^2*d*f^2 + 3*((a^3*b^2 - a*b^4)*d^3*e^2 - 2*(a^3*b^2 - a*b^4)*c*d^2*e*f + (a^3*b^2 - a*b^4)*c^2*d*f^2)*cos(f*x + e) + (-I*(2*a^3*b^2 - a*b^4)*d^3*e^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + I*(2*a^3*b^2 - a*b^4)*c^3*f^3 + (-I*(2*a^4*b - a^2*b^3)*d^3*e^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2 + I*(2*a^4*b - a^2*b^3)*c^3*f^3)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) + 2*(3*(a^2*b^3 - b^5)*d^3*e^2 - 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*(a^2*b^3 - b^5)*c^2*d*f^2 + 3*((a^3*b^2 - a*b^4)*d^3*e^2 - 2*(a^3*b^2 - a*b^4)*c*d^2*e*f + (a^3*b^2 - a*b^4)*c^2*d*f^2)*cos(f*x + e) + (I*(2*a^3*b^2 - a*b^4)*d^3*e^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 - I*(2*a^3*b^2 - a*b^4)*c^3*f^3 + (I*(2*a^4*b - a^2*b^3)*d^3*e^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2 - I*(2*a^4*b - a^2*b^3)*c^3*f^3)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) + 2*(3*(a^2*b^3 - b^5)*d^3*e^2 - 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*(a^2*b^3 - b^5)*c^2*d*f^2 + 3*((a^3*b^2 - a*b^4)*d^3*e^2 - 2*(a^3*b^2 - a*b^4)*c*d^2*e*f + (a^3*b^2 - a*b^4)*c^2*d*f^2)*cos(f*x + e) + (-I*(2*a^3*b^2 - a*b^4)*d^3*e^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + I*(2*a^3*b^2 - a*b^4)*c^3*f^3 + (-I*(2*a^4*b - a^2*b^3)*d^3*e^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2 + I*(2*a^4*b - a^2*b^3)*c^3*f^3)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) + 2*(3*(a^2*b^3 - b^5)*d^3*e^2 - 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*(a^2*b^3 - b^5)*c^2*d*f^2 + 3*((a^3*b^2 - a*b^4)*d^3*e^2 - 2*(a^3*b^2 - a*b^4)*c*d^2*e*f + (a^3*b^2 - a*b^4)*c^2*d*f^2)*cos(f*x + e) + (I*(2*a^3*b^2 - a*b^4)*d^3*e^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 - I*(2*a^3*b^2 - a*b^4)*c^3*f^3 + (I*(2*a^4*b - a^2*b^3)*d^3*e^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2 - I*(2*a^4*b - a^2*b^3)*c^3*f^3)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) + 2*(3*(a^2*b^3 - b^5)*d^3*f^2*x^2 + 6*(a^2*b^3 - b^5)*c*d^2*f^2*x - 3*(a^2*b^3 - b^5)*d^3*e^2 + 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*((a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*f^2*x - (a^3*b^2 - a*b^4)*d^3*e^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*e*f)*cos(f*x + e) + (-I*(2*a^3*b^2 - a*b^4)*d^3*f^3*x^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*f^3*x^2 - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*f^3*x - I*(2*a^3*b^2 - a*b^4)*d^3*e^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + (-I*(2*a^4*b - a^2*b^3)*d^3*f^3*x^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*f^3*x^2 - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*f^3*x - I*(2*a^4*b - a^2*b^3)*d^3*e^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(3*(a^2*b^3 - b^5)*d^3*f^2*x^2 + 6*(a^2*b^3 - b^5)*c*d^2*f^2*x - 3*(a^2*b^3 - b^5)*d^3*e^2 + 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*((a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*f^2*x - (a^3*b^2 - a*b^4)*d^3*e^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*e*f)*cos(f*x + e) + (I*(2*a^3*b^2 - a*b^4)*d^3*f^3*x^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*f^3*x^2 + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*f^3*x + I*(2*a^3*b^2 - a*b^4)*d^3*e^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + (I*(2*a^4*b - a^2*b^3)*d^3*f^3*x^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*f^3*x^2 + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*f^3*x + I*(2*a^4*b - a^2*b^3)*d^3*e^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(3*(a^2*b^3 - b^5)*d^3*f^2*x^2 + 6*(a^2*b^3 - b^5)*c*d^2*f^2*x - 3*(a^2*b^3 - b^5)*d^3*e^2 + 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*((a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*f^2*x - (a^3*b^2 - a*b^4)*d^3*e^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*e*f)*cos(f*x + e) + (I*(2*a^3*b^2 - a*b^4)*d^3*f^3*x^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*f^3*x^2 + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*f^3*x + I*(2*a^3*b^2 - a*b^4)*d^3*e^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + (I*(2*a^4*b - a^2*b^3)*d^3*f^3*x^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*f^3*x^2 + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*f^3*x + I*(2*a^4*b - a^2*b^3)*d^3*e^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(3*(a^2*b^3 - b^5)*d^3*f^2*x^2 + 6*(a^2*b^3 - b^5)*c*d^2*f^2*x - 3*(a^2*b^3 - b^5)*d^3*e^2 + 6*(a^2*b^3 - b^5)*c*d^2*e*f + 3*((a^3*b^2 - a*b^4)*d^3*f^2*x^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*f^2*x - (a^3*b^2 - a*b^4)*d^3*e^2 + 2*(a^3*b^2 - a*b^4)*c*d^2*e*f)*cos(f*x + e) + (-I*(2*a^3*b^2 - a*b^4)*d^3*f^3*x^3 - 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*f^3*x^2 - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*f^3*x - I*(2*a^3*b^2 - a*b^4)*d^3*e^3 + 3*I*(2*a^3*b^2 - a*b^4)*c*d^2*e^2*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*d*e*f^2 + (-I*(2*a^4*b - a^2*b^3)*d^3*f^3*x^3 - 3*I*(2*a^4*b - a^2*b^3)*c*d^2*f^3*x^2 - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*f^3*x - I*(2*a^4*b - a^2*b^3)*d^3*e^3 + 3*I*(2*a^4*b - a^2*b^3)*c*d^2*e^2*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*d*e*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(6*(a^3*b^2 - a*b^4)*d^3*cos(f*x + e) + 6*(a^2*b^3 - b^5)*d^3 + (-6*I*(2*a^3*b^2 - a*b^4)*d^3*f*x - 6*I*(2*a^3*b^2 - a*b^4)*c*d^2*f + (-6*I*(2*a^4*b - a^2*b^3)*d^3*f*x - 6*I*(2*a^4*b - a^2*b^3)*c*d^2*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(6*(a^3*b^2 - a*b^4)*d^3*cos(f*x + e) + 6*(a^2*b^3 - b^5)*d^3 + (6*I*(2*a^3*b^2 - a*b^4)*d^3*f*x + 6*I*(2*a^3*b^2 - a*b^4)*c*d^2*f + (6*I*(2*a^4*b - a^2*b^3)*d^3*f*x + 6*I*(2*a^4*b - a^2*b^3)*c*d^2*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(6*(a^3*b^2 - a*b^4)*d^3*cos(f*x + e) + 6*(a^2*b^3 - b^5)*d^3 + (6*I*(2*a^3*b^2 - a*b^4)*d^3*f*x + 6*I*(2*a^3*b^2 - a*b^4)*c*d^2*f + (6*I*(2*a^4*b - a^2*b^3)*d^3*f*x + 6*I*(2*a^4*b - a^2*b^3)*c*d^2*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(6*(a^3*b^2 - a*b^4)*d^3*cos(f*x + e) + 6*(a^2*b^3 - b^5)*d^3 + (-6*I*(2*a^3*b^2 - a*b^4)*d^3*f*x - 6*I*(2*a^3*b^2 - a*b^4)*c*d^2*f + (-6*I*(2*a^4*b - a^2*b^3)*d^3*f*x - 6*I*(2*a^4*b - a^2*b^3)*c*d^2*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 4*((a^3*b^2 - a*b^4)*d^3*f^3*x^3 + 3*(a^3*b^2 - a*b^4)*c*d^2*f^3*x^2 + 3*(a^3*b^2 - a*b^4)*c^2*d*f^3*x + (a^3*b^2 - a*b^4)*c^3*f^3)*sin(f*x + e))/((a^7 - 2*a^5*b^2 + a^3*b^4)*f^4*cos(f*x + e) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*f^4)","C",0
40,1,4310,0,1.408462," ","integrate((d*x+c)^2/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{3} x^{3} + 12 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c d f^{3} x^{2} + 12 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} f^{3} x + 2 \, {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} \cos\left(f x + e\right) - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} \cos\left(f x + e\right) + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} \cos\left(f x + e\right) + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 2 \, {\left(-6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} \cos\left(f x + e\right) - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm polylog}\left(3, -\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}}{2 \, a}\right) + 4 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c d f^{3} x^{2} + 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{3} x\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} \cos\left(f x + e\right) - 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} - 12 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(-12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} \cos\left(f x + e\right) - 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} + 12 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} \cos\left(f x + e\right) + 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} - 12 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(12 i \, {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} \cos\left(f x + e\right) + 12 i \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} + 12 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f x + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d f + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e - {\left(a^{3} b^{2} - a b^{4}\right)} c d f\right)} \cos\left(f x + e\right) - {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} f^{2} + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d f + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e - {\left(a^{3} b^{2} - a b^{4}\right)} c d f\right)} \cos\left(f x + e\right) - {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} f^{2} + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d f + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e - {\left(a^{3} b^{2} - a b^{4}\right)} c d f\right)} \cos\left(f x + e\right) - {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} f^{2} + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) - 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} c d f + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e - {\left(a^{3} b^{2} - a b^{4}\right)} c d f\right)} \cos\left(f x + e\right) - {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} f^{2} + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c^{2} f^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) + 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} f x + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e\right)} \cos\left(f x + e\right) + {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f^{2} x^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f^{2} x + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f^{2} x^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f^{2} x + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} f x + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e\right)} \cos\left(f x + e\right) + {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f^{2} x^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f^{2} x - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f^{2} x - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} f x + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e\right)} \cos\left(f x + e\right) + {\left(3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f^{2} x^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f^{2} x - 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + {\left(3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f^{2} x - 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} + 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 2 \, {\left(6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} f x + 6 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2} e + 6 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} f x + {\left(a^{3} b^{2} - a b^{4}\right)} d^{2} e\right)} \cos\left(f x + e\right) + {\left(-3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} f^{2} x^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d f^{2} x + 3 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c d e f + {\left(-3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} f^{2} x^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d f^{2} x + 3 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d^{2} e^{2} - 6 i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c d e f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + 12 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d f^{2} x + {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} f^{2}\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} f^{3} \cos\left(f x + e\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} f^{3}\right)}}"," ",0,"1/12*(4*(a^4*b - 2*a^2*b^3 + b^5)*d^2*f^3*x^3 + 12*(a^4*b - 2*a^2*b^3 + b^5)*c*d*f^3*x^2 + 12*(a^4*b - 2*a^2*b^3 + b^5)*c^2*f^3*x + 2*(-6*I*(2*a^4*b - a^2*b^3)*d^2*cos(f*x + e) - 6*I*(2*a^3*b^2 - a*b^4)*d^2)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(6*I*(2*a^4*b - a^2*b^3)*d^2*cos(f*x + e) + 6*I*(2*a^3*b^2 - a*b^4)*d^2)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(6*I*(2*a^4*b - a^2*b^3)*d^2*cos(f*x + e) + 6*I*(2*a^3*b^2 - a*b^4)*d^2)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 2*(-6*I*(2*a^4*b - a^2*b^3)*d^2*cos(f*x + e) - 6*I*(2*a^3*b^2 - a*b^4)*d^2)*sqrt(-(a^2 - b^2)/a^2)*polylog(3, -1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2))/a) + 4*((a^5 - 2*a^3*b^2 + a*b^4)*d^2*f^3*x^3 + 3*(a^5 - 2*a^3*b^2 + a*b^4)*c*d*f^3*x^2 + 3*(a^5 - 2*a^3*b^2 + a*b^4)*c^2*f^3*x)*cos(f*x + e) + (-12*I*(a^3*b^2 - a*b^4)*d^2*cos(f*x + e) - 12*I*(a^2*b^3 - b^5)*d^2 - 12*((2*a^3*b^2 - a*b^4)*d^2*f*x + (2*a^3*b^2 - a*b^4)*c*d*f + ((2*a^4*b - a^2*b^3)*d^2*f*x + (2*a^4*b - a^2*b^3)*c*d*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (-12*I*(a^3*b^2 - a*b^4)*d^2*cos(f*x + e) - 12*I*(a^2*b^3 - b^5)*d^2 + 12*((2*a^3*b^2 - a*b^4)*d^2*f*x + (2*a^3*b^2 - a*b^4)*c*d*f + ((2*a^4*b - a^2*b^3)*d^2*f*x + (2*a^4*b - a^2*b^3)*c*d*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (12*I*(a^3*b^2 - a*b^4)*d^2*cos(f*x + e) + 12*I*(a^2*b^3 - b^5)*d^2 - 12*((2*a^3*b^2 - a*b^4)*d^2*f*x + (2*a^3*b^2 - a*b^4)*c*d*f + ((2*a^4*b - a^2*b^3)*d^2*f*x + (2*a^4*b - a^2*b^3)*c*d*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (12*I*(a^3*b^2 - a*b^4)*d^2*cos(f*x + e) + 12*I*(a^2*b^3 - b^5)*d^2 + 12*((2*a^3*b^2 - a*b^4)*d^2*f*x + (2*a^3*b^2 - a*b^4)*c*d*f + ((2*a^4*b - a^2*b^3)*d^2*f*x + (2*a^4*b - a^2*b^3)*c*d*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - 2*(6*(a^2*b^3 - b^5)*d^2*e - 6*(a^2*b^3 - b^5)*c*d*f + 6*((a^3*b^2 - a*b^4)*d^2*e - (a^3*b^2 - a*b^4)*c*d*f)*cos(f*x + e) - (3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*f^2 + (3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(6*(a^2*b^3 - b^5)*d^2*e - 6*(a^2*b^3 - b^5)*c*d*f + 6*((a^3*b^2 - a*b^4)*d^2*e - (a^3*b^2 - a*b^4)*c*d*f)*cos(f*x + e) - (-3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*f^2 + (-3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) - 2*(6*(a^2*b^3 - b^5)*d^2*e - 6*(a^2*b^3 - b^5)*c*d*f + 6*((a^3*b^2 - a*b^4)*d^2*e - (a^3*b^2 - a*b^4)*c*d*f)*cos(f*x + e) - (3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + 3*I*(2*a^3*b^2 - a*b^4)*c^2*f^2 + (3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f + 3*I*(2*a^4*b - a^2*b^3)*c^2*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) - 2*(6*(a^2*b^3 - b^5)*d^2*e - 6*(a^2*b^3 - b^5)*c*d*f + 6*((a^3*b^2 - a*b^4)*d^2*e - (a^3*b^2 - a*b^4)*c*d*f)*cos(f*x + e) - (-3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f - 3*I*(2*a^3*b^2 - a*b^4)*c^2*f^2 + (-3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f - 3*I*(2*a^4*b - a^2*b^3)*c^2*f^2)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) + 2*(6*(a^2*b^3 - b^5)*d^2*f*x + 6*(a^2*b^3 - b^5)*d^2*e + 6*((a^3*b^2 - a*b^4)*d^2*f*x + (a^3*b^2 - a*b^4)*d^2*e)*cos(f*x + e) + (-3*I*(2*a^3*b^2 - a*b^4)*d^2*f^2*x^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*f^2*x + 3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + (-3*I*(2*a^4*b - a^2*b^3)*d^2*f^2*x^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*f^2*x + 3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(6*(a^2*b^3 - b^5)*d^2*f*x + 6*(a^2*b^3 - b^5)*d^2*e + 6*((a^3*b^2 - a*b^4)*d^2*f*x + (a^3*b^2 - a*b^4)*d^2*e)*cos(f*x + e) + (3*I*(2*a^3*b^2 - a*b^4)*d^2*f^2*x^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*f^2*x - 3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + (3*I*(2*a^4*b - a^2*b^3)*d^2*f^2*x^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*f^2*x - 3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(6*(a^2*b^3 - b^5)*d^2*f*x + 6*(a^2*b^3 - b^5)*d^2*e + 6*((a^3*b^2 - a*b^4)*d^2*f*x + (a^3*b^2 - a*b^4)*d^2*e)*cos(f*x + e) + (3*I*(2*a^3*b^2 - a*b^4)*d^2*f^2*x^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*f^2*x - 3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 + 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + (3*I*(2*a^4*b - a^2*b^3)*d^2*f^2*x^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*f^2*x - 3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 + 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 2*(6*(a^2*b^3 - b^5)*d^2*f*x + 6*(a^2*b^3 - b^5)*d^2*e + 6*((a^3*b^2 - a*b^4)*d^2*f*x + (a^3*b^2 - a*b^4)*d^2*e)*cos(f*x + e) + (-3*I*(2*a^3*b^2 - a*b^4)*d^2*f^2*x^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*f^2*x + 3*I*(2*a^3*b^2 - a*b^4)*d^2*e^2 - 6*I*(2*a^3*b^2 - a*b^4)*c*d*e*f + (-3*I*(2*a^4*b - a^2*b^3)*d^2*f^2*x^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*f^2*x + 3*I*(2*a^4*b - a^2*b^3)*d^2*e^2 - 6*I*(2*a^4*b - a^2*b^3)*c*d*e*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + 12*((a^3*b^2 - a*b^4)*d^2*f^2*x^2 + 2*(a^3*b^2 - a*b^4)*c*d*f^2*x + (a^3*b^2 - a*b^4)*c^2*f^2)*sin(f*x + e))/((a^7 - 2*a^5*b^2 + a^3*b^4)*f^3*cos(f*x + e) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*f^3)","C",0
41,1,2112,0,0.819874," ","integrate((d*x+c)/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} c f^{2} x - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) - {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left({\left(2 \, a^{4} b - a^{2} b^{3}\right)} d \cos\left(f x + e\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} {\rm Li}_2\left(-\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a} + 1\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d f x - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d f x + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) + i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d f x + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d f x - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} \log\left(\frac{2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) - 2 \, {\left(a \cos\left(f x + e\right) - i \, a \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, a}{2 \, a}\right) + {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2} x^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} c f^{2} x\right)} \cos\left(f x + e\right) + {\left({\left(a^{3} b^{2} - a b^{4}\right)} d \cos\left(f x + e\right) + {\left(a^{2} b^{3} - b^{5}\right)} d + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4}\right)} d \cos\left(f x + e\right) + {\left(a^{2} b^{3} - b^{5}\right)} d + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} + 2 \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4}\right)} d \cos\left(f x + e\right) + {\left(a^{2} b^{3} - b^{5}\right)} d + {\left(-i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left(-i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e + i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) + 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) + {\left({\left(a^{3} b^{2} - a b^{4}\right)} d \cos\left(f x + e\right) + {\left(a^{2} b^{3} - b^{5}\right)} d + {\left(i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - i \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left(i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} d e - i \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}}\right)} \log\left(-2 \, a \cos\left(f x + e\right) - 2 i \, a \sin\left(f x + e\right) + 2 \, a \sqrt{-\frac{a^{2} - b^{2}}{a^{2}}} - 2 \, b\right) + 2 \, {\left({\left(a^{3} b^{2} - a b^{4}\right)} d f x + {\left(a^{3} b^{2} - a b^{4}\right)} c f\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} f^{2} \cos\left(f x + e\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} f^{2}\right)}}"," ",0,"1/2*((a^4*b - 2*a^2*b^3 + b^5)*d*f^2*x^2 + 2*(a^4*b - 2*a^2*b^3 + b^5)*c*f^2*x - ((2*a^4*b - a^2*b^3)*d*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + ((2*a^4*b - a^2*b^3)*d*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) - ((2*a^4*b - a^2*b^3)*d*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + ((2*a^4*b - a^2*b^3)*d*cos(f*x + e) + (2*a^3*b^2 - a*b^4)*d)*sqrt(-(a^2 - b^2)/a^2)*dilog(-1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a + 1) + (-I*(2*a^3*b^2 - a*b^4)*d*f*x - I*(2*a^3*b^2 - a*b^4)*d*e + (-I*(2*a^4*b - a^2*b^3)*d*f*x - I*(2*a^4*b - a^2*b^3)*d*e)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + (I*(2*a^3*b^2 - a*b^4)*d*f*x + I*(2*a^3*b^2 - a*b^4)*d*e + (I*(2*a^4*b - a^2*b^3)*d*f*x + I*(2*a^4*b - a^2*b^3)*d*e)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) + I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + (I*(2*a^3*b^2 - a*b^4)*d*f*x + I*(2*a^3*b^2 - a*b^4)*d*e + (I*(2*a^4*b - a^2*b^3)*d*f*x + I*(2*a^4*b - a^2*b^3)*d*e)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + (-I*(2*a^3*b^2 - a*b^4)*d*f*x - I*(2*a^3*b^2 - a*b^4)*d*e + (-I*(2*a^4*b - a^2*b^3)*d*f*x - I*(2*a^4*b - a^2*b^3)*d*e)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2)*log(1/2*(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) - 2*(a*cos(f*x + e) - I*a*sin(f*x + e))*sqrt(-(a^2 - b^2)/a^2) + 2*a)/a) + ((a^5 - 2*a^3*b^2 + a*b^4)*d*f^2*x^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*c*f^2*x)*cos(f*x + e) + ((a^3*b^2 - a*b^4)*d*cos(f*x + e) + (a^2*b^3 - b^5)*d + (-I*(2*a^3*b^2 - a*b^4)*d*e + I*(2*a^3*b^2 - a*b^4)*c*f + (-I*(2*a^4*b - a^2*b^3)*d*e + I*(2*a^4*b - a^2*b^3)*c*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) + ((a^3*b^2 - a*b^4)*d*cos(f*x + e) + (a^2*b^3 - b^5)*d + (I*(2*a^3*b^2 - a*b^4)*d*e - I*(2*a^3*b^2 - a*b^4)*c*f + (I*(2*a^4*b - a^2*b^3)*d*e - I*(2*a^4*b - a^2*b^3)*c*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) + 2*b) + ((a^3*b^2 - a*b^4)*d*cos(f*x + e) + (a^2*b^3 - b^5)*d + (-I*(2*a^3*b^2 - a*b^4)*d*e + I*(2*a^3*b^2 - a*b^4)*c*f + (-I*(2*a^4*b - a^2*b^3)*d*e + I*(2*a^4*b - a^2*b^3)*c*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) + 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) + ((a^3*b^2 - a*b^4)*d*cos(f*x + e) + (a^2*b^3 - b^5)*d + (I*(2*a^3*b^2 - a*b^4)*d*e - I*(2*a^3*b^2 - a*b^4)*c*f + (I*(2*a^4*b - a^2*b^3)*d*e - I*(2*a^4*b - a^2*b^3)*c*f)*cos(f*x + e))*sqrt(-(a^2 - b^2)/a^2))*log(-2*a*cos(f*x + e) - 2*I*a*sin(f*x + e) + 2*a*sqrt(-(a^2 - b^2)/a^2) - 2*b) + 2*((a^3*b^2 - a*b^4)*d*f*x + (a^3*b^2 - a*b^4)*c*f)*sin(f*x + e))/((a^7 - 2*a^5*b^2 + a^3*b^4)*f^2*cos(f*x + e) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*f^2)","B",0
42,0,0,0,0.569114," ","integrate(1/(d*x+c)/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} \sec\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*sec(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*sec(f*x + e)), x)","F",0
43,0,0,0,0.704702," ","integrate(1/(d*x+c)^2/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sec\left(f x + e\right)^{2} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sec(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*sec(f*x + e)), x)","F",0
44,0,0,0,0.766164," ","integrate((d*x+c)^m*(a+b*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(b \sec\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*sec(f*x + e) + a)^n, x)","F",0
45,0,0,0,0.728195," ","integrate((d*x+c)^m*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)} {\left(d x + c\right)}^{m}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)*(d*x + c)^m, x)","F",0
46,0,0,0,0.738560," ","integrate((d*x+c)^m/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(b*sec(f*x + e) + a), x)","F",0
