1,1,926,0,1.387747," ","integrate((d*x+c)^3*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c^{3} + \frac{{\left(f x + e\right)}^{4} a d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a c^{2} d e}{f} + 4 \, a c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - \frac{4 \, a d^{3} e^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{3}} + \frac{12 \, a c d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, a c^{2} d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{2 \, {\left(12 i \, a d^{3} {\rm Li}_{4}(i \, e^{\left(i \, f x + i \, e\right)}) - 12 i \, a d^{3} {\rm Li}_{4}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} a d^{3} + {\left(6 i \, a d^{3} e - 6 i \, a c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a d^{3} e^{2} + 12 i \, a c d^{2} e f - 6 i \, a c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, {\left(f x + e\right)}^{3} a d^{3} + {\left(6 i \, a d^{3} e - 6 i \, a c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a d^{3} e^{2} + 12 i \, a c d^{2} e f - 6 i \, a c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} a d^{3} - 6 i \, a d^{3} e^{2} + 12 i \, a c d^{2} e f - 6 i \, a c^{2} d f^{2} + {\left(12 i \, a d^{3} e - 12 i \, a c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(6 i \, {\left(f x + e\right)}^{2} a d^{3} + 6 i \, a d^{3} e^{2} - 12 i \, a c d^{2} e f + 6 i \, a c^{2} d f^{2} + {\left(-12 i \, a d^{3} e + 12 i \, a c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left({\left(f x + e\right)}^{3} a d^{3} - 3 \, {\left(a d^{3} e - a c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a d^{3} e^{2} - 2 \, a c d^{2} e f + a c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left({\left(f x + e\right)}^{3} a d^{3} - 3 \, {\left(a d^{3} e - a c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a d^{3} e^{2} - 2 \, a c d^{2} e f + a c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + 12 \, {\left({\left(f x + e\right)} a d^{3} - a d^{3} e + a c d^{2} f\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - 12 \, {\left({\left(f x + e\right)} a d^{3} - a d^{3} e + a c d^{2} f\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)})\right)}}{f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c^3 + (f*x + e)^4*a*d^3/f^3 - 4*(f*x + e)^3*a*d^3*e/f^3 + 6*(f*x + e)^2*a*d^3*e^2/f^3 - 4*(f*x + e)*a*d^3*e^3/f^3 + 4*(f*x + e)^3*a*c*d^2/f^2 - 12*(f*x + e)^2*a*c*d^2*e/f^2 + 12*(f*x + e)*a*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c^2*d/f - 12*(f*x + e)*a*c^2*d*e/f + 4*a*c^3*log(sec(f*x + e) + tan(f*x + e)) - 4*a*d^3*e^3*log(sec(f*x + e) + tan(f*x + e))/f^3 + 12*a*c*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*a*c^2*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 2*(12*I*a*d^3*polylog(4, I*e^(I*f*x + I*e)) - 12*I*a*d^3*polylog(4, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*a*d^3 + (6*I*a*d^3*e - 6*I*a*c*d^2*f)*(f*x + e)^2 + (-6*I*a*d^3*e^2 + 12*I*a*c*d^2*e*f - 6*I*a*c^2*d*f^2)*(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (-2*I*(f*x + e)^3*a*d^3 + (6*I*a*d^3*e - 6*I*a*c*d^2*f)*(f*x + e)^2 + (-6*I*a*d^3*e^2 + 12*I*a*c*d^2*e*f - 6*I*a*c^2*d*f^2)*(f*x + e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-6*I*(f*x + e)^2*a*d^3 - 6*I*a*d^3*e^2 + 12*I*a*c*d^2*e*f - 6*I*a*c^2*d*f^2 + (12*I*a*d^3*e - 12*I*a*c*d^2*f)*(f*x + e))*dilog(I*e^(I*f*x + I*e)) + (6*I*(f*x + e)^2*a*d^3 + 6*I*a*d^3*e^2 - 12*I*a*c*d^2*e*f + 6*I*a*c^2*d*f^2 + (-12*I*a*d^3*e + 12*I*a*c*d^2*f)*(f*x + e))*dilog(-I*e^(I*f*x + I*e)) + ((f*x + e)^3*a*d^3 - 3*(a*d^3*e - a*c*d^2*f)*(f*x + e)^2 + 3*(a*d^3*e^2 - 2*a*c*d^2*e*f + a*c^2*d*f^2)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - ((f*x + e)^3*a*d^3 - 3*(a*d^3*e - a*c*d^2*f)*(f*x + e)^2 + 3*(a*d^3*e^2 - 2*a*c*d^2*e*f + a*c^2*d*f^2)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + 12*((f*x + e)*a*d^3 - a*d^3*e + a*c*d^2*f)*polylog(3, I*e^(I*f*x + I*e)) - 12*((f*x + e)*a*d^3 - a*d^3*e + a*c*d^2*f)*polylog(3, -I*e^(I*f*x + I*e)))/f^3)/f","B",0
2,1,510,0,1.121517," ","integrate((d*x+c)^2*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{6 \, {\left(f x + e\right)} a c^{2} + \frac{2 \, {\left(f x + e\right)}^{3} a d^{2}}{f^{2}} - \frac{6 \, {\left(f x + e\right)}^{2} a d^{2} e}{f^{2}} + \frac{6 \, {\left(f x + e\right)} a d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c d}{f} - \frac{12 \, {\left(f x + e\right)} a c d e}{f} + 6 \, a c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + \frac{6 \, a d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, a c d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(4 \, a d^{2} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - 4 \, a d^{2} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{2} a d^{2} + {\left(4 i \, a d^{2} e - 4 i \, a c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, {\left(f x + e\right)}^{2} a d^{2} + {\left(4 i \, a d^{2} e - 4 i \, a c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-4 i \, {\left(f x + e\right)} a d^{2} + 4 i \, a d^{2} e - 4 i \, a c d f\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(4 i \, {\left(f x + e\right)} a d^{2} - 4 i \, a d^{2} e + 4 i \, a c d f\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left({\left(f x + e\right)}^{2} a d^{2} - 2 \, {\left(a d^{2} e - a c d f\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left({\left(f x + e\right)}^{2} a d^{2} - 2 \, {\left(a d^{2} e - a c d f\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)}}{f^{2}}}{6 \, f}"," ",0,"1/6*(6*(f*x + e)*a*c^2 + 2*(f*x + e)^3*a*d^2/f^2 - 6*(f*x + e)^2*a*d^2*e/f^2 + 6*(f*x + e)*a*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c*d/f - 12*(f*x + e)*a*c*d*e/f + 6*a*c^2*log(sec(f*x + e) + tan(f*x + e)) + 6*a*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*a*c*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 3*(4*a*d^2*polylog(3, I*e^(I*f*x + I*e)) - 4*a*d^2*polylog(3, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^2*a*d^2 + (4*I*a*d^2*e - 4*I*a*c*d*f)*(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (-2*I*(f*x + e)^2*a*d^2 + (4*I*a*d^2*e - 4*I*a*c*d*f)*(f*x + e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-4*I*(f*x + e)*a*d^2 + 4*I*a*d^2*e - 4*I*a*c*d*f)*dilog(I*e^(I*f*x + I*e)) + (4*I*(f*x + e)*a*d^2 - 4*I*a*d^2*e + 4*I*a*c*d*f)*dilog(-I*e^(I*f*x + I*e)) + ((f*x + e)^2*a*d^2 - 2*(a*d^2*e - a*c*d*f)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - ((f*x + e)^2*a*d^2 - 2*(a*d^2*e - a*c*d*f)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))/f^2)/f","B",0
3,-1,0,0,0.000000," ","integrate((d*x+c)*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,-1,0,0,0.000000," ","integrate((a+a*sec(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,1,3403,0,1.997744," ","integrate((d*x+c)^3*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a^{2} c^{3} + \frac{{\left(f x + e\right)}^{4} a^{2} d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a^{2} d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{2} d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a^{2} d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a^{2} c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a^{2} c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{2} c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a^{2} c^{2} d e}{f} + 8 \, a^{2} c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - \frac{8 \, a^{2} d^{3} e^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{3}} + \frac{24 \, a^{2} c d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{24 \, a^{2} c^{2} d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} - \frac{4 \, {\left(4 \, a^{2} d^{3} e^{3} - 12 \, a^{2} c d^{2} e^{2} f + 12 \, a^{2} c^{2} d e f^{2} - 4 \, a^{2} c^{3} f^{3} + {\left(4 \, {\left(f x + e\right)}^{3} a^{2} d^{3} - 12 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)} + 4 \, {\left({\left(f x + e\right)}^{3} a^{2} d^{3} - 3 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(12 i \, a^{2} d^{3} e - 12 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a^{2} d^{3} e^{2} + 24 i \, a^{2} c d^{2} e f - 12 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(4 \, {\left(f x + e\right)}^{3} a^{2} d^{3} - 12 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)} + 4 \, {\left({\left(f x + e\right)}^{3} a^{2} d^{3} - 3 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(12 i \, a^{2} d^{3} e - 12 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a^{2} d^{3} e^{2} + 24 i \, a^{2} c d^{2} e f - 12 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - {\left(6 \, {\left(f x + e\right)}^{2} a^{2} d^{3} + 6 \, a^{2} d^{3} e^{2} - 12 \, a^{2} c d^{2} e f + 6 \, a^{2} c^{2} d f^{2} - 12 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{3} + a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2} - 2 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, {\left(f x + e\right)}^{2} a^{2} d^{3} + 6 i \, a^{2} d^{3} e^{2} - 12 i \, a^{2} c d^{2} e f + 6 i \, a^{2} c^{2} d f^{2} + {\left(-12 i \, a^{2} d^{3} e + 12 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 4 \, {\left({\left(f x + e\right)}^{3} a^{2} d^{3} - 3 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, {\left(f x + e\right)} a^{2} d^{3} - 6 \, a^{2} d^{3} e + 6 \, a^{2} c d^{2} f + 6 \, {\left({\left(f x + e\right)} a^{2} d^{3} - a^{2} d^{3} e + a^{2} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-6 i \, {\left(f x + e\right)} a^{2} d^{3} + 6 i \, a^{2} d^{3} e - 6 i \, a^{2} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, f x + 2 i \, e\right)}\right) + {\left(12 \, {\left(f x + e\right)}^{2} a^{2} d^{3} + 12 \, a^{2} d^{3} e^{2} - 24 \, a^{2} c d^{2} e f + 12 \, a^{2} c^{2} d f^{2} - 24 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)} + 12 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{3} + a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2} - 2 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-12 i \, {\left(f x + e\right)}^{2} a^{2} d^{3} - 12 i \, a^{2} d^{3} e^{2} + 24 i \, a^{2} c d^{2} e f - 12 i \, a^{2} c^{2} d f^{2} + {\left(24 i \, a^{2} d^{3} e - 24 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(12 \, {\left(f x + e\right)}^{2} a^{2} d^{3} + 12 \, a^{2} d^{3} e^{2} - 24 \, a^{2} c d^{2} e f + 12 \, a^{2} c^{2} d f^{2} - 24 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)} + 12 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{3} + a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2} - 2 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(12 i \, {\left(f x + e\right)}^{2} a^{2} d^{3} + 12 i \, a^{2} d^{3} e^{2} - 24 i \, a^{2} c d^{2} e f + 12 i \, a^{2} c^{2} d f^{2} + {\left(-24 i \, a^{2} d^{3} e + 24 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(-3 i \, {\left(f x + e\right)}^{2} a^{2} d^{3} - 3 i \, a^{2} d^{3} e^{2} + 6 i \, a^{2} c d^{2} e f - 3 i \, a^{2} c^{2} d f^{2} + {\left(6 i \, a^{2} d^{3} e - 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} a^{2} d^{3} - 3 i \, a^{2} d^{3} e^{2} + 6 i \, a^{2} c d^{2} e f - 3 i \, a^{2} c^{2} d f^{2} + {\left(6 i \, a^{2} d^{3} e - 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{3} + a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2} - 2 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right) - {\left(-2 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(6 i \, a^{2} d^{3} e - 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a^{2} d^{3} e^{2} + 12 i \, a^{2} c d^{2} e f - 6 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)} + {\left(-2 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(6 i \, a^{2} d^{3} e - 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a^{2} d^{3} e^{2} + 12 i \, a^{2} c d^{2} e f - 6 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left({\left(f x + e\right)}^{3} a^{2} d^{3} - 3 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(2 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(-6 i \, a^{2} d^{3} e + 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, a^{2} d^{3} e^{2} - 12 i \, a^{2} c d^{2} e f + 6 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)} + {\left(2 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(-6 i \, a^{2} d^{3} e + 6 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, a^{2} d^{3} e^{2} - 12 i \, a^{2} c d^{2} e f + 6 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left({\left(f x + e\right)}^{3} a^{2} d^{3} - 3 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 24 \, {\left(a^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} d^{3} \sin\left(2 \, f x + 2 \, e\right) + a^{2} d^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, f x + i \, e\right)}) + 24 \, {\left(a^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} d^{3} \sin\left(2 \, f x + 2 \, e\right) + a^{2} d^{3}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, f x + i \, e\right)}) - {\left(-3 i \, a^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} d^{3} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2} d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, f x + 2 i \, e\right)}) - {\left(-24 i \, {\left(f x + e\right)} a^{2} d^{3} + 24 i \, a^{2} d^{3} e - 24 i \, a^{2} c d^{2} f + {\left(-24 i \, {\left(f x + e\right)} a^{2} d^{3} + 24 i \, a^{2} d^{3} e - 24 i \, a^{2} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 24 \, {\left({\left(f x + e\right)} a^{2} d^{3} - a^{2} d^{3} e + a^{2} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - {\left(24 i \, {\left(f x + e\right)} a^{2} d^{3} - 24 i \, a^{2} d^{3} e + 24 i \, a^{2} c d^{2} f + {\left(24 i \, {\left(f x + e\right)} a^{2} d^{3} - 24 i \, a^{2} d^{3} e + 24 i \, a^{2} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 24 \, {\left({\left(f x + e\right)} a^{2} d^{3} - a^{2} d^{3} e + a^{2} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) - {\left(-4 i \, {\left(f x + e\right)}^{3} a^{2} d^{3} + {\left(12 i \, a^{2} d^{3} e - 12 i \, a^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a^{2} d^{3} e^{2} + 24 i \, a^{2} c d^{2} e f - 12 i \, a^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-2 i \, f^{3} \cos\left(2 \, f x + 2 \, e\right) + 2 \, f^{3} \sin\left(2 \, f x + 2 \, e\right) - 2 i \, f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a^2*c^3 + (f*x + e)^4*a^2*d^3/f^3 - 4*(f*x + e)^3*a^2*d^3*e/f^3 + 6*(f*x + e)^2*a^2*d^3*e^2/f^3 - 4*(f*x + e)*a^2*d^3*e^3/f^3 + 4*(f*x + e)^3*a^2*c*d^2/f^2 - 12*(f*x + e)^2*a^2*c*d^2*e/f^2 + 12*(f*x + e)*a^2*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a^2*c^2*d/f - 12*(f*x + e)*a^2*c^2*d*e/f + 8*a^2*c^3*log(sec(f*x + e) + tan(f*x + e)) - 8*a^2*d^3*e^3*log(sec(f*x + e) + tan(f*x + e))/f^3 + 24*a^2*c*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 24*a^2*c^2*d*e*log(sec(f*x + e) + tan(f*x + e))/f - 4*(4*a^2*d^3*e^3 - 12*a^2*c*d^2*e^2*f + 12*a^2*c^2*d*e*f^2 - 4*a^2*c^3*f^3 + (4*(f*x + e)^3*a^2*d^3 - 12*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 12*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e) + 4*((f*x + e)^3*a^2*d^3 - 3*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 3*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - (-4*I*(f*x + e)^3*a^2*d^3 + (12*I*a^2*d^3*e - 12*I*a^2*c*d^2*f)*(f*x + e)^2 + (-12*I*a^2*d^3*e^2 + 24*I*a^2*c*d^2*e*f - 12*I*a^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (4*(f*x + e)^3*a^2*d^3 - 12*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 12*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e) + 4*((f*x + e)^3*a^2*d^3 - 3*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 3*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - (-4*I*(f*x + e)^3*a^2*d^3 + (12*I*a^2*d^3*e - 12*I*a^2*c*d^2*f)*(f*x + e)^2 + (-12*I*a^2*d^3*e^2 + 24*I*a^2*c*d^2*e*f - 12*I*a^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - (6*(f*x + e)^2*a^2*d^3 + 6*a^2*d^3*e^2 - 12*a^2*c*d^2*e*f + 6*a^2*c^2*d*f^2 - 12*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e) + 6*((f*x + e)^2*a^2*d^3 + a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2 - 2*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (6*I*(f*x + e)^2*a^2*d^3 + 6*I*a^2*d^3*e^2 - 12*I*a^2*c*d^2*e*f + 6*I*a^2*c^2*d*f^2 + (-12*I*a^2*d^3*e + 12*I*a^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 4*((f*x + e)^3*a^2*d^3 - 3*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 3*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) + (6*(f*x + e)*a^2*d^3 - 6*a^2*d^3*e + 6*a^2*c*d^2*f + 6*((f*x + e)*a^2*d^3 - a^2*d^3*e + a^2*c*d^2*f)*cos(2*f*x + 2*e) - (-6*I*(f*x + e)*a^2*d^3 + 6*I*a^2*d^3*e - 6*I*a^2*c*d^2*f)*sin(2*f*x + 2*e))*dilog(-e^(2*I*f*x + 2*I*e)) + (12*(f*x + e)^2*a^2*d^3 + 12*a^2*d^3*e^2 - 24*a^2*c*d^2*e*f + 12*a^2*c^2*d*f^2 - 24*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e) + 12*((f*x + e)^2*a^2*d^3 + a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2 - 2*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) - (-12*I*(f*x + e)^2*a^2*d^3 - 12*I*a^2*d^3*e^2 + 24*I*a^2*c*d^2*e*f - 12*I*a^2*c^2*d*f^2 + (24*I*a^2*d^3*e - 24*I*a^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*dilog(I*e^(I*f*x + I*e)) - (12*(f*x + e)^2*a^2*d^3 + 12*a^2*d^3*e^2 - 24*a^2*c*d^2*e*f + 12*a^2*c^2*d*f^2 - 24*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e) + 12*((f*x + e)^2*a^2*d^3 + a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2 - 2*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (12*I*(f*x + e)^2*a^2*d^3 + 12*I*a^2*d^3*e^2 - 24*I*a^2*c*d^2*e*f + 12*I*a^2*c^2*d*f^2 + (-24*I*a^2*d^3*e + 24*I*a^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*dilog(-I*e^(I*f*x + I*e)) - (-3*I*(f*x + e)^2*a^2*d^3 - 3*I*a^2*d^3*e^2 + 6*I*a^2*c*d^2*e*f - 3*I*a^2*c^2*d*f^2 + (6*I*a^2*d^3*e - 6*I*a^2*c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*a^2*d^3 - 3*I*a^2*d^3*e^2 + 6*I*a^2*c*d^2*e*f - 3*I*a^2*c^2*d*f^2 + (6*I*a^2*d^3*e - 6*I*a^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + 3*((f*x + e)^2*a^2*d^3 + a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2 - 2*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1) - (-2*I*(f*x + e)^3*a^2*d^3 + (6*I*a^2*d^3*e - 6*I*a^2*c*d^2*f)*(f*x + e)^2 + (-6*I*a^2*d^3*e^2 + 12*I*a^2*c*d^2*e*f - 6*I*a^2*c^2*d*f^2)*(f*x + e) + (-2*I*(f*x + e)^3*a^2*d^3 + (6*I*a^2*d^3*e - 6*I*a^2*c*d^2*f)*(f*x + e)^2 + (-6*I*a^2*d^3*e^2 + 12*I*a^2*c*d^2*e*f - 6*I*a^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) + 2*((f*x + e)^3*a^2*d^3 - 3*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 3*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (2*I*(f*x + e)^3*a^2*d^3 + (-6*I*a^2*d^3*e + 6*I*a^2*c*d^2*f)*(f*x + e)^2 + (6*I*a^2*d^3*e^2 - 12*I*a^2*c*d^2*e*f + 6*I*a^2*c^2*d*f^2)*(f*x + e) + (2*I*(f*x + e)^3*a^2*d^3 + (-6*I*a^2*d^3*e + 6*I*a^2*c*d^2*f)*(f*x + e)^2 + (6*I*a^2*d^3*e^2 - 12*I*a^2*c*d^2*e*f + 6*I*a^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - 2*((f*x + e)^3*a^2*d^3 - 3*(a^2*d^3*e - a^2*c*d^2*f)*(f*x + e)^2 + 3*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 24*(a^2*d^3*cos(2*f*x + 2*e) + I*a^2*d^3*sin(2*f*x + 2*e) + a^2*d^3)*polylog(4, I*e^(I*f*x + I*e)) + 24*(a^2*d^3*cos(2*f*x + 2*e) + I*a^2*d^3*sin(2*f*x + 2*e) + a^2*d^3)*polylog(4, -I*e^(I*f*x + I*e)) - (-3*I*a^2*d^3*cos(2*f*x + 2*e) + 3*a^2*d^3*sin(2*f*x + 2*e) - 3*I*a^2*d^3)*polylog(3, -e^(2*I*f*x + 2*I*e)) - (-24*I*(f*x + e)*a^2*d^3 + 24*I*a^2*d^3*e - 24*I*a^2*c*d^2*f + (-24*I*(f*x + e)*a^2*d^3 + 24*I*a^2*d^3*e - 24*I*a^2*c*d^2*f)*cos(2*f*x + 2*e) + 24*((f*x + e)*a^2*d^3 - a^2*d^3*e + a^2*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, I*e^(I*f*x + I*e)) - (24*I*(f*x + e)*a^2*d^3 - 24*I*a^2*d^3*e + 24*I*a^2*c*d^2*f + (24*I*(f*x + e)*a^2*d^3 - 24*I*a^2*d^3*e + 24*I*a^2*c*d^2*f)*cos(2*f*x + 2*e) - 24*((f*x + e)*a^2*d^3 - a^2*d^3*e + a^2*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, -I*e^(I*f*x + I*e)) - (-4*I*(f*x + e)^3*a^2*d^3 + (12*I*a^2*d^3*e - 12*I*a^2*c*d^2*f)*(f*x + e)^2 + (-12*I*a^2*d^3*e^2 + 24*I*a^2*c*d^2*e*f - 12*I*a^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))/(-2*I*f^3*cos(2*f*x + 2*e) + 2*f^3*sin(2*f*x + 2*e) - 2*I*f^3))/f","B",0
7,1,1707,0,0.838269," ","integrate((d*x+c)^2*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a^{2} c^{2} + \frac{{\left(f x + e\right)}^{3} a^{2} d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a^{2} d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a^{2} c d}{f} - \frac{6 \, {\left(f x + e\right)} a^{2} c d e}{f} + 6 \, a^{2} c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + \frac{6 \, a^{2} d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, a^{2} c d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(2 \, a^{2} d^{2} e^{2} - 4 \, a^{2} c d e f + 2 \, a^{2} c^{2} f^{2} - {\left(2 \, {\left(f x + e\right)}^{2} a^{2} d^{2} - 4 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)} + 2 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{2} - 2 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(4 i \, a^{2} d^{2} e - 4 i \, a^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - {\left(2 \, {\left(f x + e\right)}^{2} a^{2} d^{2} - 4 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)} + 2 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{2} - 2 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(4 i \, a^{2} d^{2} e - 4 i \, a^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(2 \, {\left(f x + e\right)} a^{2} d^{2} - 2 \, a^{2} d^{2} e + 2 \, a^{2} c d f + 2 \, {\left({\left(f x + e\right)} a^{2} d^{2} - a^{2} d^{2} e + a^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 i \, {\left(f x + e\right)} a^{2} d^{2} - 2 i \, a^{2} d^{2} e + 2 i \, a^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{2} a^{2} d^{2} - 2 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(a^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} d^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2} d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, f x + 2 i \, e\right)}\right) - {\left(4 \, {\left(f x + e\right)} a^{2} d^{2} - 4 \, a^{2} d^{2} e + 4 \, a^{2} c d f + 4 \, {\left({\left(f x + e\right)} a^{2} d^{2} - a^{2} d^{2} e + a^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)} a^{2} d^{2} + 4 i \, a^{2} d^{2} e - 4 i \, a^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(4 \, {\left(f x + e\right)} a^{2} d^{2} - 4 \, a^{2} d^{2} e + 4 \, a^{2} c d f + 4 \, {\left({\left(f x + e\right)} a^{2} d^{2} - a^{2} d^{2} e + a^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(4 i \, {\left(f x + e\right)} a^{2} d^{2} - 4 i \, a^{2} d^{2} e + 4 i \, a^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(-i \, {\left(f x + e\right)} a^{2} d^{2} + i \, a^{2} d^{2} e - i \, a^{2} c d f + {\left(-i \, {\left(f x + e\right)} a^{2} d^{2} + i \, a^{2} d^{2} e - i \, a^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(f x + e\right)} a^{2} d^{2} - a^{2} d^{2} e + a^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right) + {\left(-i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(2 i \, a^{2} d^{2} e - 2 i \, a^{2} c d f\right)} {\left(f x + e\right)} + {\left(-i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(2 i \, a^{2} d^{2} e - 2 i \, a^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(f x + e\right)}^{2} a^{2} d^{2} - 2 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(-2 i \, a^{2} d^{2} e + 2 i \, a^{2} c d f\right)} {\left(f x + e\right)} + {\left(i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(-2 i \, a^{2} d^{2} e + 2 i \, a^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(f x + e\right)}^{2} a^{2} d^{2} - 2 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-4 i \, a^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a^{2} d^{2} \sin\left(2 \, f x + 2 \, e\right) - 4 i \, a^{2} d^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) + {\left(4 i \, a^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) - 4 \, a^{2} d^{2} \sin\left(2 \, f x + 2 \, e\right) + 4 i \, a^{2} d^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{2} a^{2} d^{2} + {\left(4 i \, a^{2} d^{2} e - 4 i \, a^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-i \, f^{2} \cos\left(2 \, f x + 2 \, e\right) + f^{2} \sin\left(2 \, f x + 2 \, e\right) - i \, f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a^2*c^2 + (f*x + e)^3*a^2*d^2/f^2 - 3*(f*x + e)^2*a^2*d^2*e/f^2 + 3*(f*x + e)*a^2*d^2*e^2/f^2 + 3*(f*x + e)^2*a^2*c*d/f - 6*(f*x + e)*a^2*c*d*e/f + 6*a^2*c^2*log(sec(f*x + e) + tan(f*x + e)) + 6*a^2*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*a^2*c*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 3*(2*a^2*d^2*e^2 - 4*a^2*c*d*e*f + 2*a^2*c^2*f^2 - (2*(f*x + e)^2*a^2*d^2 - 4*(a^2*d^2*e - a^2*c*d*f)*(f*x + e) + 2*((f*x + e)^2*a^2*d^2 - 2*(a^2*d^2*e - a^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (-2*I*(f*x + e)^2*a^2*d^2 + (4*I*a^2*d^2*e - 4*I*a^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) - (2*(f*x + e)^2*a^2*d^2 - 4*(a^2*d^2*e - a^2*c*d*f)*(f*x + e) + 2*((f*x + e)^2*a^2*d^2 - 2*(a^2*d^2*e - a^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (-2*I*(f*x + e)^2*a^2*d^2 + (4*I*a^2*d^2*e - 4*I*a^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (2*(f*x + e)*a^2*d^2 - 2*a^2*d^2*e + 2*a^2*c*d*f + 2*((f*x + e)*a^2*d^2 - a^2*d^2*e + a^2*c*d*f)*cos(2*f*x + 2*e) + (2*I*(f*x + e)*a^2*d^2 - 2*I*a^2*d^2*e + 2*I*a^2*c*d*f)*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*((f*x + e)^2*a^2*d^2 - 2*(a^2*d^2*e - a^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (a^2*d^2*cos(2*f*x + 2*e) + I*a^2*d^2*sin(2*f*x + 2*e) + a^2*d^2)*dilog(-e^(2*I*f*x + 2*I*e)) - (4*(f*x + e)*a^2*d^2 - 4*a^2*d^2*e + 4*a^2*c*d*f + 4*((f*x + e)*a^2*d^2 - a^2*d^2*e + a^2*c*d*f)*cos(2*f*x + 2*e) - (-4*I*(f*x + e)*a^2*d^2 + 4*I*a^2*d^2*e - 4*I*a^2*c*d*f)*sin(2*f*x + 2*e))*dilog(I*e^(I*f*x + I*e)) + (4*(f*x + e)*a^2*d^2 - 4*a^2*d^2*e + 4*a^2*c*d*f + 4*((f*x + e)*a^2*d^2 - a^2*d^2*e + a^2*c*d*f)*cos(2*f*x + 2*e) + (4*I*(f*x + e)*a^2*d^2 - 4*I*a^2*d^2*e + 4*I*a^2*c*d*f)*sin(2*f*x + 2*e))*dilog(-I*e^(I*f*x + I*e)) + (-I*(f*x + e)*a^2*d^2 + I*a^2*d^2*e - I*a^2*c*d*f + (-I*(f*x + e)*a^2*d^2 + I*a^2*d^2*e - I*a^2*c*d*f)*cos(2*f*x + 2*e) + ((f*x + e)*a^2*d^2 - a^2*d^2*e + a^2*c*d*f)*sin(2*f*x + 2*e))*log(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1) + (-I*(f*x + e)^2*a^2*d^2 + (2*I*a^2*d^2*e - 2*I*a^2*c*d*f)*(f*x + e) + (-I*(f*x + e)^2*a^2*d^2 + (2*I*a^2*d^2*e - 2*I*a^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) + ((f*x + e)^2*a^2*d^2 - 2*(a^2*d^2*e - a^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (I*(f*x + e)^2*a^2*d^2 + (-2*I*a^2*d^2*e + 2*I*a^2*c*d*f)*(f*x + e) + (I*(f*x + e)^2*a^2*d^2 + (-2*I*a^2*d^2*e + 2*I*a^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - ((f*x + e)^2*a^2*d^2 - 2*(a^2*d^2*e - a^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + (-4*I*a^2*d^2*cos(2*f*x + 2*e) + 4*a^2*d^2*sin(2*f*x + 2*e) - 4*I*a^2*d^2)*polylog(3, I*e^(I*f*x + I*e)) + (4*I*a^2*d^2*cos(2*f*x + 2*e) - 4*a^2*d^2*sin(2*f*x + 2*e) + 4*I*a^2*d^2)*polylog(3, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^2*a^2*d^2 + (4*I*a^2*d^2*e - 4*I*a^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))/(-I*f^2*cos(2*f*x + 2*e) + f^2*sin(2*f*x + 2*e) - I*f^2))/f","B",0
8,-1,0,0,0.000000," ","integrate((d*x+c)*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{{\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} \log\left(d x + c\right) + 2 \, a^{2} d \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d f x + a^{2} c f\right)} \log\left(d x + c\right) \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) \log\left(d x + c\right) + 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right) + {\left(a^{2} d + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f + {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)}\,{d x} + {\left(a^{2} d f x + a^{2} c f\right)} \log\left(d x + c\right)}{d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"((a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)^2*log(d*x + c) + 2*a^2*d*sin(2*f*x + 2*e) + (a^2*d*f*x + a^2*c*f)*log(d*x + c)*sin(2*f*x + 2*e)^2 + 2*(a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)*log(d*x + c) + (d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e))*integrate(2*(2*(a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)*cos(f*x + e) + 2*(a^2*d*f*x + a^2*c*f)*cos(f*x + e) + (a^2*d + 2*(a^2*d*f*x + a^2*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(d^2*f*x^2 + 2*c*d*f*x + c^2*f + (d^2*f*x^2 + 2*c*d*f*x + c^2*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x^2 + 2*c*d*f*x + c^2*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x^2 + 2*c*d*f*x + c^2*f)*cos(2*f*x + 2*e)), x) + (a^2*d*f*x + a^2*c*f)*log(d*x + c))/(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e))","F",0
10,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{a^{2} d f x + a^{2} c f - 2 \, a^{2} d \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right) + {\left(a^{2} d + {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f + {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)}\,{d x}}{d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"-(a^2*d*f*x + a^2*c*f - 2*a^2*d*sin(2*f*x + 2*e) + (a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)^2 + (a^2*d*f*x + a^2*c*f)*sin(2*f*x + 2*e)^2 + 2*(a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e) - (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e))*integrate(4*((a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)*cos(f*x + e) + (a^2*d*f*x + a^2*c*f)*cos(f*x + e) + (a^2*d + (a^2*d*f*x + a^2*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*cos(2*f*x + 2*e)), x))/(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e))","F",0
11,1,1284,0,0.786442," ","integrate((d*x+c)^3/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{6 \, c d^{2} e^{2} {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a f^{2}} - \frac{\sin\left(f x + e\right)}{a f^{2} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 6 \, c^{2} d e {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a f} - \frac{\sin\left(f x + e\right)}{a f {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{6 \, {\left({\left(f x + e\right)}^{2} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)}^{2} \sin\left(f x + e\right)^{2} + 2 \, {\left(f x + e\right)}^{2} \cos\left(f x + e\right) + {\left(f x + e\right)}^{2} - 2 \, {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 4 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c d^{2} e}{a f^{2} \cos\left(f x + e\right)^{2} + a f^{2} \sin\left(f x + e\right)^{2} + 2 \, a f^{2} \cos\left(f x + e\right) + a f^{2}} + 2 \, c^{3} {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + \frac{3 \, {\left({\left(f x + e\right)}^{2} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)}^{2} \sin\left(f x + e\right)^{2} + 2 \, {\left(f x + e\right)}^{2} \cos\left(f x + e\right) + {\left(f x + e\right)}^{2} - 2 \, {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 4 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c^{2} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \cos\left(f x + e\right) + a f} - \frac{2 \, {\left(i \, {\left(f x + e\right)}^{4} d^{3} + 6 i \, {\left(f x + e\right)}^{2} d^{3} e^{2} - 4 i \, {\left(f x + e\right)} d^{3} e^{3} - 8 \, d^{3} e^{3} + {\left(-4 i \, d^{3} e + 4 i \, c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\left(24 \, {\left(f x + e\right)}^{2} d^{3} + 24 \, d^{3} e^{2} - 48 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} + 24 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(24 i \, {\left(f x + e\right)}^{2} d^{3} + 24 i \, d^{3} e^{2} + {\left(-48 i \, d^{3} e + 48 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(i \, {\left(f x + e\right)}^{4} d^{3} + {\left(-4 i \, d^{3} e + 4 i \, c d^{2} f - 8 \, d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(6 i \, d^{3} e^{2} + 24 \, d^{3} e - 24 \, c d^{2} f\right)} {\left(f x + e\right)}^{2} - 4 \, {\left(i \, d^{3} e^{3} + 6 \, d^{3} e^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) - {\left(48 \, {\left(f x + e\right)} d^{3} - 48 \, d^{3} e + 48 \, c d^{2} f + 48 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) - {\left(-48 i \, {\left(f x + e\right)} d^{3} + 48 i \, d^{3} e - 48 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-12 i \, {\left(f x + e\right)}^{2} d^{3} - 12 i \, d^{3} e^{2} + {\left(24 i \, d^{3} e - 24 i \, c d^{2} f\right)} {\left(f x + e\right)} + {\left(-12 i \, {\left(f x + e\right)}^{2} d^{3} - 12 i \, d^{3} e^{2} + {\left(24 i \, d^{3} e - 24 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 12 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + {\left(-48 i \, d^{3} \cos\left(f x + e\right) + 48 \, d^{3} \sin\left(f x + e\right) - 48 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) - {\left({\left(f x + e\right)}^{4} d^{3} - {\left(4 \, d^{3} e - 4 \, c d^{2} f - 8 i \, d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(6 \, d^{3} e^{2} - 24 i \, d^{3} e + 24 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2} - {\left(4 \, d^{3} e^{3} - 24 i \, d^{3} e^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)}}{-4 i \, a f^{3} \cos\left(f x + e\right) + 4 \, a f^{3} \sin\left(f x + e\right) - 4 i \, a f^{3}}}{2 \, f}"," ",0,"1/2*(6*c*d^2*e^2*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a*f^2) - sin(f*x + e)/(a*f^2*(cos(f*x + e) + 1))) - 6*c^2*d*e*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a*f) - sin(f*x + e)/(a*f*(cos(f*x + e) + 1))) - 6*((f*x + e)^2*cos(f*x + e)^2 + (f*x + e)^2*sin(f*x + e)^2 + 2*(f*x + e)^2*cos(f*x + e) + (f*x + e)^2 - 2*(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 4*(f*x + e)*sin(f*x + e))*c*d^2*e/(a*f^2*cos(f*x + e)^2 + a*f^2*sin(f*x + e)^2 + 2*a*f^2*cos(f*x + e) + a*f^2) + 2*c^3*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) + 3*((f*x + e)^2*cos(f*x + e)^2 + (f*x + e)^2*sin(f*x + e)^2 + 2*(f*x + e)^2*cos(f*x + e) + (f*x + e)^2 - 2*(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 4*(f*x + e)*sin(f*x + e))*c^2*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*cos(f*x + e) + a*f) - 2*(I*(f*x + e)^4*d^3 + 6*I*(f*x + e)^2*d^3*e^2 - 4*I*(f*x + e)*d^3*e^3 - 8*d^3*e^3 + (-4*I*d^3*e + 4*I*c*d^2*f)*(f*x + e)^3 + (24*(f*x + e)^2*d^3 + 24*d^3*e^2 - 48*(d^3*e - c*d^2*f)*(f*x + e) + 24*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (24*I*(f*x + e)^2*d^3 + 24*I*d^3*e^2 + (-48*I*d^3*e + 48*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (I*(f*x + e)^4*d^3 + (-4*I*d^3*e + 4*I*c*d^2*f - 8*d^3)*(f*x + e)^3 + (6*I*d^3*e^2 + 24*d^3*e - 24*c*d^2*f)*(f*x + e)^2 - 4*(I*d^3*e^3 + 6*d^3*e^2)*(f*x + e))*cos(f*x + e) - (48*(f*x + e)*d^3 - 48*d^3*e + 48*c*d^2*f + 48*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) - (-48*I*(f*x + e)*d^3 + 48*I*d^3*e - 48*I*c*d^2*f)*sin(f*x + e))*dilog(-e^(I*f*x + I*e)) + (-12*I*(f*x + e)^2*d^3 - 12*I*d^3*e^2 + (24*I*d^3*e - 24*I*c*d^2*f)*(f*x + e) + (-12*I*(f*x + e)^2*d^3 - 12*I*d^3*e^2 + (24*I*d^3*e - 24*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 12*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (-48*I*d^3*cos(f*x + e) + 48*d^3*sin(f*x + e) - 48*I*d^3)*polylog(3, -e^(I*f*x + I*e)) - ((f*x + e)^4*d^3 - (4*d^3*e - 4*c*d^2*f - 8*I*d^3)*(f*x + e)^3 + (6*d^3*e^2 - 24*I*d^3*e + 24*I*c*d^2*f)*(f*x + e)^2 - (4*d^3*e^3 - 24*I*d^3*e^2)*(f*x + e))*sin(f*x + e))/(-4*I*a*f^3*cos(f*x + e) + 4*a*f^3*sin(f*x + e) - 4*I*a*f^3))/f","B",0
12,1,376,0,1.138666," ","integrate((d*x+c)^2/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{i \, d^{2} f^{3} x^{3} + 3 i \, c d f^{3} x^{2} + 3 i \, c^{2} f^{3} x + 6 \, c^{2} f^{2} + {\left(12 \, d^{2} f x + 12 \, c d f + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + {\left(12 i \, d^{2} f x + 12 i \, c d f\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(i \, d^{2} f^{3} x^{3} - 3 \, {\left(-i \, c d f^{3} + 2 \, d^{2} f^{2}\right)} x^{2} + {\left(3 i \, c^{2} f^{3} - 12 \, c d f^{2}\right)} x\right)} \cos\left(f x + e\right) - 12 \, {\left(d^{2} \cos\left(f x + e\right) + i \, d^{2} \sin\left(f x + e\right) + d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-6 i \, d^{2} f x - 6 i \, c d f + {\left(-6 i \, d^{2} f x - 6 i \, c d f\right)} \cos\left(f x + e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - {\left(d^{2} f^{3} x^{3} + {\left(3 \, c d f^{3} + 6 i \, d^{2} f^{2}\right)} x^{2} + 3 \, {\left(c^{2} f^{3} + 4 i \, c d f^{2}\right)} x\right)} \sin\left(f x + e\right)}{-3 i \, a f^{3} \cos\left(f x + e\right) + 3 \, a f^{3} \sin\left(f x + e\right) - 3 i \, a f^{3}}"," ",0,"-(I*d^2*f^3*x^3 + 3*I*c*d*f^3*x^2 + 3*I*c^2*f^3*x + 6*c^2*f^2 + (12*d^2*f*x + 12*c*d*f + 12*(d^2*f*x + c*d*f)*cos(f*x + e) + (12*I*d^2*f*x + 12*I*c*d*f)*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (I*d^2*f^3*x^3 - 3*(-I*c*d*f^3 + 2*d^2*f^2)*x^2 + (3*I*c^2*f^3 - 12*c*d*f^2)*x)*cos(f*x + e) - 12*(d^2*cos(f*x + e) + I*d^2*sin(f*x + e) + d^2)*dilog(-e^(I*f*x + I*e)) + (-6*I*d^2*f*x - 6*I*c*d*f + (-6*I*d^2*f*x - 6*I*c*d*f)*cos(f*x + e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - (d^2*f^3*x^3 + (3*c*d*f^3 + 6*I*d^2*f^2)*x^2 + 3*(c^2*f^3 + 4*I*c*d*f^2)*x)*sin(f*x + e))/(-3*I*a*f^3*cos(f*x + e) + 3*a*f^3*sin(f*x + e) - 3*I*a*f^3)","B",0
13,1,273,0,1.041849," ","integrate((d*x+c)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, d e {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a f} - \frac{\sin\left(f x + e\right)}{a f {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - 2 \, c {\left(\frac{2 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} - \frac{\sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - \frac{{\left({\left(f x + e\right)}^{2} \cos\left(f x + e\right)^{2} + {\left(f x + e\right)}^{2} \sin\left(f x + e\right)^{2} + 2 \, {\left(f x + e\right)}^{2} \cos\left(f x + e\right) + {\left(f x + e\right)}^{2} - 2 \, {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 4 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \cos\left(f x + e\right) + a f}}{2 \, f}"," ",0,"-1/2*(2*d*e*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a*f) - sin(f*x + e)/(a*f*(cos(f*x + e) + 1))) - 2*c*(2*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a - sin(f*x + e)/(a*(cos(f*x + e) + 1))) - ((f*x + e)^2*cos(f*x + e)^2 + (f*x + e)^2*sin(f*x + e)^2 + 2*(f*x + e)^2*cos(f*x + e) + (f*x + e)^2 - 2*(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 4*(f*x + e)*sin(f*x + e))*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*cos(f*x + e) + a*f))/f","B",0
14,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(d f x + c f\right)} \cos\left(f x + e\right)^{2} \log\left(d x + c\right) + {\left(d f x + c f\right)} \log\left(d x + c\right) \sin\left(f x + e\right)^{2} + 2 \, {\left(d f x + c f\right)} \cos\left(f x + e\right) \log\left(d x + c\right) + {\left(d f x + c f\right)} \log\left(d x + c\right) - 2 \, d \sin\left(f x + e\right) - \frac{2 \, {\left(a d^{3} f x + a c d^{2} f + {\left(a d^{3} f x + a c d^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left(a d^{3} f x + a c d^{2} f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a d^{3} f x + a c d^{2} f\right)} \cos\left(f x + e\right)\right)} \int \frac{\sin\left(f x + e\right)}{{\left(d x + c\right)}^{2} {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)}}\,{d x}}{a f}}{a d^{2} f x + a c d f + {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)^{2} + {\left(a d^{2} f x + a c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)}"," ",0,"((d*f*x + c*f)*cos(f*x + e)^2*log(d*x + c) + (d*f*x + c*f)*log(d*x + c)*sin(f*x + e)^2 + 2*(d*f*x + c*f)*cos(f*x + e)*log(d*x + c) - 2*(a*d^3*f*x + a*c*d^2*f + (a*d^3*f*x + a*c*d^2*f)*cos(f*x + e)^2 + (a*d^3*f*x + a*c*d^2*f)*sin(f*x + e)^2 + 2*(a*d^3*f*x + a*c*d^2*f)*cos(f*x + e))*integrate(sin(f*x + e)/(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)^2 + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*sin(f*x + e)^2 + 2*(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)), x) + (d*f*x + c*f)*log(d*x + c) - 2*d*sin(f*x + e))/(a*d^2*f*x + a*c*d*f + (a*d^2*f*x + a*c*d*f)*cos(f*x + e)^2 + (a*d^2*f*x + a*c*d*f)*sin(f*x + e)^2 + 2*(a*d^2*f*x + a*c*d*f)*cos(f*x + e))","F",0
15,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,4261,0,3.094213," ","integrate((d*x+c)^3/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{3 \, c d^{2} e^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2} f^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} f^{2}}\right)} - 3 \, c^{2} d e {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2} f} - \frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} f}\right)} + \frac{6 \, {\left(3 \, {\left(f x + e\right)}^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} + 2 \, {\left(3 \, {\left(f x + e\right)}^{2} + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) + 12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 10 \, {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(10 \, f x + 12 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right) + 10 \, e\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(6 \, f x + 6 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right) + 6 \, e\right)} \sin\left(2 \, f x + 2 \, e\right) - 24 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c d^{2} e}{a^{2} f^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(f x + e\right)^{2} + a^{2} f^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f^{2} \sin\left(f x + e\right)^{2} + 6 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2} + 2 \, {\left(3 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2} f^{2} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)} + c^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{3 \, {\left(3 \, {\left(f x + e\right)}^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} + 2 \, {\left(3 \, {\left(f x + e\right)}^{2} + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) + 12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 10 \, {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(10 \, f x + 12 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right) + 10 \, e\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(6 \, f x + 6 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right) + 6 \, e\right)} \sin\left(2 \, f x + 2 \, e\right) - 24 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c^{2} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \cos\left(f x + e\right) + a^{2} f + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f \sin\left(2 \, f x + 2 \, e\right) + a^{2} f \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)} + \frac{6 \, {\left(3 i \, {\left(f x + e\right)}^{4} d^{3} + 18 i \, {\left(f x + e\right)}^{2} d^{3} e^{2} - 12 i \, {\left(f x + e\right)} d^{3} e^{3} - 40 \, d^{3} e^{3} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f\right)} {\left(f x + e\right)}^{3} + 48 \, d^{3} e - 48 \, c d^{2} f + {\left(120 \, {\left(f x + e\right)}^{2} d^{3} + 120 \, d^{3} e^{2} - 48 \, d^{3} - 240 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} + 24 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + 72 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 72 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(120 i \, {\left(f x + e\right)}^{2} d^{3} + 120 i \, d^{3} e^{2} - 48 i \, d^{3} + {\left(-240 i \, d^{3} e + 240 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(360 i \, {\left(f x + e\right)}^{2} d^{3} + 360 i \, d^{3} e^{2} - 144 i \, d^{3} + {\left(-720 i \, d^{3} e + 720 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(360 i \, {\left(f x + e\right)}^{2} d^{3} + 360 i \, d^{3} e^{2} - 144 i \, d^{3} + {\left(-720 i \, d^{3} e + 720 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(3 i \, {\left(f x + e\right)}^{4} d^{3} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f - 40 \, d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(18 i \, d^{3} e^{2} + 120 \, d^{3} e - 120 \, c d^{2} f\right)} {\left(f x + e\right)}^{2} - 12 \, {\left(i \, d^{3} e^{3} + 10 \, d^{3} e^{2} - 4 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(9 i \, {\left(f x + e\right)}^{4} d^{3} - 48 \, d^{3} e^{3} - 24 i \, d^{3} e^{2} + {\left(-36 i \, d^{3} e + 36 i \, c d^{2} f - 72 \, d^{3}\right)} {\left(f x + e\right)}^{3} + 48 \, d^{3} e - 48 \, c d^{2} f + {\left(54 i \, d^{3} e^{2} + 216 \, d^{3} e - 216 \, c d^{2} f - 24 i \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-36 i \, d^{3} e^{3} - 216 \, d^{3} e^{2} + 48 i \, d^{3} e - 48 i \, c d^{2} f + 96 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 i \, {\left(f x + e\right)}^{4} d^{3} - 72 \, d^{3} e^{3} - 24 i \, d^{3} e^{2} + {\left(-36 i \, d^{3} e + 36 i \, c d^{2} f - 48 \, d^{3}\right)} {\left(f x + e\right)}^{3} + 96 \, d^{3} e - 96 \, c d^{2} f + {\left(54 i \, d^{3} e^{2} + 144 \, d^{3} e - 144 \, c d^{2} f - 24 i \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-36 i \, d^{3} e^{3} - 144 \, d^{3} e^{2} + 48 i \, d^{3} e - 48 i \, c d^{2} f + 48 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) - {\left(240 \, {\left(f x + e\right)} d^{3} - 240 \, d^{3} e + 240 \, c d^{2} f + 240 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 720 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 720 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) - {\left(-240 i \, {\left(f x + e\right)} d^{3} + 240 i \, d^{3} e - 240 i \, c d^{2} f\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(-720 i \, {\left(f x + e\right)} d^{3} + 720 i \, d^{3} e - 720 i \, c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(-720 i \, {\left(f x + e\right)} d^{3} + 720 i \, d^{3} e - 720 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-60 i \, {\left(f x + e\right)}^{2} d^{3} - 60 i \, d^{3} e^{2} + 24 i \, d^{3} + {\left(120 i \, d^{3} e - 120 i \, c d^{2} f\right)} {\left(f x + e\right)} + {\left(-60 i \, {\left(f x + e\right)}^{2} d^{3} - 60 i \, d^{3} e^{2} + 24 i \, d^{3} + {\left(120 i \, d^{3} e - 120 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-180 i \, {\left(f x + e\right)}^{2} d^{3} - 180 i \, d^{3} e^{2} + 72 i \, d^{3} + {\left(360 i \, d^{3} e - 360 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-180 i \, {\left(f x + e\right)}^{2} d^{3} - 180 i \, d^{3} e^{2} + 72 i \, d^{3} + {\left(360 i \, d^{3} e - 360 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 12 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + 36 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(5 \, {\left(f x + e\right)}^{2} d^{3} + 5 \, d^{3} e^{2} - 2 \, d^{3} - 10 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + {\left(-240 i \, d^{3} \cos\left(3 \, f x + 3 \, e\right) - 720 i \, d^{3} \cos\left(2 \, f x + 2 \, e\right) - 720 i \, d^{3} \cos\left(f x + e\right) + 240 \, d^{3} \sin\left(3 \, f x + 3 \, e\right) + 720 \, d^{3} \sin\left(2 \, f x + 2 \, e\right) + 720 \, d^{3} \sin\left(f x + e\right) - 240 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) - {\left(3 \, {\left(f x + e\right)}^{4} d^{3} - {\left(12 \, d^{3} e - 12 \, c d^{2} f - 40 i \, d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(18 \, d^{3} e^{2} - 120 i \, d^{3} e + 120 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2} - {\left(12 \, d^{3} e^{3} - 120 i \, d^{3} e^{2} + 48 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(9 \, {\left(f x + e\right)}^{4} d^{3} + 48 i \, d^{3} e^{3} - 24 \, d^{3} e^{2} - {\left(36 \, d^{3} e - 36 \, c d^{2} f - 72 i \, d^{3}\right)} {\left(f x + e\right)}^{3} - 48 i \, d^{3} e + 48 i \, c d^{2} f + {\left(54 \, d^{3} e^{2} - 216 i \, d^{3} e + 216 i \, c d^{2} f - 24 \, d^{3}\right)} {\left(f x + e\right)}^{2} - {\left(36 \, d^{3} e^{3} - 216 i \, d^{3} e^{2} - 48 \, d^{3} e + 48 \, c d^{2} f + 96 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(9 \, {\left(f x + e\right)}^{4} d^{3} + 72 i \, d^{3} e^{3} - 24 \, d^{3} e^{2} - {\left(36 \, d^{3} e - 36 \, c d^{2} f - 48 i \, d^{3}\right)} {\left(f x + e\right)}^{3} - 96 i \, d^{3} e + 96 i \, c d^{2} f + {\left(54 \, d^{3} e^{2} - 144 i \, d^{3} e + 144 i \, c d^{2} f - 24 \, d^{3}\right)} {\left(f x + e\right)}^{2} - {\left(36 \, d^{3} e^{3} - 144 i \, d^{3} e^{2} - 48 \, d^{3} e + 48 \, c d^{2} f + 48 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)}}{-12 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) - 36 i \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) - 36 i \, a^{2} f^{3} \cos\left(f x + e\right) + 12 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 36 \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) + 36 \, a^{2} f^{3} \sin\left(f x + e\right) - 12 i \, a^{2} f^{3}}}{6 \, f}"," ",0,"-1/6*(3*c*d^2*e^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f^2) - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*f^2)) - 3*c^2*d*e*((9*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f) - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*f)) + 6*(3*(f*x + e)^2*cos(3*f*x + 3*e)^2 + 3*(f*x + e)^2*sin(3*f*x + 3*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(f*x + e)^2 + 3*(f*x + e)^2 + 2*(3*(f*x + e)^2 + (9*(f*x + e)^2 - 2)*cos(2*f*x + 2*e) + (9*(f*x + e)^2 - 2)*cos(f*x + e) + 12*(f*x + e)*sin(2*f*x + 2*e) + 18*(f*x + e)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e) + 18*(f*x + e)*sin(f*x + e) - 2)*cos(2*f*x + 2*e) + 2*(9*(f*x + e)^2 - 2)*cos(f*x + e) - 10*(2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(10*f*x + 12*(f*x + e)*cos(2*f*x + 2*e) + 18*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 2)*sin(2*f*x + 2*e) - (9*(f*x + e)^2 - 2)*sin(f*x + e) + 10*e)*sin(3*f*x + 3*e) - 6*(6*f*x + 6*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 4)*sin(f*x + e) + 6*e)*sin(2*f*x + 2*e) - 24*(f*x + e)*sin(f*x + e))*c*d^2*e/(a^2*f^2*cos(3*f*x + 3*e)^2 + 9*a^2*f^2*cos(2*f*x + 2*e)^2 + 9*a^2*f^2*cos(f*x + e)^2 + a^2*f^2*sin(3*f*x + 3*e)^2 + 9*a^2*f^2*sin(2*f*x + 2*e)^2 + 18*a^2*f^2*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f^2*sin(f*x + e)^2 + 6*a^2*f^2*cos(f*x + e) + a^2*f^2 + 2*(3*a^2*f^2*cos(2*f*x + 2*e) + 3*a^2*f^2*cos(f*x + e) + a^2*f^2)*cos(3*f*x + 3*e) + 6*(3*a^2*f^2*cos(f*x + e) + a^2*f^2)*cos(2*f*x + 2*e) + 6*(a^2*f^2*sin(2*f*x + 2*e) + a^2*f^2*sin(f*x + e))*sin(3*f*x + 3*e)) + c^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 3*(3*(f*x + e)^2*cos(3*f*x + 3*e)^2 + 3*(f*x + e)^2*sin(3*f*x + 3*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(f*x + e)^2 + 3*(f*x + e)^2 + 2*(3*(f*x + e)^2 + (9*(f*x + e)^2 - 2)*cos(2*f*x + 2*e) + (9*(f*x + e)^2 - 2)*cos(f*x + e) + 12*(f*x + e)*sin(2*f*x + 2*e) + 18*(f*x + e)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e) + 18*(f*x + e)*sin(f*x + e) - 2)*cos(2*f*x + 2*e) + 2*(9*(f*x + e)^2 - 2)*cos(f*x + e) - 10*(2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(10*f*x + 12*(f*x + e)*cos(2*f*x + 2*e) + 18*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 2)*sin(2*f*x + 2*e) - (9*(f*x + e)^2 - 2)*sin(f*x + e) + 10*e)*sin(3*f*x + 3*e) - 6*(6*f*x + 6*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 4)*sin(f*x + e) + 6*e)*sin(2*f*x + 2*e) - 24*(f*x + e)*sin(f*x + e))*c^2*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 9*a^2*f*sin(2*f*x + 2*e)^2 + 18*a^2*f*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*cos(f*x + e) + a^2*f + 2*(3*a^2*f*cos(2*f*x + 2*e) + 3*a^2*f*cos(f*x + e) + a^2*f)*cos(3*f*x + 3*e) + 6*(3*a^2*f*cos(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 6*(a^2*f*sin(2*f*x + 2*e) + a^2*f*sin(f*x + e))*sin(3*f*x + 3*e)) + 6*(3*I*(f*x + e)^4*d^3 + 18*I*(f*x + e)^2*d^3*e^2 - 12*I*(f*x + e)*d^3*e^3 - 40*d^3*e^3 + (-12*I*d^3*e + 12*I*c*d^2*f)*(f*x + e)^3 + 48*d^3*e - 48*c*d^2*f + (120*(f*x + e)^2*d^3 + 120*d^3*e^2 - 48*d^3 - 240*(d^3*e - c*d^2*f)*(f*x + e) + 24*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) + 72*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + 72*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (120*I*(f*x + e)^2*d^3 + 120*I*d^3*e^2 - 48*I*d^3 + (-240*I*d^3*e + 240*I*c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) + (360*I*(f*x + e)^2*d^3 + 360*I*d^3*e^2 - 144*I*d^3 + (-720*I*d^3*e + 720*I*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + (360*I*(f*x + e)^2*d^3 + 360*I*d^3*e^2 - 144*I*d^3 + (-720*I*d^3*e + 720*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (3*I*(f*x + e)^4*d^3 + (-12*I*d^3*e + 12*I*c*d^2*f - 40*d^3)*(f*x + e)^3 + (18*I*d^3*e^2 + 120*d^3*e - 120*c*d^2*f)*(f*x + e)^2 - 12*(I*d^3*e^3 + 10*d^3*e^2 - 4*d^3)*(f*x + e))*cos(3*f*x + 3*e) + (9*I*(f*x + e)^4*d^3 - 48*d^3*e^3 - 24*I*d^3*e^2 + (-36*I*d^3*e + 36*I*c*d^2*f - 72*d^3)*(f*x + e)^3 + 48*d^3*e - 48*c*d^2*f + (54*I*d^3*e^2 + 216*d^3*e - 216*c*d^2*f - 24*I*d^3)*(f*x + e)^2 + (-36*I*d^3*e^3 - 216*d^3*e^2 + 48*I*d^3*e - 48*I*c*d^2*f + 96*d^3)*(f*x + e))*cos(2*f*x + 2*e) + (9*I*(f*x + e)^4*d^3 - 72*d^3*e^3 - 24*I*d^3*e^2 + (-36*I*d^3*e + 36*I*c*d^2*f - 48*d^3)*(f*x + e)^3 + 96*d^3*e - 96*c*d^2*f + (54*I*d^3*e^2 + 144*d^3*e - 144*c*d^2*f - 24*I*d^3)*(f*x + e)^2 + (-36*I*d^3*e^3 - 144*d^3*e^2 + 48*I*d^3*e - 48*I*c*d^2*f + 48*d^3)*(f*x + e))*cos(f*x + e) - (240*(f*x + e)*d^3 - 240*d^3*e + 240*c*d^2*f + 240*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(3*f*x + 3*e) + 720*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(2*f*x + 2*e) + 720*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) - (-240*I*(f*x + e)*d^3 + 240*I*d^3*e - 240*I*c*d^2*f)*sin(3*f*x + 3*e) - (-720*I*(f*x + e)*d^3 + 720*I*d^3*e - 720*I*c*d^2*f)*sin(2*f*x + 2*e) - (-720*I*(f*x + e)*d^3 + 720*I*d^3*e - 720*I*c*d^2*f)*sin(f*x + e))*dilog(-e^(I*f*x + I*e)) + (-60*I*(f*x + e)^2*d^3 - 60*I*d^3*e^2 + 24*I*d^3 + (120*I*d^3*e - 120*I*c*d^2*f)*(f*x + e) + (-60*I*(f*x + e)^2*d^3 - 60*I*d^3*e^2 + 24*I*d^3 + (120*I*d^3*e - 120*I*c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) + (-180*I*(f*x + e)^2*d^3 - 180*I*d^3*e^2 + 72*I*d^3 + (360*I*d^3*e - 360*I*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (-180*I*(f*x + e)^2*d^3 - 180*I*d^3*e^2 + 72*I*d^3 + (360*I*d^3*e - 360*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 12*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) + 36*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + 36*(5*(f*x + e)^2*d^3 + 5*d^3*e^2 - 2*d^3 - 10*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (-240*I*d^3*cos(3*f*x + 3*e) - 720*I*d^3*cos(2*f*x + 2*e) - 720*I*d^3*cos(f*x + e) + 240*d^3*sin(3*f*x + 3*e) + 720*d^3*sin(2*f*x + 2*e) + 720*d^3*sin(f*x + e) - 240*I*d^3)*polylog(3, -e^(I*f*x + I*e)) - (3*(f*x + e)^4*d^3 - (12*d^3*e - 12*c*d^2*f - 40*I*d^3)*(f*x + e)^3 + (18*d^3*e^2 - 120*I*d^3*e + 120*I*c*d^2*f)*(f*x + e)^2 - (12*d^3*e^3 - 120*I*d^3*e^2 + 48*I*d^3)*(f*x + e))*sin(3*f*x + 3*e) - (9*(f*x + e)^4*d^3 + 48*I*d^3*e^3 - 24*d^3*e^2 - (36*d^3*e - 36*c*d^2*f - 72*I*d^3)*(f*x + e)^3 - 48*I*d^3*e + 48*I*c*d^2*f + (54*d^3*e^2 - 216*I*d^3*e + 216*I*c*d^2*f - 24*d^3)*(f*x + e)^2 - (36*d^3*e^3 - 216*I*d^3*e^2 - 48*d^3*e + 48*c*d^2*f + 96*I*d^3)*(f*x + e))*sin(2*f*x + 2*e) - (9*(f*x + e)^4*d^3 + 72*I*d^3*e^3 - 24*d^3*e^2 - (36*d^3*e - 36*c*d^2*f - 48*I*d^3)*(f*x + e)^3 - 96*I*d^3*e + 96*I*c*d^2*f + (54*d^3*e^2 - 144*I*d^3*e + 144*I*c*d^2*f - 24*d^3)*(f*x + e)^2 - (36*d^3*e^3 - 144*I*d^3*e^2 - 48*d^3*e + 48*c*d^2*f + 48*I*d^3)*(f*x + e))*sin(f*x + e))/(-12*I*a^2*f^3*cos(3*f*x + 3*e) - 36*I*a^2*f^3*cos(2*f*x + 2*e) - 36*I*a^2*f^3*cos(f*x + e) + 12*a^2*f^3*sin(3*f*x + 3*e) + 36*a^2*f^3*sin(2*f*x + 2*e) + 36*a^2*f^3*sin(f*x + e) - 12*I*a^2*f^3))/f","B",0
17,1,1033,0,2.430445," ","integrate((d*x+c)^2/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, d^{2} f^{3} x^{3} + 3 i \, c d f^{3} x^{2} + 3 i \, c^{2} f^{3} x + 10 \, c^{2} f^{2} - 4 \, d^{2} + {\left(20 \, d^{2} f x + 20 \, c d f + 20 \, {\left(d^{2} f x + c d f\right)} \cos\left(3 \, f x + 3 \, e\right) + 60 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + 60 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + {\left(20 i \, d^{2} f x + 20 i \, c d f\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(60 i \, d^{2} f x + 60 i \, c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(60 i \, d^{2} f x + 60 i \, c d f\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(i \, d^{2} f^{3} x^{3} + {\left(3 i \, c d f^{3} - 10 \, d^{2} f^{2}\right)} x^{2} + {\left(3 i \, c^{2} f^{3} - 20 \, c d f^{2}\right)} x\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(3 i \, d^{2} f^{3} x^{3} + 12 \, c^{2} f^{2} - 4 i \, c d f - 9 \, {\left(-i \, c d f^{3} + 2 \, d^{2} f^{2}\right)} x^{2} - 4 \, d^{2} + {\left(9 i \, c^{2} f^{3} - 36 \, c d f^{2} - 4 i \, d^{2} f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(3 i \, d^{2} f^{3} x^{3} + 18 \, c^{2} f^{2} - 4 i \, c d f - 3 \, {\left(-3 i \, c d f^{3} + 4 \, d^{2} f^{2}\right)} x^{2} - 8 \, d^{2} + {\left(9 i \, c^{2} f^{3} - 24 \, c d f^{2} - 4 i \, d^{2} f\right)} x\right)} \cos\left(f x + e\right) - {\left(20 \, d^{2} \cos\left(3 \, f x + 3 \, e\right) + 60 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 60 \, d^{2} \cos\left(f x + e\right) + 20 i \, d^{2} \sin\left(3 \, f x + 3 \, e\right) + 60 i \, d^{2} \sin\left(2 \, f x + 2 \, e\right) + 60 i \, d^{2} \sin\left(f x + e\right) + 20 \, d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-10 i \, d^{2} f x - 10 i \, c d f + {\left(-10 i \, d^{2} f x - 10 i \, c d f\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-30 i \, d^{2} f x - 30 i \, c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-30 i \, d^{2} f x - 30 i \, c d f\right)} \cos\left(f x + e\right) + 10 \, {\left(d^{2} f x + c d f\right)} \sin\left(3 \, f x + 3 \, e\right) + 30 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + 30 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - {\left(d^{2} f^{3} x^{3} + {\left(3 \, c d f^{3} + 10 i \, d^{2} f^{2}\right)} x^{2} + {\left(3 \, c^{2} f^{3} + 20 i \, c d f^{2}\right)} x\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(3 \, d^{2} f^{3} x^{3} - 12 i \, c^{2} f^{2} - 4 \, c d f + {\left(9 \, c d f^{3} + 18 i \, d^{2} f^{2}\right)} x^{2} + 4 i \, d^{2} + {\left(9 \, c^{2} f^{3} + 36 i \, c d f^{2} - 4 \, d^{2} f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(3 \, d^{2} f^{3} x^{3} - 18 i \, c^{2} f^{2} - 4 \, c d f + {\left(9 \, c d f^{3} + 12 i \, d^{2} f^{2}\right)} x^{2} + 8 i \, d^{2} + {\left(9 \, c^{2} f^{3} + 24 i \, c d f^{2} - 4 \, d^{2} f\right)} x\right)} \sin\left(f x + e\right)}{-3 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(f x + e\right) + 3 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 9 \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f^{3} \sin\left(f x + e\right) - 3 i \, a^{2} f^{3}}"," ",0,"-(I*d^2*f^3*x^3 + 3*I*c*d*f^3*x^2 + 3*I*c^2*f^3*x + 10*c^2*f^2 - 4*d^2 + (20*d^2*f*x + 20*c*d*f + 20*(d^2*f*x + c*d*f)*cos(3*f*x + 3*e) + 60*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e) + 60*(d^2*f*x + c*d*f)*cos(f*x + e) + (20*I*d^2*f*x + 20*I*c*d*f)*sin(3*f*x + 3*e) + (60*I*d^2*f*x + 60*I*c*d*f)*sin(2*f*x + 2*e) + (60*I*d^2*f*x + 60*I*c*d*f)*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (I*d^2*f^3*x^3 + (3*I*c*d*f^3 - 10*d^2*f^2)*x^2 + (3*I*c^2*f^3 - 20*c*d*f^2)*x)*cos(3*f*x + 3*e) + (3*I*d^2*f^3*x^3 + 12*c^2*f^2 - 4*I*c*d*f - 9*(-I*c*d*f^3 + 2*d^2*f^2)*x^2 - 4*d^2 + (9*I*c^2*f^3 - 36*c*d*f^2 - 4*I*d^2*f)*x)*cos(2*f*x + 2*e) + (3*I*d^2*f^3*x^3 + 18*c^2*f^2 - 4*I*c*d*f - 3*(-3*I*c*d*f^3 + 4*d^2*f^2)*x^2 - 8*d^2 + (9*I*c^2*f^3 - 24*c*d*f^2 - 4*I*d^2*f)*x)*cos(f*x + e) - (20*d^2*cos(3*f*x + 3*e) + 60*d^2*cos(2*f*x + 2*e) + 60*d^2*cos(f*x + e) + 20*I*d^2*sin(3*f*x + 3*e) + 60*I*d^2*sin(2*f*x + 2*e) + 60*I*d^2*sin(f*x + e) + 20*d^2)*dilog(-e^(I*f*x + I*e)) + (-10*I*d^2*f*x - 10*I*c*d*f + (-10*I*d^2*f*x - 10*I*c*d*f)*cos(3*f*x + 3*e) + (-30*I*d^2*f*x - 30*I*c*d*f)*cos(2*f*x + 2*e) + (-30*I*d^2*f*x - 30*I*c*d*f)*cos(f*x + e) + 10*(d^2*f*x + c*d*f)*sin(3*f*x + 3*e) + 30*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + 30*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - (d^2*f^3*x^3 + (3*c*d*f^3 + 10*I*d^2*f^2)*x^2 + (3*c^2*f^3 + 20*I*c*d*f^2)*x)*sin(3*f*x + 3*e) - (3*d^2*f^3*x^3 - 12*I*c^2*f^2 - 4*c*d*f + (9*c*d*f^3 + 18*I*d^2*f^2)*x^2 + 4*I*d^2 + (9*c^2*f^3 + 36*I*c*d*f^2 - 4*d^2*f)*x)*sin(2*f*x + 2*e) - (3*d^2*f^3*x^3 - 18*I*c^2*f^2 - 4*c*d*f + (9*c*d*f^3 + 12*I*d^2*f^2)*x^2 + 8*I*d^2 + (9*c^2*f^3 + 24*I*c*d*f^2 - 4*d^2*f)*x)*sin(f*x + e))/(-3*I*a^2*f^3*cos(3*f*x + 3*e) - 9*I*a^2*f^3*cos(2*f*x + 2*e) - 9*I*a^2*f^3*cos(f*x + e) + 3*a^2*f^3*sin(3*f*x + 3*e) + 9*a^2*f^3*sin(2*f*x + 2*e) + 9*a^2*f^3*sin(f*x + e) - 3*I*a^2*f^3)","B",0
18,1,1058,0,0.615044," ","integrate((d*x+c)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{d e {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2} f} - \frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2} f}\right)} - c {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{{\left(3 \, {\left(f x + e\right)}^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right)^{2} + 3 \, {\left(f x + e\right)}^{2} + 2 \, {\left(3 \, {\left(f x + e\right)}^{2} + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) + 12 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} + 3 \, {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \cos\left(f x + e\right) + 18 \, {\left(f x + e\right)} \sin\left(f x + e\right) - 2\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 10 \, {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(10 \, f x + 12 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right) + 10 \, e\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(6 \, f x + 6 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(9 \, {\left(f x + e\right)}^{2} - 4\right)} \sin\left(f x + e\right) + 6 \, e\right)} \sin\left(2 \, f x + 2 \, e\right) - 24 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \cos\left(f x + e\right) + a^{2} f + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f \sin\left(2 \, f x + 2 \, e\right) + a^{2} f \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)}}{6 \, f}"," ",0,"1/6*(d*e*((9*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f) - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/(a^2*f)) - c*((9*sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 - 12*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + (3*(f*x + e)^2*cos(3*f*x + 3*e)^2 + 3*(f*x + e)^2*sin(3*f*x + 3*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(2*f*x + 2*e)^2 + 3*(9*(f*x + e)^2 - 4)*sin(f*x + e)^2 + 3*(f*x + e)^2 + 2*(3*(f*x + e)^2 + (9*(f*x + e)^2 - 2)*cos(2*f*x + 2*e) + (9*(f*x + e)^2 - 2)*cos(f*x + e) + 12*(f*x + e)*sin(2*f*x + 2*e) + 18*(f*x + e)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)^2 + 3*(9*(f*x + e)^2 - 4)*cos(f*x + e) + 18*(f*x + e)*sin(f*x + e) - 2)*cos(2*f*x + 2*e) + 2*(9*(f*x + e)^2 - 2)*cos(f*x + e) - 10*(2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(10*f*x + 12*(f*x + e)*cos(2*f*x + 2*e) + 18*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 2)*sin(2*f*x + 2*e) - (9*(f*x + e)^2 - 2)*sin(f*x + e) + 10*e)*sin(3*f*x + 3*e) - 6*(6*f*x + 6*(f*x + e)*cos(f*x + e) - (9*(f*x + e)^2 - 4)*sin(f*x + e) + 6*e)*sin(2*f*x + 2*e) - 24*(f*x + e)*sin(f*x + e))*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 9*a^2*f*sin(2*f*x + 2*e)^2 + 18*a^2*f*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*cos(f*x + e) + a^2*f + 2*(3*a^2*f*cos(2*f*x + 2*e) + 3*a^2*f*cos(f*x + e) + a^2*f)*cos(3*f*x + 3*e) + 6*(3*a^2*f*cos(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 6*(a^2*f*sin(2*f*x + 2*e) + a^2*f*sin(f*x + e))*sin(3*f*x + 3*e)))/f","B",0
19,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, {\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)} \cos\left(3 \, f x + 3 \, e\right)^{2} \log\left(d x + c\right) + 3 \, {\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)} \log\left(d x + c\right) \sin\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(d^{3} f x + c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(d^{3} f x + c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(f x + e\right) + 3 \, {\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)} \log\left(d x + c\right) + 2 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(9 \, d^{3} f^{2} x^{2} + 18 \, c d^{2} f^{2} x + 9 \, c^{2} d f^{2} - 4 \, d^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(d^{3} f x + c d^{2} f + 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(f x + e\right) + 9 \, {\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)} \log\left(d x + c\right) + 3 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(d^{3} f x + c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \cos\left(f x + e\right) - 2 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \int \frac{{\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 6 \, d^{3}\right)} \sin\left(f x + e\right)}{a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)}\,{d x} + 3 \, {\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)} \log\left(d x + c\right) - 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} + 2 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 \, d^{3} f^{2} x^{2} + 18 \, c d^{2} f^{2} x + 9 \, c^{2} d f^{2} - 4 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(d^{3} f x + c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(d^{3} f x + c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 2 \, {\left(9 \, d^{3} f^{2} x^{2} + 18 \, c d^{2} f^{2} x + 9 \, c^{2} d f^{2} - 4 \, d^{3} + 3 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right) - 3 \, {\left(2 \, d^{3} f x + 2 \, c d^{2} f + 9 \, {\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)} \log\left(d x + c\right)\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) - 4 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - d^{3}\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{4} f^{3} x^{3} + 3 \, a^{2} c d^{3} f^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} f^{3} x + a^{2} c^{3} d f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)}}"," ",0,"1/3*(3*(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)*cos(3*f*x + 3*e)^2*log(d*x + c) + 3*(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)*log(d*x + c)*sin(3*f*x + 3*e)^2 + 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*cos(2*f*x + 2*e)^2 + 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*cos(f*x + e)^2 + 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*sin(2*f*x + 2*e)^2 + 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*sin(f*x + e)^2 + 2*((d^3*f*x + c*d^2*f + 9*(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)*log(d*x + c))*cos(2*f*x + 2*e) + (d^3*f*x + c*d^2*f + 9*(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)*log(d*x + c))*cos(f*x + e) + 3*(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)*log(d*x + c) + 2*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - d^3)*sin(2*f*x + 2*e) + (9*d^3*f^2*x^2 + 18*c*d^2*f^2*x + 9*c^2*d*f^2 - 4*d^3)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(d^3*f*x + c*d^2*f + 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*cos(f*x + e) + 9*(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)*log(d*x + c) + 3*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - 2*d^3)*sin(f*x + e))*cos(2*f*x + 2*e) + 2*(d^3*f*x + c*d^2*f + 9*(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)*log(d*x + c))*cos(f*x + e) - 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e) + 6*((a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e) + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))*integrate(2/3*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 6*d^3)*sin(f*x + e)/(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)), x) + 3*(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)*log(d*x + c) - 2*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 2*d^3 + 2*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - d^3)*cos(2*f*x + 2*e) + (9*d^3*f^2*x^2 + 18*c*d^2*f^2*x + 9*c^2*d*f^2 - 4*d^3)*cos(f*x + e) - (d^3*f*x + c*d^2*f + 9*(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)*log(d*x + c))*sin(2*f*x + 2*e) - (d^3*f*x + c*d^2*f + 9*(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)*log(d*x + c))*sin(f*x + e))*sin(3*f*x + 3*e) - 2*(9*d^3*f^2*x^2 + 18*c*d^2*f^2*x + 9*c^2*d*f^2 - 4*d^3 + 3*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - 2*d^3)*cos(f*x + e) - 3*(2*d^3*f*x + 2*c*d^2*f + 9*(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)*log(d*x + c))*sin(f*x + e))*sin(2*f*x + 2*e) - 4*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - d^3)*sin(f*x + e))/(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3 + 3*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*cos(f*x + e) + 6*((a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(2*f*x + 2*e) + (a^2*d^4*f^3*x^3 + 3*a^2*c*d^3*f^3*x^2 + 3*a^2*c^2*d^2*f^3*x + a^2*c^3*d*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))","F",0
20,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","-\frac{3 \, d^{3} f^{3} x^{3} + 9 \, c d^{2} f^{3} x^{2} + 9 \, c^{2} d f^{3} x + 3 \, c^{3} f^{3} + 3 \, {\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)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right)^{2} + 3 \, {\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(3 \, f x + 3 \, e\right)^{2} + 3 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 3 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, c d^{2} f^{3} x^{2} + 9 \, c^{2} d f^{3} x + 3 \, c^{3} f^{3} + {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right) - 6 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - 4 \, d^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x + 3 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right) - 9 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right) + 4 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \int \frac{{\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 12 \, d^{3}\right)} \sin\left(f x + e\right)}{a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \cos\left(f x + e\right)}\,{d x} + 2 \, {\left(5 \, d^{3} f^{2} x^{2} + 10 \, c d^{2} f^{2} x + 5 \, c^{2} d f^{2} - 6 \, d^{3} + 6 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - 4 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 2 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} - 4 \, d^{3} + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(9 \, d^{3} f^{3} x^{3} + 27 \, c d^{2} f^{3} x^{2} + 9 \, c^{3} f^{3} - 4 \, c d^{2} f + {\left(27 \, c^{2} d f^{3} - 4 \, d^{3} f\right)} x\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 12 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - d^{3}\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3} + 3 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{5} f^{3} x^{4} + 4 \, a^{2} c d^{4} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{3} f^{3} x^{2} + 4 \, a^{2} c^{3} d^{2} f^{3} x + a^{2} c^{4} d f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)}}"," ",0,"-1/3*(3*d^3*f^3*x^3 + 9*c*d^2*f^3*x^2 + 9*c^2*d*f^3*x + 3*c^3*f^3 + 3*(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)*cos(3*f*x + 3*e)^2 + 3*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*cos(2*f*x + 2*e)^2 + 3*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*cos(f*x + e)^2 + 3*(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(3*f*x + 3*e)^2 + 3*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*sin(2*f*x + 2*e)^2 + 3*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*sin(f*x + e)^2 + 2*(3*d^3*f^3*x^3 + 9*c*d^2*f^3*x^2 + 9*c^2*d*f^3*x + 3*c^3*f^3 + (9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x)*cos(2*f*x + 2*e) + (9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x)*cos(f*x + e) - 6*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - d^3)*sin(2*f*x + 2*e) - 3*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - 4*d^3)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x + 3*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*cos(f*x + e) - 9*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*sin(f*x + e))*cos(2*f*x + 2*e) + 2*(9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x)*cos(f*x + e) + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e)^2 + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(f*x + e)^2 + 2*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e) + 6*((a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e) + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))*integrate(4/3*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 12*d^3)*sin(f*x + e)/(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*cos(f*x + e)^2 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*sin(f*x + e)^2 + 2*(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*cos(f*x + e)), x) + 2*(5*d^3*f^2*x^2 + 10*c*d^2*f^2*x + 5*c^2*d*f^2 - 6*d^3 + 6*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - d^3)*cos(2*f*x + 2*e) + 3*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - 4*d^3)*cos(f*x + e) + (9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x)*sin(2*f*x + 2*e) + (9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 2*c*d^2*f + (27*c^2*d*f^3 - 2*d^3*f)*x)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 - 4*d^3 + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cos(f*x + e) + (9*d^3*f^3*x^3 + 27*c*d^2*f^3*x^2 + 9*c^3*f^3 - 4*c*d^2*f + (27*c^2*d*f^3 - 4*d^3*f)*x)*sin(f*x + e))*sin(2*f*x + 2*e) + 12*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - d^3)*sin(f*x + e))/(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e)^2 + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(f*x + e)^2 + 2*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3 + 3*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*cos(f*x + e) + 6*((a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(2*f*x + 2*e) + (a^2*d^5*f^3*x^4 + 4*a^2*c*d^4*f^3*x^3 + 6*a^2*c^2*d^3*f^3*x^2 + 4*a^2*c^3*d^2*f^3*x + a^2*c^4*d*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))","F",0
21,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} {\left(a \sec\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(a*sec(f*x + e) + a)^n, x)","F",0
22,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","2 \, a \int \frac{{\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + {\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + {\left(d x + c\right)}^{m} \cos\left(f x + e\right)}{\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1}\,{d x} + \frac{{\left(d x + c\right)}^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"2*a*integrate(((d*x + c)^m*cos(2*f*x + 2*e)*cos(f*x + e) + (d*x + c)^m*sin(2*f*x + 2*e)*sin(f*x + e) + (d*x + c)^m*cos(f*x + e))/(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1), x) + (d*x + c)^(m + 1)*a/(d*(m + 1))","F",0
23,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*sec(f*x + e) + a), x)","F",0
24,1,926,0,1.259825," ","integrate((d*x+c)^3*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c^{3} + \frac{{\left(f x + e\right)}^{4} a d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a c^{2} d e}{f} + 4 \, b c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - \frac{4 \, b d^{3} e^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{3}} + \frac{12 \, b c d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, b c^{2} d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{2 \, {\left(12 i \, b d^{3} {\rm Li}_{4}(i \, e^{\left(i \, f x + i \, e\right)}) - 12 i \, b d^{3} {\rm Li}_{4}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} b d^{3} + {\left(6 i \, b d^{3} e - 6 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, b d^{3} e^{2} + 12 i \, b c d^{2} e f - 6 i \, b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, {\left(f x + e\right)}^{3} b d^{3} + {\left(6 i \, b d^{3} e - 6 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, b d^{3} e^{2} + 12 i \, b c d^{2} e f - 6 i \, b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} b d^{3} - 6 i \, b d^{3} e^{2} + 12 i \, b c d^{2} e f - 6 i \, b c^{2} d f^{2} + {\left(12 i \, b d^{3} e - 12 i \, b c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(6 i \, {\left(f x + e\right)}^{2} b d^{3} + 6 i \, b d^{3} e^{2} - 12 i \, b c d^{2} e f + 6 i \, b c^{2} d f^{2} + {\left(-12 i \, b d^{3} e + 12 i \, b c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left({\left(f x + e\right)}^{3} b d^{3} - 3 \, {\left(b d^{3} e - b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b d^{3} e^{2} - 2 \, b c d^{2} e f + b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left({\left(f x + e\right)}^{3} b d^{3} - 3 \, {\left(b d^{3} e - b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b d^{3} e^{2} - 2 \, b c d^{2} e f + b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + 12 \, {\left({\left(f x + e\right)} b d^{3} - b d^{3} e + b c d^{2} f\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - 12 \, {\left({\left(f x + e\right)} b d^{3} - b d^{3} e + b c d^{2} f\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)})\right)}}{f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c^3 + (f*x + e)^4*a*d^3/f^3 - 4*(f*x + e)^3*a*d^3*e/f^3 + 6*(f*x + e)^2*a*d^3*e^2/f^3 - 4*(f*x + e)*a*d^3*e^3/f^3 + 4*(f*x + e)^3*a*c*d^2/f^2 - 12*(f*x + e)^2*a*c*d^2*e/f^2 + 12*(f*x + e)*a*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c^2*d/f - 12*(f*x + e)*a*c^2*d*e/f + 4*b*c^3*log(sec(f*x + e) + tan(f*x + e)) - 4*b*d^3*e^3*log(sec(f*x + e) + tan(f*x + e))/f^3 + 12*b*c*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*b*c^2*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 2*(12*I*b*d^3*polylog(4, I*e^(I*f*x + I*e)) - 12*I*b*d^3*polylog(4, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*b*d^3 + (6*I*b*d^3*e - 6*I*b*c*d^2*f)*(f*x + e)^2 + (-6*I*b*d^3*e^2 + 12*I*b*c*d^2*e*f - 6*I*b*c^2*d*f^2)*(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (-2*I*(f*x + e)^3*b*d^3 + (6*I*b*d^3*e - 6*I*b*c*d^2*f)*(f*x + e)^2 + (-6*I*b*d^3*e^2 + 12*I*b*c*d^2*e*f - 6*I*b*c^2*d*f^2)*(f*x + e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-6*I*(f*x + e)^2*b*d^3 - 6*I*b*d^3*e^2 + 12*I*b*c*d^2*e*f - 6*I*b*c^2*d*f^2 + (12*I*b*d^3*e - 12*I*b*c*d^2*f)*(f*x + e))*dilog(I*e^(I*f*x + I*e)) + (6*I*(f*x + e)^2*b*d^3 + 6*I*b*d^3*e^2 - 12*I*b*c*d^2*e*f + 6*I*b*c^2*d*f^2 + (-12*I*b*d^3*e + 12*I*b*c*d^2*f)*(f*x + e))*dilog(-I*e^(I*f*x + I*e)) + ((f*x + e)^3*b*d^3 - 3*(b*d^3*e - b*c*d^2*f)*(f*x + e)^2 + 3*(b*d^3*e^2 - 2*b*c*d^2*e*f + b*c^2*d*f^2)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - ((f*x + e)^3*b*d^3 - 3*(b*d^3*e - b*c*d^2*f)*(f*x + e)^2 + 3*(b*d^3*e^2 - 2*b*c*d^2*e*f + b*c^2*d*f^2)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + 12*((f*x + e)*b*d^3 - b*d^3*e + b*c*d^2*f)*polylog(3, I*e^(I*f*x + I*e)) - 12*((f*x + e)*b*d^3 - b*d^3*e + b*c*d^2*f)*polylog(3, -I*e^(I*f*x + I*e)))/f^3)/f","B",0
25,1,510,0,1.227779," ","integrate((d*x+c)^2*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\frac{6 \, {\left(f x + e\right)} a c^{2} + \frac{2 \, {\left(f x + e\right)}^{3} a d^{2}}{f^{2}} - \frac{6 \, {\left(f x + e\right)}^{2} a d^{2} e}{f^{2}} + \frac{6 \, {\left(f x + e\right)} a d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c d}{f} - \frac{12 \, {\left(f x + e\right)} a c d e}{f} + 6 \, b c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + \frac{6 \, b d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, b c d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(4 \, b d^{2} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - 4 \, b d^{2} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{2} b d^{2} + {\left(4 i \, b d^{2} e - 4 i \, b c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, {\left(f x + e\right)}^{2} b d^{2} + {\left(4 i \, b d^{2} e - 4 i \, b c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-4 i \, {\left(f x + e\right)} b d^{2} + 4 i \, b d^{2} e - 4 i \, b c d f\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(4 i \, {\left(f x + e\right)} b d^{2} - 4 i \, b d^{2} e + 4 i \, b c d f\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left({\left(f x + e\right)}^{2} b d^{2} - 2 \, {\left(b d^{2} e - b c d f\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left({\left(f x + e\right)}^{2} b d^{2} - 2 \, {\left(b d^{2} e - b c d f\right)} {\left(f x + e\right)}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)}}{f^{2}}}{6 \, f}"," ",0,"1/6*(6*(f*x + e)*a*c^2 + 2*(f*x + e)^3*a*d^2/f^2 - 6*(f*x + e)^2*a*d^2*e/f^2 + 6*(f*x + e)*a*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c*d/f - 12*(f*x + e)*a*c*d*e/f + 6*b*c^2*log(sec(f*x + e) + tan(f*x + e)) + 6*b*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*b*c*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 3*(4*b*d^2*polylog(3, I*e^(I*f*x + I*e)) - 4*b*d^2*polylog(3, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^2*b*d^2 + (4*I*b*d^2*e - 4*I*b*c*d*f)*(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (-2*I*(f*x + e)^2*b*d^2 + (4*I*b*d^2*e - 4*I*b*c*d*f)*(f*x + e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-4*I*(f*x + e)*b*d^2 + 4*I*b*d^2*e - 4*I*b*c*d*f)*dilog(I*e^(I*f*x + I*e)) + (4*I*(f*x + e)*b*d^2 - 4*I*b*d^2*e + 4*I*b*c*d*f)*dilog(-I*e^(I*f*x + I*e)) + ((f*x + e)^2*b*d^2 - 2*(b*d^2*e - b*c*d*f)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - ((f*x + e)^2*b*d^2 - 2*(b*d^2*e - b*c*d*f)*(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))/f^2)/f","B",0
26,-1,0,0,0.000000," ","integrate((d*x+c)*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,1,3267,0,2.263480," ","integrate((d*x+c)^3*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a^{2} c^{3} + \frac{{\left(f x + e\right)}^{4} a^{2} d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a^{2} d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{2} d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a^{2} d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a^{2} c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a^{2} c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{2} c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a^{2} c^{2} d e}{f} + 8 \, a b c^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) - \frac{8 \, a b d^{3} e^{3} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{3}} + \frac{24 \, a b c d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{24 \, a b c^{2} d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} - \frac{4 \, {\left(4 \, b^{2} d^{3} e^{3} - 12 \, b^{2} c d^{2} e^{2} f + 12 \, b^{2} c^{2} d e f^{2} - 4 \, b^{2} c^{3} f^{3} + {\left(4 \, {\left(f x + e\right)}^{3} a b d^{3} - 12 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)} + 4 \, {\left({\left(f x + e\right)}^{3} a b d^{3} - 3 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(12 i \, a b d^{3} e - 12 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a b d^{3} e^{2} + 24 i \, a b c d^{2} e f - 12 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(4 \, {\left(f x + e\right)}^{3} a b d^{3} - 12 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)} + 4 \, {\left({\left(f x + e\right)}^{3} a b d^{3} - 3 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(12 i \, a b d^{3} e - 12 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a b d^{3} e^{2} + 24 i \, a b c d^{2} e f - 12 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - {\left(6 \, {\left(f x + e\right)}^{2} b^{2} d^{3} + 6 \, b^{2} d^{3} e^{2} - 12 \, b^{2} c d^{2} e f + 6 \, b^{2} c^{2} d f^{2} - 12 \, {\left(b^{2} d^{3} e - b^{2} c d^{2} f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(f x + e\right)}^{2} b^{2} d^{3} + b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f + b^{2} c^{2} d f^{2} - 2 \, {\left(b^{2} d^{3} e - b^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, {\left(f x + e\right)}^{2} b^{2} d^{3} + 6 i \, b^{2} d^{3} e^{2} - 12 i \, b^{2} c d^{2} e f + 6 i \, b^{2} c^{2} d f^{2} + {\left(-12 i \, b^{2} d^{3} e + 12 i \, b^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) + 4 \, {\left({\left(f x + e\right)}^{3} b^{2} d^{3} - 3 \, {\left(b^{2} d^{3} e - b^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f + b^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, {\left(f x + e\right)} b^{2} d^{3} - 6 \, b^{2} d^{3} e + 6 \, b^{2} c d^{2} f + 6 \, {\left({\left(f x + e\right)} b^{2} d^{3} - b^{2} d^{3} e + b^{2} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-6 i \, {\left(f x + e\right)} b^{2} d^{3} + 6 i \, b^{2} d^{3} e - 6 i \, b^{2} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, f x + 2 i \, e\right)}\right) + {\left(12 \, {\left(f x + e\right)}^{2} a b d^{3} + 12 \, a b d^{3} e^{2} - 24 \, a b c d^{2} e f + 12 \, a b c^{2} d f^{2} - 24 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)} + 12 \, {\left({\left(f x + e\right)}^{2} a b d^{3} + a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2} - 2 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-12 i \, {\left(f x + e\right)}^{2} a b d^{3} - 12 i \, a b d^{3} e^{2} + 24 i \, a b c d^{2} e f - 12 i \, a b c^{2} d f^{2} + {\left(24 i \, a b d^{3} e - 24 i \, a b c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(12 \, {\left(f x + e\right)}^{2} a b d^{3} + 12 \, a b d^{3} e^{2} - 24 \, a b c d^{2} e f + 12 \, a b c^{2} d f^{2} - 24 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)} + 12 \, {\left({\left(f x + e\right)}^{2} a b d^{3} + a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2} - 2 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(12 i \, {\left(f x + e\right)}^{2} a b d^{3} + 12 i \, a b d^{3} e^{2} - 24 i \, a b c d^{2} e f + 12 i \, a b c^{2} d f^{2} + {\left(-24 i \, a b d^{3} e + 24 i \, a b c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(-3 i \, {\left(f x + e\right)}^{2} b^{2} d^{3} - 3 i \, b^{2} d^{3} e^{2} + 6 i \, b^{2} c d^{2} e f - 3 i \, b^{2} c^{2} d f^{2} + {\left(6 i \, b^{2} d^{3} e - 6 i \, b^{2} c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} b^{2} d^{3} - 3 i \, b^{2} d^{3} e^{2} + 6 i \, b^{2} c d^{2} e f - 3 i \, b^{2} c^{2} d f^{2} + {\left(6 i \, b^{2} d^{3} e - 6 i \, b^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left({\left(f x + e\right)}^{2} b^{2} d^{3} + b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f + b^{2} c^{2} d f^{2} - 2 \, {\left(b^{2} d^{3} e - b^{2} c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right) - {\left(-2 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(6 i \, a b d^{3} e - 6 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a b d^{3} e^{2} + 12 i \, a b c d^{2} e f - 6 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)} + {\left(-2 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(6 i \, a b d^{3} e - 6 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, a b d^{3} e^{2} + 12 i \, a b c d^{2} e f - 6 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left({\left(f x + e\right)}^{3} a b d^{3} - 3 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(2 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(-6 i \, a b d^{3} e + 6 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, a b d^{3} e^{2} - 12 i \, a b c d^{2} e f + 6 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)} + {\left(2 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(-6 i \, a b d^{3} e + 6 i \, a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, a b d^{3} e^{2} - 12 i \, a b c d^{2} e f + 6 i \, a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left({\left(f x + e\right)}^{3} a b d^{3} - 3 \, {\left(a b d^{3} e - a b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 24 \, {\left(a b d^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a b d^{3} \sin\left(2 \, f x + 2 \, e\right) + a b d^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, f x + i \, e\right)}) + 24 \, {\left(a b d^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a b d^{3} \sin\left(2 \, f x + 2 \, e\right) + a b d^{3}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, f x + i \, e\right)}) - {\left(-3 i \, b^{2} d^{3} \cos\left(2 \, f x + 2 \, e\right) + 3 \, b^{2} d^{3} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, b^{2} d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, f x + 2 i \, e\right)}) - {\left(-24 i \, {\left(f x + e\right)} a b d^{3} + 24 i \, a b d^{3} e - 24 i \, a b c d^{2} f + {\left(-24 i \, {\left(f x + e\right)} a b d^{3} + 24 i \, a b d^{3} e - 24 i \, a b c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 24 \, {\left({\left(f x + e\right)} a b d^{3} - a b d^{3} e + a b c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) - {\left(24 i \, {\left(f x + e\right)} a b d^{3} - 24 i \, a b d^{3} e + 24 i \, a b c d^{2} f + {\left(24 i \, {\left(f x + e\right)} a b d^{3} - 24 i \, a b d^{3} e + 24 i \, a b c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 24 \, {\left({\left(f x + e\right)} a b d^{3} - a b d^{3} e + a b c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) - {\left(-4 i \, {\left(f x + e\right)}^{3} b^{2} d^{3} + {\left(12 i \, b^{2} d^{3} e - 12 i \, b^{2} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b^{2} d^{3} e^{2} + 24 i \, b^{2} c d^{2} e f - 12 i \, b^{2} c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-2 i \, f^{3} \cos\left(2 \, f x + 2 \, e\right) + 2 \, f^{3} \sin\left(2 \, f x + 2 \, e\right) - 2 i \, f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a^2*c^3 + (f*x + e)^4*a^2*d^3/f^3 - 4*(f*x + e)^3*a^2*d^3*e/f^3 + 6*(f*x + e)^2*a^2*d^3*e^2/f^3 - 4*(f*x + e)*a^2*d^3*e^3/f^3 + 4*(f*x + e)^3*a^2*c*d^2/f^2 - 12*(f*x + e)^2*a^2*c*d^2*e/f^2 + 12*(f*x + e)*a^2*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a^2*c^2*d/f - 12*(f*x + e)*a^2*c^2*d*e/f + 8*a*b*c^3*log(sec(f*x + e) + tan(f*x + e)) - 8*a*b*d^3*e^3*log(sec(f*x + e) + tan(f*x + e))/f^3 + 24*a*b*c*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 24*a*b*c^2*d*e*log(sec(f*x + e) + tan(f*x + e))/f - 4*(4*b^2*d^3*e^3 - 12*b^2*c*d^2*e^2*f + 12*b^2*c^2*d*e*f^2 - 4*b^2*c^3*f^3 + (4*(f*x + e)^3*a*b*d^3 - 12*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 12*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e) + 4*((f*x + e)^3*a*b*d^3 - 3*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 3*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - (-4*I*(f*x + e)^3*a*b*d^3 + (12*I*a*b*d^3*e - 12*I*a*b*c*d^2*f)*(f*x + e)^2 + (-12*I*a*b*d^3*e^2 + 24*I*a*b*c*d^2*e*f - 12*I*a*b*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (4*(f*x + e)^3*a*b*d^3 - 12*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 12*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e) + 4*((f*x + e)^3*a*b*d^3 - 3*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 3*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - (-4*I*(f*x + e)^3*a*b*d^3 + (12*I*a*b*d^3*e - 12*I*a*b*c*d^2*f)*(f*x + e)^2 + (-12*I*a*b*d^3*e^2 + 24*I*a*b*c*d^2*e*f - 12*I*a*b*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - (6*(f*x + e)^2*b^2*d^3 + 6*b^2*d^3*e^2 - 12*b^2*c*d^2*e*f + 6*b^2*c^2*d*f^2 - 12*(b^2*d^3*e - b^2*c*d^2*f)*(f*x + e) + 6*((f*x + e)^2*b^2*d^3 + b^2*d^3*e^2 - 2*b^2*c*d^2*e*f + b^2*c^2*d*f^2 - 2*(b^2*d^3*e - b^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (6*I*(f*x + e)^2*b^2*d^3 + 6*I*b^2*d^3*e^2 - 12*I*b^2*c*d^2*e*f + 6*I*b^2*c^2*d*f^2 + (-12*I*b^2*d^3*e + 12*I*b^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) + 4*((f*x + e)^3*b^2*d^3 - 3*(b^2*d^3*e - b^2*c*d^2*f)*(f*x + e)^2 + 3*(b^2*d^3*e^2 - 2*b^2*c*d^2*e*f + b^2*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) + (6*(f*x + e)*b^2*d^3 - 6*b^2*d^3*e + 6*b^2*c*d^2*f + 6*((f*x + e)*b^2*d^3 - b^2*d^3*e + b^2*c*d^2*f)*cos(2*f*x + 2*e) - (-6*I*(f*x + e)*b^2*d^3 + 6*I*b^2*d^3*e - 6*I*b^2*c*d^2*f)*sin(2*f*x + 2*e))*dilog(-e^(2*I*f*x + 2*I*e)) + (12*(f*x + e)^2*a*b*d^3 + 12*a*b*d^3*e^2 - 24*a*b*c*d^2*e*f + 12*a*b*c^2*d*f^2 - 24*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e) + 12*((f*x + e)^2*a*b*d^3 + a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2 - 2*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) - (-12*I*(f*x + e)^2*a*b*d^3 - 12*I*a*b*d^3*e^2 + 24*I*a*b*c*d^2*e*f - 12*I*a*b*c^2*d*f^2 + (24*I*a*b*d^3*e - 24*I*a*b*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*dilog(I*e^(I*f*x + I*e)) - (12*(f*x + e)^2*a*b*d^3 + 12*a*b*d^3*e^2 - 24*a*b*c*d^2*e*f + 12*a*b*c^2*d*f^2 - 24*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e) + 12*((f*x + e)^2*a*b*d^3 + a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2 - 2*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (12*I*(f*x + e)^2*a*b*d^3 + 12*I*a*b*d^3*e^2 - 24*I*a*b*c*d^2*e*f + 12*I*a*b*c^2*d*f^2 + (-24*I*a*b*d^3*e + 24*I*a*b*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*dilog(-I*e^(I*f*x + I*e)) - (-3*I*(f*x + e)^2*b^2*d^3 - 3*I*b^2*d^3*e^2 + 6*I*b^2*c*d^2*e*f - 3*I*b^2*c^2*d*f^2 + (6*I*b^2*d^3*e - 6*I*b^2*c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*b^2*d^3 - 3*I*b^2*d^3*e^2 + 6*I*b^2*c*d^2*e*f - 3*I*b^2*c^2*d*f^2 + (6*I*b^2*d^3*e - 6*I*b^2*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + 3*((f*x + e)^2*b^2*d^3 + b^2*d^3*e^2 - 2*b^2*c*d^2*e*f + b^2*c^2*d*f^2 - 2*(b^2*d^3*e - b^2*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1) - (-2*I*(f*x + e)^3*a*b*d^3 + (6*I*a*b*d^3*e - 6*I*a*b*c*d^2*f)*(f*x + e)^2 + (-6*I*a*b*d^3*e^2 + 12*I*a*b*c*d^2*e*f - 6*I*a*b*c^2*d*f^2)*(f*x + e) + (-2*I*(f*x + e)^3*a*b*d^3 + (6*I*a*b*d^3*e - 6*I*a*b*c*d^2*f)*(f*x + e)^2 + (-6*I*a*b*d^3*e^2 + 12*I*a*b*c*d^2*e*f - 6*I*a*b*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) + 2*((f*x + e)^3*a*b*d^3 - 3*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 3*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (2*I*(f*x + e)^3*a*b*d^3 + (-6*I*a*b*d^3*e + 6*I*a*b*c*d^2*f)*(f*x + e)^2 + (6*I*a*b*d^3*e^2 - 12*I*a*b*c*d^2*e*f + 6*I*a*b*c^2*d*f^2)*(f*x + e) + (2*I*(f*x + e)^3*a*b*d^3 + (-6*I*a*b*d^3*e + 6*I*a*b*c*d^2*f)*(f*x + e)^2 + (6*I*a*b*d^3*e^2 - 12*I*a*b*c*d^2*e*f + 6*I*a*b*c^2*d*f^2)*(f*x + e))*cos(2*f*x + 2*e) - 2*((f*x + e)^3*a*b*d^3 - 3*(a*b*d^3*e - a*b*c*d^2*f)*(f*x + e)^2 + 3*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 24*(a*b*d^3*cos(2*f*x + 2*e) + I*a*b*d^3*sin(2*f*x + 2*e) + a*b*d^3)*polylog(4, I*e^(I*f*x + I*e)) + 24*(a*b*d^3*cos(2*f*x + 2*e) + I*a*b*d^3*sin(2*f*x + 2*e) + a*b*d^3)*polylog(4, -I*e^(I*f*x + I*e)) - (-3*I*b^2*d^3*cos(2*f*x + 2*e) + 3*b^2*d^3*sin(2*f*x + 2*e) - 3*I*b^2*d^3)*polylog(3, -e^(2*I*f*x + 2*I*e)) - (-24*I*(f*x + e)*a*b*d^3 + 24*I*a*b*d^3*e - 24*I*a*b*c*d^2*f + (-24*I*(f*x + e)*a*b*d^3 + 24*I*a*b*d^3*e - 24*I*a*b*c*d^2*f)*cos(2*f*x + 2*e) + 24*((f*x + e)*a*b*d^3 - a*b*d^3*e + a*b*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, I*e^(I*f*x + I*e)) - (24*I*(f*x + e)*a*b*d^3 - 24*I*a*b*d^3*e + 24*I*a*b*c*d^2*f + (24*I*(f*x + e)*a*b*d^3 - 24*I*a*b*d^3*e + 24*I*a*b*c*d^2*f)*cos(2*f*x + 2*e) - 24*((f*x + e)*a*b*d^3 - a*b*d^3*e + a*b*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, -I*e^(I*f*x + I*e)) - (-4*I*(f*x + e)^3*b^2*d^3 + (12*I*b^2*d^3*e - 12*I*b^2*c*d^2*f)*(f*x + e)^2 + (-12*I*b^2*d^3*e^2 + 24*I*b^2*c*d^2*e*f - 12*I*b^2*c^2*d*f^2)*(f*x + e))*sin(2*f*x + 2*e))/(-2*I*f^3*cos(2*f*x + 2*e) + 2*f^3*sin(2*f*x + 2*e) - 2*I*f^3))/f","B",0
30,1,1644,0,1.055588," ","integrate((d*x+c)^2*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a^{2} c^{2} + \frac{{\left(f x + e\right)}^{3} a^{2} d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a^{2} d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a^{2} c d}{f} - \frac{6 \, {\left(f x + e\right)} a^{2} c d e}{f} + 6 \, a b c^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right) + \frac{6 \, a b d^{2} e^{2} \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, a b c d e \log\left(\sec\left(f x + e\right) + \tan\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(2 \, b^{2} d^{2} e^{2} - 4 \, b^{2} c d e f + 2 \, b^{2} c^{2} f^{2} - {\left(2 \, {\left(f x + e\right)}^{2} a b d^{2} - 4 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)} + 2 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - 2 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(4 i \, a b d^{2} e - 4 i \, a b c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - {\left(2 \, {\left(f x + e\right)}^{2} a b d^{2} - 4 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)} + 2 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - 2 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(4 i \, a b d^{2} e - 4 i \, a b c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(2 \, {\left(f x + e\right)} b^{2} d^{2} - 2 \, b^{2} d^{2} e + 2 \, b^{2} c d f + 2 \, {\left({\left(f x + e\right)} b^{2} d^{2} - b^{2} d^{2} e + b^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 i \, {\left(f x + e\right)} b^{2} d^{2} - 2 i \, b^{2} d^{2} e + 2 i \, b^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{2} b^{2} d^{2} - 2 \, {\left(b^{2} d^{2} e - b^{2} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(b^{2} d^{2} \cos\left(2 \, f x + 2 \, e\right) + i \, b^{2} d^{2} \sin\left(2 \, f x + 2 \, e\right) + b^{2} d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, f x + 2 i \, e\right)}\right) - {\left(4 \, {\left(f x + e\right)} a b d^{2} - 4 \, a b d^{2} e + 4 \, a b c d f + 4 \, {\left({\left(f x + e\right)} a b d^{2} - a b d^{2} e + a b c d f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, {\left(f x + e\right)} a b d^{2} + 4 i \, a b d^{2} e - 4 i \, a b c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(4 \, {\left(f x + e\right)} a b d^{2} - 4 \, a b d^{2} e + 4 \, a b c d f + 4 \, {\left({\left(f x + e\right)} a b d^{2} - a b d^{2} e + a b c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(4 i \, {\left(f x + e\right)} a b d^{2} - 4 i \, a b d^{2} e + 4 i \, a b c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(-i \, {\left(f x + e\right)} b^{2} d^{2} + i \, b^{2} d^{2} e - i \, b^{2} c d f + {\left(-i \, {\left(f x + e\right)} b^{2} d^{2} + i \, b^{2} d^{2} e - i \, b^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(f x + e\right)} b^{2} d^{2} - b^{2} d^{2} e + b^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right) + {\left(-i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(2 i \, a b d^{2} e - 2 i \, a b c d f\right)} {\left(f x + e\right)} + {\left(-i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(2 i \, a b d^{2} e - 2 i \, a b c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(f x + e\right)}^{2} a b d^{2} - 2 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(-2 i \, a b d^{2} e + 2 i \, a b c d f\right)} {\left(f x + e\right)} + {\left(i \, {\left(f x + e\right)}^{2} a b d^{2} + {\left(-2 i \, a b d^{2} e + 2 i \, a b c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(f x + e\right)}^{2} a b d^{2} - 2 \, {\left(a b d^{2} e - a b c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-4 i \, a b d^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, a b d^{2} \sin\left(2 \, f x + 2 \, e\right) - 4 i \, a b d^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) + {\left(4 i \, a b d^{2} \cos\left(2 \, f x + 2 \, e\right) - 4 \, a b d^{2} \sin\left(2 \, f x + 2 \, e\right) + 4 i \, a b d^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{2} b^{2} d^{2} + {\left(4 i \, b^{2} d^{2} e - 4 i \, b^{2} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-i \, f^{2} \cos\left(2 \, f x + 2 \, e\right) + f^{2} \sin\left(2 \, f x + 2 \, e\right) - i \, f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a^2*c^2 + (f*x + e)^3*a^2*d^2/f^2 - 3*(f*x + e)^2*a^2*d^2*e/f^2 + 3*(f*x + e)*a^2*d^2*e^2/f^2 + 3*(f*x + e)^2*a^2*c*d/f - 6*(f*x + e)*a^2*c*d*e/f + 6*a*b*c^2*log(sec(f*x + e) + tan(f*x + e)) + 6*a*b*d^2*e^2*log(sec(f*x + e) + tan(f*x + e))/f^2 - 12*a*b*c*d*e*log(sec(f*x + e) + tan(f*x + e))/f + 3*(2*b^2*d^2*e^2 - 4*b^2*c*d*e*f + 2*b^2*c^2*f^2 - (2*(f*x + e)^2*a*b*d^2 - 4*(a*b*d^2*e - a*b*c*d*f)*(f*x + e) + 2*((f*x + e)^2*a*b*d^2 - 2*(a*b*d^2*e - a*b*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (-2*I*(f*x + e)^2*a*b*d^2 + (4*I*a*b*d^2*e - 4*I*a*b*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) - (2*(f*x + e)^2*a*b*d^2 - 4*(a*b*d^2*e - a*b*c*d*f)*(f*x + e) + 2*((f*x + e)^2*a*b*d^2 - 2*(a*b*d^2*e - a*b*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (-2*I*(f*x + e)^2*a*b*d^2 + (4*I*a*b*d^2*e - 4*I*a*b*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (2*(f*x + e)*b^2*d^2 - 2*b^2*d^2*e + 2*b^2*c*d*f + 2*((f*x + e)*b^2*d^2 - b^2*d^2*e + b^2*c*d*f)*cos(2*f*x + 2*e) + (2*I*(f*x + e)*b^2*d^2 - 2*I*b^2*d^2*e + 2*I*b^2*c*d*f)*sin(2*f*x + 2*e))*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*((f*x + e)^2*b^2*d^2 - 2*(b^2*d^2*e - b^2*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - (b^2*d^2*cos(2*f*x + 2*e) + I*b^2*d^2*sin(2*f*x + 2*e) + b^2*d^2)*dilog(-e^(2*I*f*x + 2*I*e)) - (4*(f*x + e)*a*b*d^2 - 4*a*b*d^2*e + 4*a*b*c*d*f + 4*((f*x + e)*a*b*d^2 - a*b*d^2*e + a*b*c*d*f)*cos(2*f*x + 2*e) - (-4*I*(f*x + e)*a*b*d^2 + 4*I*a*b*d^2*e - 4*I*a*b*c*d*f)*sin(2*f*x + 2*e))*dilog(I*e^(I*f*x + I*e)) + (4*(f*x + e)*a*b*d^2 - 4*a*b*d^2*e + 4*a*b*c*d*f + 4*((f*x + e)*a*b*d^2 - a*b*d^2*e + a*b*c*d*f)*cos(2*f*x + 2*e) + (4*I*(f*x + e)*a*b*d^2 - 4*I*a*b*d^2*e + 4*I*a*b*c*d*f)*sin(2*f*x + 2*e))*dilog(-I*e^(I*f*x + I*e)) + (-I*(f*x + e)*b^2*d^2 + I*b^2*d^2*e - I*b^2*c*d*f + (-I*(f*x + e)*b^2*d^2 + I*b^2*d^2*e - I*b^2*c*d*f)*cos(2*f*x + 2*e) + ((f*x + e)*b^2*d^2 - b^2*d^2*e + b^2*c*d*f)*sin(2*f*x + 2*e))*log(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1) + (-I*(f*x + e)^2*a*b*d^2 + (2*I*a*b*d^2*e - 2*I*a*b*c*d*f)*(f*x + e) + (-I*(f*x + e)^2*a*b*d^2 + (2*I*a*b*d^2*e - 2*I*a*b*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) + ((f*x + e)^2*a*b*d^2 - 2*(a*b*d^2*e - a*b*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (I*(f*x + e)^2*a*b*d^2 + (-2*I*a*b*d^2*e + 2*I*a*b*c*d*f)*(f*x + e) + (I*(f*x + e)^2*a*b*d^2 + (-2*I*a*b*d^2*e + 2*I*a*b*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - ((f*x + e)^2*a*b*d^2 - 2*(a*b*d^2*e - a*b*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + (-4*I*a*b*d^2*cos(2*f*x + 2*e) + 4*a*b*d^2*sin(2*f*x + 2*e) - 4*I*a*b*d^2)*polylog(3, I*e^(I*f*x + I*e)) + (4*I*a*b*d^2*cos(2*f*x + 2*e) - 4*a*b*d^2*sin(2*f*x + 2*e) + 4*I*a*b*d^2)*polylog(3, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^2*b^2*d^2 + (4*I*b^2*d^2*e - 4*I*b^2*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))/(-I*f^2*cos(2*f*x + 2*e) + f^2*sin(2*f*x + 2*e) - I*f^2))/f","B",0
31,-1,0,0,0.000000," ","integrate((d*x+c)*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{{\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} \log\left(d x + c\right) + 2 \, b^{2} d \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d f x + a^{2} c f\right)} \log\left(d x + c\right) \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) \log\left(d x + c\right) + 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{2 \, {\left(a b d f x + a b c f\right)} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + 2 \, {\left(a b d f x + a b c f\right)} \cos\left(f x + e\right) + {\left(b^{2} d + 2 \, {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f + {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x^{2} + 2 \, c d f x + c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)}\,{d x} + {\left(a^{2} d f x + a^{2} c f\right)} \log\left(d x + c\right)}{d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"((a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)^2*log(d*x + c) + 2*b^2*d*sin(2*f*x + 2*e) + (a^2*d*f*x + a^2*c*f)*log(d*x + c)*sin(2*f*x + 2*e)^2 + 2*(a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)*log(d*x + c) + (d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e))*integrate(2*(2*(a*b*d*f*x + a*b*c*f)*cos(2*f*x + 2*e)*cos(f*x + e) + 2*(a*b*d*f*x + a*b*c*f)*cos(f*x + e) + (b^2*d + 2*(a*b*d*f*x + a*b*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(d^2*f*x^2 + 2*c*d*f*x + c^2*f + (d^2*f*x^2 + 2*c*d*f*x + c^2*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x^2 + 2*c*d*f*x + c^2*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x^2 + 2*c*d*f*x + c^2*f)*cos(2*f*x + 2*e)), x) + (a^2*d*f*x + a^2*c*f)*log(d*x + c))/(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + (d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e))","F",0
33,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{a^{2} d f x + a^{2} c f - 2 \, b^{2} d \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left(a b d f x + a b c f\right)} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + {\left(a b d f x + a b c f\right)} \cos\left(f x + e\right) + {\left(b^{2} d + {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f + {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{3} + 3 \, c d^{2} f x^{2} + 3 \, c^{2} d f x + c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)}\,{d x}}{d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f x^{2} + 2 \, c d^{2} f x + c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"-(a^2*d*f*x + a^2*c*f - 2*b^2*d*sin(2*f*x + 2*e) + (a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e)^2 + (a^2*d*f*x + a^2*c*f)*sin(2*f*x + 2*e)^2 + 2*(a^2*d*f*x + a^2*c*f)*cos(2*f*x + 2*e) - (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e))*integrate(4*((a*b*d*f*x + a*b*c*f)*cos(2*f*x + 2*e)*cos(f*x + e) + (a*b*d*f*x + a*b*c*f)*cos(f*x + e) + (b^2*d + (a*b*d*f*x + a*b*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*cos(2*f*x + 2*e)), x))/(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e)^2 + (d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*sin(2*f*x + 2*e)^2 + 2*(d^3*f*x^2 + 2*c*d^2*f*x + c^2*d*f)*cos(2*f*x + 2*e))","F",0
34,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
35,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
36,-2,0,0,0.000000," ","integrate((d*x+c)/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
37,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
40,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
41,-2,0,0,0.000000," ","integrate((d*x+c)/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
42,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, a b^{3} d \sin\left(f x + e\right) + {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} \log\left(d x + c\right) + 4 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(f x + e\right)^{2} \log\left(d x + c\right) + {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \log\left(d x + c\right) \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \log\left(d x + c\right) \sin\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) \log\left(d x + c\right) - 2 \, {\left(a b^{3} d \sin\left(f x + e\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) \log\left(d x + c\right) - {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \int \frac{a b^{3} d \sin\left(f x + e\right) - 2 \, {\left({\left(2 \, a^{2} b^{2} - b^{4}\right)} d f x + {\left(2 \, a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(2 \, a^{2} b^{2} - b^{4}\right)} d f x + {\left(2 \, a^{2} b^{2} - b^{4}\right)} c f\right)} \sin\left(f x + e\right)^{2} - {\left(a b^{3} d \sin\left(f x + e\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) + {\left(a b^{3} d \cos\left(f x + e\right) + a^{2} b^{2} d - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} f\right)} \cos\left(f x + e\right)}\,{d x} + {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \log\left(d x + c\right) + 2 \, {\left(a b^{3} d \cos\left(f x + e\right) + a^{2} b^{2} d + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \log\left(d x + c\right) \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c d f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c d f\right)} \cos\left(f x + e\right)}"," ",0,"(2*a*b^3*d*sin(f*x + e) + ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*cos(2*f*x + 2*e)^2*log(d*x + c) + 4*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*cos(f*x + e)^2*log(d*x + c) + ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*log(d*x + c)*sin(2*f*x + 2*e)^2 + 4*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*log(d*x + c)*sin(f*x + e)^2 + 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e)*log(d*x + c) - 2*(a*b^3*d*sin(f*x + e) - 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e)*log(d*x + c) - ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*log(d*x + c))*cos(2*f*x + 2*e) - ((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f + ((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x + (a^4*b^2 - a^2*b^4)*c*d*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x + (a^4*b^2 - a^2*b^4)*c*d*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f + 2*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*cos(f*x + e))*integrate(-2*(a*b^3*d*sin(f*x + e) - 2*((2*a^2*b^2 - b^4)*d*f*x + (2*a^2*b^2 - b^4)*c*f)*cos(f*x + e)^2 - 2*((2*a^2*b^2 - b^4)*d*f*x + (2*a^2*b^2 - b^4)*c*f)*sin(f*x + e)^2 - (a*b^3*d*sin(f*x + e) + ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*cos(f*x + e))*cos(2*f*x + 2*e) - ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*cos(f*x + e) + (a*b^3*d*cos(f*x + e) + a^2*b^2*d - ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/((a^6 - a^4*b^2)*d^2*f*x^2 + 2*(a^6 - a^4*b^2)*c*d*f*x + (a^6 - a^4*b^2)*c^2*f + ((a^6 - a^4*b^2)*d^2*f*x^2 + 2*(a^6 - a^4*b^2)*c*d*f*x + (a^6 - a^4*b^2)*c^2*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d*f*x + (a^4*b^2 - a^2*b^4)*c^2*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^2*f*x^2 + 2*(a^6 - a^4*b^2)*c*d*f*x + (a^6 - a^4*b^2)*c^2*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^2*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d*f*x + (a^5*b - a^3*b^3)*c^2*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d*f*x + (a^4*b^2 - a^2*b^4)*c^2*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^2*f*x^2 + 2*(a^6 - a^4*b^2)*c*d*f*x + (a^6 - a^4*b^2)*c^2*f + 2*((a^5*b - a^3*b^3)*d^2*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d*f*x + (a^5*b - a^3*b^3)*c^2*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^2*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d*f*x + (a^5*b - a^3*b^3)*c^2*f)*cos(f*x + e)), x) + ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*log(d*x + c) + 2*(a*b^3*d*cos(f*x + e) + a^2*b^2*d + 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*log(d*x + c)*sin(f*x + e))*sin(2*f*x + 2*e))/((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f + ((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x + (a^4*b^2 - a^2*b^4)*c*d*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^2*f*x + (a^4*b^2 - a^2*b^4)*c*d*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^2*f*x + (a^6 - a^4*b^2)*c*d*f + 2*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^2*f*x + (a^5*b - a^3*b^3)*c*d*f)*cos(f*x + e))","F",0
43,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, a b^{3} d \sin\left(f x + e\right) - {\left(a^{4} - a^{2} b^{2}\right)} d f x - {\left(a^{4} - a^{2} b^{2}\right)} c f - {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(f x + e\right)^{2} - {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(a b^{3} d \sin\left(f x + e\right) + {\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \cos\left(f x + e\right)\right)} \int \frac{2 \, a b^{3} d \sin\left(f x + e\right) - 2 \, {\left({\left(2 \, a^{2} b^{2} - b^{4}\right)} d f x + {\left(2 \, a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(2 \, a^{2} b^{2} - b^{4}\right)} d f x + {\left(2 \, a^{2} b^{2} - b^{4}\right)} c f\right)} \sin\left(f x + e\right)^{2} - {\left(2 \, a b^{3} d \sin\left(f x + e\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) + {\left(2 \, a b^{3} d \cos\left(f x + e\right) + 2 \, a^{2} b^{2} d - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f x + {\left(2 \, a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{3} f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{3} f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{3} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{3} f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{3} f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{3} f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{3} f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{3} f\right)} \cos\left(f x + e\right)}\,{d x} + 2 \, {\left(a b^{3} d \cos\left(f x + e\right) + a^{2} b^{2} d - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f\right)} \cos\left(f x + e\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(a^{4} b^{2} - a^{2} b^{4}\right)} d^{3} f x^{2} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c d^{2} f x + {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2} d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d^{3} f x^{2} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} c d^{2} f x + {\left(a^{6} - a^{4} b^{2}\right)} c^{2} d f + 2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d^{3} f x^{2} + 2 \, {\left(a^{5} b - a^{3} b^{3}\right)} c d^{2} f x + {\left(a^{5} b - a^{3} b^{3}\right)} c^{2} d f\right)} \cos\left(f x + e\right)}"," ",0,"(2*a*b^3*d*sin(f*x + e) - (a^4 - a^2*b^2)*d*f*x - (a^4 - a^2*b^2)*c*f - ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*cos(2*f*x + 2*e)^2 - 4*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*cos(f*x + e)^2 - ((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*sin(2*f*x + 2*e)^2 - 4*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*sin(f*x + e)^2 - 2*(a*b^3*d*sin(f*x + e) + (a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f + 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e))*cos(2*f*x + 2*e) - 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e) - ((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f + ((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d^2*f*x + (a^4*b^2 - a^2*b^4)*c^2*d*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d^2*f*x + (a^4*b^2 - a^2*b^4)*c^2*d*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f + 2*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*cos(f*x + e))*integrate(-2*(2*a*b^3*d*sin(f*x + e) - 2*((2*a^2*b^2 - b^4)*d*f*x + (2*a^2*b^2 - b^4)*c*f)*cos(f*x + e)^2 - 2*((2*a^2*b^2 - b^4)*d*f*x + (2*a^2*b^2 - b^4)*c*f)*sin(f*x + e)^2 - (2*a*b^3*d*sin(f*x + e) + ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*cos(f*x + e))*cos(2*f*x + 2*e) - ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*cos(f*x + e) + (2*a*b^3*d*cos(f*x + e) + 2*a^2*b^2*d - ((2*a^3*b - a*b^3)*d*f*x + (2*a^3*b - a*b^3)*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/((a^6 - a^4*b^2)*d^3*f*x^3 + 3*(a^6 - a^4*b^2)*c*d^2*f*x^2 + 3*(a^6 - a^4*b^2)*c^2*d*f*x + (a^6 - a^4*b^2)*c^3*f + ((a^6 - a^4*b^2)*d^3*f*x^3 + 3*(a^6 - a^4*b^2)*c*d^2*f*x^2 + 3*(a^6 - a^4*b^2)*c^2*d*f*x + (a^6 - a^4*b^2)*c^3*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^3 + 3*(a^4*b^2 - a^2*b^4)*c*d^2*f*x^2 + 3*(a^4*b^2 - a^2*b^4)*c^2*d*f*x + (a^4*b^2 - a^2*b^4)*c^3*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^3*f*x^3 + 3*(a^6 - a^4*b^2)*c*d^2*f*x^2 + 3*(a^6 - a^4*b^2)*c^2*d*f*x + (a^6 - a^4*b^2)*c^3*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^3*f*x^3 + 3*(a^5*b - a^3*b^3)*c*d^2*f*x^2 + 3*(a^5*b - a^3*b^3)*c^2*d*f*x + (a^5*b - a^3*b^3)*c^3*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^3 + 3*(a^4*b^2 - a^2*b^4)*c*d^2*f*x^2 + 3*(a^4*b^2 - a^2*b^4)*c^2*d*f*x + (a^4*b^2 - a^2*b^4)*c^3*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^3*f*x^3 + 3*(a^6 - a^4*b^2)*c*d^2*f*x^2 + 3*(a^6 - a^4*b^2)*c^2*d*f*x + (a^6 - a^4*b^2)*c^3*f + 2*((a^5*b - a^3*b^3)*d^3*f*x^3 + 3*(a^5*b - a^3*b^3)*c*d^2*f*x^2 + 3*(a^5*b - a^3*b^3)*c^2*d*f*x + (a^5*b - a^3*b^3)*c^3*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^3*f*x^3 + 3*(a^5*b - a^3*b^3)*c*d^2*f*x^2 + 3*(a^5*b - a^3*b^3)*c^2*d*f*x + (a^5*b - a^3*b^3)*c^3*f)*cos(f*x + e)), x) + 2*(a*b^3*d*cos(f*x + e) + a^2*b^2*d - 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*sin(f*x + e))*sin(2*f*x + 2*e))/((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f + ((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f)*cos(2*f*x + 2*e)^2 + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d^2*f*x + (a^4*b^2 - a^2*b^4)*c^2*d*f)*cos(f*x + e)^2 + ((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f)*sin(2*f*x + 2*e)^2 + 4*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*sin(2*f*x + 2*e)*sin(f*x + e) + 4*((a^4*b^2 - a^2*b^4)*d^3*f*x^2 + 2*(a^4*b^2 - a^2*b^4)*c*d^2*f*x + (a^4*b^2 - a^2*b^4)*c^2*d*f)*sin(f*x + e)^2 + 2*((a^6 - a^4*b^2)*d^3*f*x^2 + 2*(a^6 - a^4*b^2)*c*d^2*f*x + (a^6 - a^4*b^2)*c^2*d*f + 2*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*cos(f*x + e))*cos(2*f*x + 2*e) + 4*((a^5*b - a^3*b^3)*d^3*f*x^2 + 2*(a^5*b - a^3*b^3)*c*d^2*f*x + (a^5*b - a^3*b^3)*c^2*d*f)*cos(f*x + e))","F",0
44,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sec(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} {\left(b \sec\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(b*sec(f*x + e) + a)^n, x)","F",0
45,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","2 \, b \int \frac{{\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + {\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + {\left(d x + c\right)}^{m} \cos\left(f x + e\right)}{\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1}\,{d x} + \frac{{\left(d x + c\right)}^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"2*b*integrate(((d*x + c)^m*cos(2*f*x + 2*e)*cos(f*x + e) + (d*x + c)^m*sin(2*f*x + 2*e)*sin(f*x + e) + (d*x + c)^m*cos(f*x + e))/(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1), x) + (d*x + c)^(m + 1)*a/(d*(m + 1))","F",0
46,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(b*sec(f*x + e) + a), x)","F",0
