1,1,391,0,0.483816," ","integrate(x^3*cot(b*x+a),x, algorithm=""maxima"")","-\frac{i \, {\left(b x + a\right)}^{4} - 4 i \, {\left(b x + a\right)}^{3} a + 6 i \, {\left(b x + a\right)}^{2} a^{2} + 4 \, a^{3} \log\left(\sin\left(b x + a\right)\right) - 24 \, b x {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 24 \, b x {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(4 i \, {\left(b x + a\right)}^{3} - 12 i \, {\left(b x + a\right)}^{2} a + 12 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 12 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - 2 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 24 i \, {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - 24 i \, {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)})}{4 \, b^{4}}"," ",0,"-1/4*(I*(b*x + a)^4 - 4*I*(b*x + a)^3*a + 6*I*(b*x + a)^2*a^2 + 4*a^3*log(sin(b*x + a)) - 24*b*x*polylog(3, -e^(I*b*x + I*a)) - 24*b*x*polylog(3, e^(I*b*x + I*a)) - (4*I*(b*x + a)^3 - 12*I*(b*x + a)^2*a + 12*I*(b*x + a)*a^2)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 12*I*(b*x + a)*a^2)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2)*dilog(-e^(I*b*x + I*a)) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2)*dilog(e^(I*b*x + I*a)) - 2*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - 2*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 24*I*polylog(4, -e^(I*b*x + I*a)) - 24*I*polylog(4, e^(I*b*x + I*a)))/b^4","B",0
2,1,257,0,0.485590," ","integrate(x^2*cot(b*x+a),x, algorithm=""maxima"")","-\frac{2 i \, {\left(b x + a\right)}^{3} - 6 i \, {\left(b x + a\right)}^{2} a + 12 i \, b x {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + 12 i \, b x {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - 6 \, a^{2} \log\left(\sin\left(b x + a\right)\right) - {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 12 \, {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 12 \, {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)})}{6 \, b^{3}}"," ",0,"-1/6*(2*I*(b*x + a)^3 - 6*I*(b*x + a)^2*a + 12*I*b*x*dilog(-e^(I*b*x + I*a)) + 12*I*b*x*dilog(e^(I*b*x + I*a)) - 6*a^2*log(sin(b*x + a)) - (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 12*polylog(3, -e^(I*b*x + I*a)) - 12*polylog(3, e^(I*b*x + I*a)))/b^3","B",0
3,1,140,0,0.455879," ","integrate(x*cot(b*x+a),x, algorithm=""maxima"")","\frac{-i \, b^{2} x^{2} + 2 i \, b x \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - 2 i \, b x \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + b x \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + b x \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 2 i \, {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 2 i \, {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b^{2}}"," ",0,"1/2*(-I*b^2*x^2 + 2*I*b*x*arctan2(sin(b*x + a), cos(b*x + a) + 1) - 2*I*b*x*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + b*x*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + b*x*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 2*I*dilog(-e^(I*b*x + I*a)) - 2*I*dilog(e^(I*b*x + I*a)))/b^2","B",0
4,0,0,0,0.000000," ","integrate(cot(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\cot\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(cot(b*x + a)/x, x)","F",0
5,0,0,0,0.000000," ","integrate(cot(b*x+a)/x^2,x, algorithm=""maxima"")","\int \frac{\cot\left(b x + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(cot(b*x + a)/x^2, x)","F",0
6,1,953,0,0.594286," ","integrate(x^3*cot(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{3} - \frac{3 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{2} - {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2}}{\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1} + \frac{2 \, {\left(-i \, {\left(b x + a\right)}^{4} + 4 i \, {\left(b x + a\right)}^{3} a - {\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(i \, {\left(b x + a\right)}^{4} - 4 \, {\left(b x + a\right)}^{3} {\left(i \, a + 2\right)} + 24 \, {\left(b x + a\right)}^{2} a\right)} \cos\left(2 \, b x + 2 \, a\right) - 24 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) + i \, b x \sin\left(2 \, b x + 2 \, a\right) - b x\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 24 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) + i \, b x \sin\left(2 \, b x + 2 \, a\right) - b x\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + {\left(-24 i \, \cos\left(2 \, b x + 2 \, a\right) + 24 \, \sin\left(2 \, b x + 2 \, a\right) + 24 i\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, \cos\left(2 \, b x + 2 \, a\right) + 24 \, \sin\left(2 \, b x + 2 \, a\right) + 24 i\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left({\left(b x + a\right)}^{4} - {\left(b x + a\right)}^{3} {\left(4 \, a - 8 i\right)} - 24 i \, {\left(b x + a\right)}^{2} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-4 i \, \cos\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 4 i}}{2 \, b^{4}}"," ",0,"1/2*(2*(b*x + a + 1/tan(b*x + a))*a^3 - 3*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^2 - (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 4*(b*x + a)*sin(2*b*x + 2*a))*a^2/(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1) + 2*(-I*(b*x + a)^4 + 4*I*(b*x + a)^3*a - (12*(b*x + a)^2 - 24*(b*x + a)*a - 12*((b*x + a)^2 - 2*(b*x + a)*a)*cos(2*b*x + 2*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (12*(b*x + a)^2 - 24*(b*x + a)*a - 12*((b*x + a)^2 - 2*(b*x + a)*a)*cos(2*b*x + 2*a) + (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (I*(b*x + a)^4 - 4*(b*x + a)^3*(I*a + 2) + 24*(b*x + a)^2*a)*cos(2*b*x + 2*a) - 24*(b*x*cos(2*b*x + 2*a) + I*b*x*sin(2*b*x + 2*a) - b*x)*dilog(-e^(I*b*x + I*a)) - 24*(b*x*cos(2*b*x + 2*a) + I*b*x*sin(2*b*x + 2*a) - b*x)*dilog(e^(I*b*x + I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*cos(2*b*x + 2*a) + 6*((b*x + a)^2 - 2*(b*x + a)*a)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*cos(2*b*x + 2*a) + 6*((b*x + a)^2 - 2*(b*x + a)*a)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (-24*I*cos(2*b*x + 2*a) + 24*sin(2*b*x + 2*a) + 24*I)*polylog(3, -e^(I*b*x + I*a)) + (-24*I*cos(2*b*x + 2*a) + 24*sin(2*b*x + 2*a) + 24*I)*polylog(3, e^(I*b*x + I*a)) - ((b*x + a)^4 - (b*x + a)^3*(4*a - 8*I) - 24*I*(b*x + a)^2*a)*sin(2*b*x + 2*a))/(-4*I*cos(2*b*x + 2*a) + 4*sin(2*b*x + 2*a) + 4*I))/b^4","B",0
7,1,384,0,0.617627," ","integrate(x^2*cot(b*x+a)^2,x, algorithm=""maxima"")","\frac{-i \, b^{3} x^{3} + 6 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) + i \, b x \sin\left(2 \, b x + 2 \, a\right) - b x\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - 6 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) + i \, b x \sin\left(2 \, b x + 2 \, a\right) - b x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(i \, b^{3} x^{3} - 6 \, b^{2} x^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) - 1\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) - 1\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-3 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, b x \sin\left(2 \, b x + 2 \, a\right) + 3 i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(-3 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, b x \sin\left(2 \, b x + 2 \, a\right) + 3 i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(b^{3} x^{3} + 6 i \, b^{2} x^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{-3 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 3 i \, b^{3}}"," ",0,"(-I*b^3*x^3 + 6*(b*x*cos(2*b*x + 2*a) + I*b*x*sin(2*b*x + 2*a) - b*x)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - 6*(b*x*cos(2*b*x + 2*a) + I*b*x*sin(2*b*x + 2*a) - b*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (I*b^3*x^3 - 6*b^2*x^2)*cos(2*b*x + 2*a) - 6*(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) - 1)*dilog(-e^(I*b*x + I*a)) - 6*(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) - 1)*dilog(e^(I*b*x + I*a)) + (-3*I*b*x*cos(2*b*x + 2*a) + 3*b*x*sin(2*b*x + 2*a) + 3*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (-3*I*b*x*cos(2*b*x + 2*a) + 3*b*x*sin(2*b*x + 2*a) + 3*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (b^3*x^3 + 6*I*b^2*x^2)*sin(2*b*x + 2*a))/(-3*I*b^3*cos(2*b*x + 2*a) + 3*b^3*sin(2*b*x + 2*a) + 3*I*b^3)","B",0
8,1,269,0,0.466790," ","integrate(x*cot(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a - \frac{{\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{2} - {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)}{\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1}}{2 \, b^{2}}"," ",0,"1/2*(2*(b*x + a + 1/tan(b*x + a))*a - ((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^2 - (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 4*(b*x + a)*sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1))/b^2","B",0
9,0,0,0,0.000000," ","integrate(cot(b*x+a)^2/x,x, algorithm=""maxima"")","-\frac{b x \cos\left(2 \, b x + 2 \, a\right)^{2} \log\left(x\right) + b x \log\left(x\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) \log\left(x\right) + b x \log\left(x\right) - \frac{{\left(b^{2} x \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b^{2} x \cos\left(2 \, b x + 2 \, a\right) + b^{2} x\right)} \int \frac{\sin\left(b x + a\right)}{{\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right)} x^{2}}\,{d x}}{b^{2}} + \frac{{\left(b^{2} x \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b^{2} x \cos\left(2 \, b x + 2 \, a\right) + b^{2} x\right)} \int \frac{\sin\left(b x + a\right)}{{\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right)} x^{2}}\,{d x}}{b^{2}} + 2 \, \sin\left(2 \, b x + 2 \, a\right)}{b x \cos\left(2 \, b x + 2 \, a\right)^{2} + b x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) + b x}"," ",0,"-(b*x*cos(2*b*x + 2*a)^2*log(x) + b*x*log(x)*sin(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a)*log(x) + b*x*log(x) - (b^2*x*cos(2*b*x + 2*a)^2 + b^2*x*sin(2*b*x + 2*a)^2 - 2*b^2*x*cos(2*b*x + 2*a) + b^2*x)*integrate(sin(b*x + a)/(b^2*x^2*cos(b*x + a)^2 + b^2*x^2*sin(b*x + a)^2 + 2*b^2*x^2*cos(b*x + a) + b^2*x^2), x) + (b^2*x*cos(2*b*x + 2*a)^2 + b^2*x*sin(2*b*x + 2*a)^2 - 2*b^2*x*cos(2*b*x + 2*a) + b^2*x)*integrate(sin(b*x + a)/(b^2*x^2*cos(b*x + a)^2 + b^2*x^2*sin(b*x + a)^2 - 2*b^2*x^2*cos(b*x + a) + b^2*x^2), x) + 2*sin(2*b*x + 2*a))/(b*x*cos(2*b*x + 2*a)^2 + b*x*sin(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a) + b*x)","F",0
10,0,0,0,0.000000," ","integrate(cot(b*x+a)^2/x^2,x, algorithm=""maxima"")","\frac{b x \cos\left(2 \, b x + 2 \, a\right)^{2} + b x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) + b x + \frac{2 \, {\left(b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{2}\right)} \int \frac{\sin\left(b x + a\right)}{{\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right)} x^{3}}\,{d x}}{b^{2}} - \frac{2 \, {\left(b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{2}\right)} \int \frac{\sin\left(b x + a\right)}{{\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right)} x^{3}}\,{d x}}{b^{2}} - 2 \, \sin\left(2 \, b x + 2 \, a\right)}{b x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x^{2} \cos\left(2 \, b x + 2 \, a\right) + b x^{2}}"," ",0,"(b*x*cos(2*b*x + 2*a)^2 + b*x*sin(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a) + b*x + 2*(b^2*x^2*cos(2*b*x + 2*a)^2 + b^2*x^2*sin(2*b*x + 2*a)^2 - 2*b^2*x^2*cos(2*b*x + 2*a) + b^2*x^2)*integrate(sin(b*x + a)/(b^2*x^3*cos(b*x + a)^2 + b^2*x^3*sin(b*x + a)^2 + 2*b^2*x^3*cos(b*x + a) + b^2*x^3), x) - 2*(b^2*x^2*cos(2*b*x + 2*a)^2 + b^2*x^2*sin(2*b*x + 2*a)^2 - 2*b^2*x^2*cos(2*b*x + 2*a) + b^2*x^2)*integrate(sin(b*x + a)/(b^2*x^3*cos(b*x + a)^2 + b^2*x^3*sin(b*x + a)^2 - 2*b^2*x^3*cos(b*x + a) + b^2*x^3), x) - 2*sin(2*b*x + 2*a))/(b*x^2*cos(2*b*x + 2*a)^2 + b*x^2*sin(2*b*x + 2*a)^2 - 2*b*x^2*cos(2*b*x + 2*a) + b*x^2)","F",0
11,1,1970,0,0.753792," ","integrate(x^3*cot(b*x+a)^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)} + \frac{2 \, {\left({\left(b x + a\right)}^{4} - 4 \, {\left(b x + a\right)}^{3} a + 6 \, {\left(b x + a\right)}^{2} a^{2} + 12 \, a^{2} - {\left(4 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)}^{2} a + 12 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 4 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} - 12 i \, {\left(b x + a\right)}^{2} a + {\left(12 i \, a^{2} - 12 i\right)} {\left(b x + a\right)} + 12 i \, a\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{3} + 24 i \, {\left(b x + a\right)}^{2} a + {\left(-24 i \, a^{2} + 24 i\right)} {\left(b x + a\right)} - 24 i \, a\right)} \sin\left(2 \, b x + 2 \, a\right) + 12 \, a\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(12 \, a \cos\left(4 \, b x + 4 \, a\right) - 24 \, a \cos\left(2 \, b x + 2 \, a\right) + 12 i \, a \sin\left(4 \, b x + 4 \, a\right) - 24 i \, a \sin\left(2 \, b x + 2 \, a\right) + 12 \, a\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)}^{2} a + 12 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 4 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a + {\left(-12 i \, a^{2} + 12 i\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(8 i \, {\left(b x + a\right)}^{3} - 24 i \, {\left(b x + a\right)}^{2} a + {\left(24 i \, a^{2} - 24 i\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left({\left(b x + a\right)}^{4} - 4 \, {\left(b x + a\right)}^{3} a + 6 \, {\left(a^{2} - 2\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b x + a\right)} a\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(b x + a\right)}^{4} - {\left(b x + a\right)}^{3} {\left(8 \, a - 8 i\right)} + 12 \, {\left(a^{2} - 2 i \, a - 1\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, a^{2} + 24 \, a\right)} {\left(b x + a\right)} + 12 \, a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a + 12 \, a^{2} + 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2} + 12 i\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, {\left(b x + a\right)}^{2} - 48 i \, {\left(b x + a\right)} a + 24 i \, a^{2} - 24 i\right)} \sin\left(2 \, b x + 2 \, a\right) - 12\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a + 12 \, a^{2} + 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2} + 12 i\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, {\left(b x + a\right)}^{2} - 48 i \, {\left(b x + a\right)} a + 24 i \, a^{2} - 24 i\right)} \sin\left(2 \, b x + 2 \, a\right) - 12\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(-2 i \, {\left(b x + a\right)}^{3} + 6 i \, {\left(b x + a\right)}^{2} a + {\left(-6 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} + 6 i \, {\left(b x + a\right)}^{2} a + {\left(-6 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} - 6 i \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} - 12 i \, {\left(b x + a\right)}^{2} a + {\left(12 i \, a^{2} - 12 i\right)} {\left(b x + a\right)} + 12 i \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, a\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-2 i \, {\left(b x + a\right)}^{3} + 6 i \, {\left(b x + a\right)}^{2} a + {\left(-6 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} + 6 i \, {\left(b x + a\right)}^{2} a + {\left(-6 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} - 6 i \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} - 12 i \, {\left(b x + a\right)}^{2} a + {\left(12 i \, a^{2} - 12 i\right)} {\left(b x + a\right)} + 12 i \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(a^{2} - 1\right)} {\left(b x + a\right)} + 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, a\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(24 \, \cos\left(4 \, b x + 4 \, a\right) - 48 \, \cos\left(2 \, b x + 2 \, a\right) + 24 i \, \sin\left(4 \, b x + 4 \, a\right) - 48 i \, \sin\left(2 \, b x + 2 \, a\right) + 24\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(24 \, \cos\left(4 \, b x + 4 \, a\right) - 48 \, \cos\left(2 \, b x + 2 \, a\right) + 24 i \, \sin\left(4 \, b x + 4 \, a\right) - 48 i \, \sin\left(2 \, b x + 2 \, a\right) + 24\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b x \cos\left(4 \, b x + 4 \, a\right) + 48 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 24 \, b x \sin\left(4 \, b x + 4 \, a\right) - 48 \, b x \sin\left(2 \, b x + 2 \, a\right) - 24 i \, b x\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b x \cos\left(4 \, b x + 4 \, a\right) + 48 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 24 \, b x \sin\left(4 \, b x + 4 \, a\right) - 48 \, b x \sin\left(2 \, b x + 2 \, a\right) - 24 i \, b x\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-i \, {\left(b x + a\right)}^{4} + 4 i \, {\left(b x + a\right)}^{3} a + {\left(-6 i \, a^{2} + 12 i\right)} {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(2 i \, {\left(b x + a\right)}^{4} - 8 \, {\left(b x + a\right)}^{3} {\left(i \, a + 1\right)} + {\left(12 i \, a^{2} + 24 \, a - 12 i\right)} {\left(b x + a\right)}^{2} - 24 \, {\left(a^{2} - i \, a\right)} {\left(b x + a\right)} + 12 i \, a^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-4 i \, \cos\left(4 \, b x + 4 \, a\right) + 8 i \, \cos\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right) - 4 i}}{2 \, b^{4}}"," ",0,"1/2*(a^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2)) + 2*((b*x + a)^4 - 4*(b*x + a)^3*a + 6*(b*x + a)^2*a^2 + 12*a^2 - (4*(b*x + a)^3 - 12*(b*x + a)^2*a + 12*(a^2 - 1)*(b*x + a) + 4*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*cos(4*b*x + 4*a) - 8*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*cos(2*b*x + 2*a) + (4*I*(b*x + a)^3 - 12*I*(b*x + a)^2*a + (12*I*a^2 - 12*I)*(b*x + a) + 12*I*a)*sin(4*b*x + 4*a) + (-8*I*(b*x + a)^3 + 24*I*(b*x + a)^2*a + (-24*I*a^2 + 24*I)*(b*x + a) - 24*I*a)*sin(2*b*x + 2*a) + 12*a)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (12*a*cos(4*b*x + 4*a) - 24*a*cos(2*b*x + 2*a) + 12*I*a*sin(4*b*x + 4*a) - 24*I*a*sin(2*b*x + 2*a) + 12*a)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (4*(b*x + a)^3 - 12*(b*x + a)^2*a + 12*(a^2 - 1)*(b*x + a) + 4*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a))*cos(4*b*x + 4*a) - 8*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a))*cos(2*b*x + 2*a) - (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a + (-12*I*a^2 + 12*I)*(b*x + a))*sin(4*b*x + 4*a) - (8*I*(b*x + a)^3 - 24*I*(b*x + a)^2*a + (24*I*a^2 - 24*I)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + ((b*x + a)^4 - 4*(b*x + a)^3*a + 6*(a^2 - 2)*(b*x + a)^2 + 24*(b*x + a)*a)*cos(4*b*x + 4*a) - (2*(b*x + a)^4 - (b*x + a)^3*(8*a - 8*I) + 12*(a^2 - 2*I*a - 1)*(b*x + a)^2 + (24*I*a^2 + 24*a)*(b*x + a) + 12*a^2)*cos(2*b*x + 2*a) + (12*(b*x + a)^2 - 24*(b*x + a)*a + 12*a^2 + 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2 - 1)*cos(4*b*x + 4*a) - 24*((b*x + a)^2 - 2*(b*x + a)*a + a^2 - 1)*cos(2*b*x + 2*a) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2 + 12*I)*sin(4*b*x + 4*a) - (24*I*(b*x + a)^2 - 48*I*(b*x + a)*a + 24*I*a^2 - 24*I)*sin(2*b*x + 2*a) - 12)*dilog(-e^(I*b*x + I*a)) + (12*(b*x + a)^2 - 24*(b*x + a)*a + 12*a^2 + 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2 - 1)*cos(4*b*x + 4*a) - 24*((b*x + a)^2 - 2*(b*x + a)*a + a^2 - 1)*cos(2*b*x + 2*a) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2 + 12*I)*sin(4*b*x + 4*a) - (24*I*(b*x + a)^2 - 48*I*(b*x + a)*a + 24*I*a^2 - 24*I)*sin(2*b*x + 2*a) - 12)*dilog(e^(I*b*x + I*a)) - (-2*I*(b*x + a)^3 + 6*I*(b*x + a)^2*a + (-6*I*a^2 + 6*I)*(b*x + a) + (-2*I*(b*x + a)^3 + 6*I*(b*x + a)^2*a + (-6*I*a^2 + 6*I)*(b*x + a) - 6*I*a)*cos(4*b*x + 4*a) + (4*I*(b*x + a)^3 - 12*I*(b*x + a)^2*a + (12*I*a^2 - 12*I)*(b*x + a) + 12*I*a)*cos(2*b*x + 2*a) + 2*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*sin(4*b*x + 4*a) - 4*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*sin(2*b*x + 2*a) - 6*I*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (-2*I*(b*x + a)^3 + 6*I*(b*x + a)^2*a + (-6*I*a^2 + 6*I)*(b*x + a) + (-2*I*(b*x + a)^3 + 6*I*(b*x + a)^2*a + (-6*I*a^2 + 6*I)*(b*x + a) - 6*I*a)*cos(4*b*x + 4*a) + (4*I*(b*x + a)^3 - 12*I*(b*x + a)^2*a + (12*I*a^2 - 12*I)*(b*x + a) + 12*I*a)*cos(2*b*x + 2*a) + 2*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*sin(4*b*x + 4*a) - 4*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(a^2 - 1)*(b*x + a) + 3*a)*sin(2*b*x + 2*a) - 6*I*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (24*cos(4*b*x + 4*a) - 48*cos(2*b*x + 2*a) + 24*I*sin(4*b*x + 4*a) - 48*I*sin(2*b*x + 2*a) + 24)*polylog(4, -e^(I*b*x + I*a)) - (24*cos(4*b*x + 4*a) - 48*cos(2*b*x + 2*a) + 24*I*sin(4*b*x + 4*a) - 48*I*sin(2*b*x + 2*a) + 24)*polylog(4, e^(I*b*x + I*a)) - (-24*I*b*x*cos(4*b*x + 4*a) + 48*I*b*x*cos(2*b*x + 2*a) + 24*b*x*sin(4*b*x + 4*a) - 48*b*x*sin(2*b*x + 2*a) - 24*I*b*x)*polylog(3, -e^(I*b*x + I*a)) - (-24*I*b*x*cos(4*b*x + 4*a) + 48*I*b*x*cos(2*b*x + 2*a) + 24*b*x*sin(4*b*x + 4*a) - 48*b*x*sin(2*b*x + 2*a) - 24*I*b*x)*polylog(3, e^(I*b*x + I*a)) - (-I*(b*x + a)^4 + 4*I*(b*x + a)^3*a + (-6*I*a^2 + 12*I)*(b*x + a)^2 - 24*I*(b*x + a)*a)*sin(4*b*x + 4*a) - (2*I*(b*x + a)^4 - 8*(b*x + a)^3*(I*a + 1) + (12*I*a^2 + 24*a - 12*I)*(b*x + a)^2 - 24*(a^2 - I*a)*(b*x + a) + 12*I*a^2)*sin(2*b*x + 2*a))/(-4*I*cos(4*b*x + 4*a) + 8*I*cos(2*b*x + 2*a) + 4*sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a) - 4*I))/b^4","B",0
12,1,1216,0,1.178856," ","integrate(x^2*cot(b*x+a)^3,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)}^{2} a - {\left(6 \, {\left(b x + a\right)}^{2} - 12 \, {\left(b x + a\right)} a + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a - 6 i\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a + 12 i\right)} \sin\left(2 \, b x + 2 \, a\right) - 6\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(6 \, \cos\left(4 \, b x + 4 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) + 6 i \, \sin\left(4 \, b x + 4 \, a\right) - 12 i \, \sin\left(2 \, b x + 2 \, a\right) + 6\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(6 \, {\left(b x + a\right)}^{2} - 12 \, {\left(b x + a\right)} a + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a - 6 \, b x - 6 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(4 \, {\left(b x + a\right)}^{3} - {\left(b x + a\right)}^{2} {\left(12 \, a - 12 i\right)} - 12 \, {\left(b x + a\right)} {\left(2 i \, a + 1\right)} - 12 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, b x \cos\left(4 \, b x + 4 \, a\right) - 24 \, b x \cos\left(2 \, b x + 2 \, a\right) + 12 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 24 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 12 \, b x\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(12 \, b x \cos\left(4 \, b x + 4 \, a\right) - 24 \, b x \cos\left(2 \, b x + 2 \, a\right) + 12 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 24 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 12 \, b x\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a + {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a + 3 i\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a - 6 i\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + 3 i\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a + {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a + 3 i\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a - 6 i\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + 3 i\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-12 i \, \cos\left(4 \, b x + 4 \, a\right) + 24 i \, \cos\left(2 \, b x + 2 \, a\right) + 12 \, \sin\left(4 \, b x + 4 \, a\right) - 24 \, \sin\left(2 \, b x + 2 \, a\right) - 12 i\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-12 i \, \cos\left(4 \, b x + 4 \, a\right) + 24 i \, \cos\left(2 \, b x + 2 \, a\right) + 12 \, \sin\left(4 \, b x + 4 \, a\right) - 24 \, \sin\left(2 \, b x + 2 \, a\right) - 12 i\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-2 i \, {\left(b x + a\right)}^{3} + 6 i \, {\left(b x + a\right)}^{2} a + 12 i \, b x + 12 i \, a\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)}^{2} {\left(i \, a + 1\right)} + {\left(b x + a\right)} {\left(24 \, a - 12 i\right)} - 12 i \, a\right)} \sin\left(2 \, b x + 2 \, a\right) - 12 \, a\right)}}{-6 i \, \cos\left(4 \, b x + 4 \, a\right) + 12 i \, \cos\left(2 \, b x + 2 \, a\right) + 6 \, \sin\left(4 \, b x + 4 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right) - 6 i}}{2 \, b^{3}}"," ",0,"-1/2*(a^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2)) - 2*(2*(b*x + a)^3 - 6*(b*x + a)^2*a - (6*(b*x + a)^2 - 12*(b*x + a)*a + 6*((b*x + a)^2 - 2*(b*x + a)*a - 1)*cos(4*b*x + 4*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a - 1)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a - 6*I)*sin(4*b*x + 4*a) + (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a + 12*I)*sin(2*b*x + 2*a) - 6)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*cos(4*b*x + 4*a) - 12*cos(2*b*x + 2*a) + 6*I*sin(4*b*x + 4*a) - 12*I*sin(2*b*x + 2*a) + 6)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (6*(b*x + a)^2 - 12*(b*x + a)*a + 6*((b*x + a)^2 - 2*(b*x + a)*a)*cos(4*b*x + 4*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a)*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*sin(4*b*x + 4*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*((b*x + a)^3 - 3*(b*x + a)^2*a - 6*b*x - 6*a)*cos(4*b*x + 4*a) - (4*(b*x + a)^3 - (b*x + a)^2*(12*a - 12*I) - 12*(b*x + a)*(2*I*a + 1) - 12*a)*cos(2*b*x + 2*a) + (12*b*x*cos(4*b*x + 4*a) - 24*b*x*cos(2*b*x + 2*a) + 12*I*b*x*sin(4*b*x + 4*a) - 24*I*b*x*sin(2*b*x + 2*a) + 12*b*x)*dilog(-e^(I*b*x + I*a)) + (12*b*x*cos(4*b*x + 4*a) - 24*b*x*cos(2*b*x + 2*a) + 12*I*b*x*sin(4*b*x + 4*a) - 24*I*b*x*sin(2*b*x + 2*a) + 12*b*x)*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a + (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a + 3*I)*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a - 6*I)*cos(2*b*x + 2*a) + 3*((b*x + a)^2 - 2*(b*x + a)*a - 1)*sin(4*b*x + 4*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a - 1)*sin(2*b*x + 2*a) + 3*I)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a + (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a + 3*I)*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a - 6*I)*cos(2*b*x + 2*a) + 3*((b*x + a)^2 - 2*(b*x + a)*a - 1)*sin(4*b*x + 4*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a - 1)*sin(2*b*x + 2*a) + 3*I)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-12*I*cos(4*b*x + 4*a) + 24*I*cos(2*b*x + 2*a) + 12*sin(4*b*x + 4*a) - 24*sin(2*b*x + 2*a) - 12*I)*polylog(3, -e^(I*b*x + I*a)) - (-12*I*cos(4*b*x + 4*a) + 24*I*cos(2*b*x + 2*a) + 12*sin(4*b*x + 4*a) - 24*sin(2*b*x + 2*a) - 12*I)*polylog(3, e^(I*b*x + I*a)) - (-2*I*(b*x + a)^3 + 6*I*(b*x + a)^2*a + 12*I*b*x + 12*I*a)*sin(4*b*x + 4*a) - (4*I*(b*x + a)^3 - 12*(b*x + a)^2*(I*a + 1) + (b*x + a)*(24*a - 12*I) - 12*I*a)*sin(2*b*x + 2*a) - 12*a)/(-6*I*cos(4*b*x + 4*a) + 12*I*cos(2*b*x + 2*a) + 6*sin(4*b*x + 4*a) - 12*sin(2*b*x + 2*a) - 6*I))/b^3","B",0
13,1,591,0,0.881750," ","integrate(x*cot(b*x+a)^3,x, algorithm=""maxima"")","\frac{b^{2} x^{2} \cos\left(4 \, b x + 4 \, a\right) + i \, b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right) + b^{2} x^{2} - {\left(2 \, b x \cos\left(4 \, b x + 4 \, a\right) - 4 \, b x \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 4 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 2 \, b x\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(2 \, b x \cos\left(4 \, b x + 4 \, a\right) - 4 \, b x \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 4 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 2 \, b x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 2 \, {\left(b^{2} x^{2} + 2 i \, b x + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) + 2 i \, \sin\left(4 \, b x + 4 \, a\right) - 4 i \, \sin\left(2 \, b x + 2 \, a\right) + 2\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) + 2 i \, \sin\left(4 \, b x + 4 \, a\right) - 4 i \, \sin\left(2 \, b x + 2 \, a\right) + 2\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(-i \, b x \cos\left(4 \, b x + 4 \, a\right) + 2 i \, b x \cos\left(2 \, b x + 2 \, a\right) + b x \sin\left(4 \, b x + 4 \, a\right) - 2 \, b x \sin\left(2 \, b x + 2 \, a\right) - i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-i \, b x \cos\left(4 \, b x + 4 \, a\right) + 2 i \, b x \cos\left(2 \, b x + 2 \, a\right) + b x \sin\left(4 \, b x + 4 \, a\right) - 2 \, b x \sin\left(2 \, b x + 2 \, a\right) - i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(2 i \, b^{2} x^{2} - 4 \, b x + 2 i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}"," ",0,"(b^2*x^2*cos(4*b*x + 4*a) + I*b^2*x^2*sin(4*b*x + 4*a) + b^2*x^2 - (2*b*x*cos(4*b*x + 4*a) - 4*b*x*cos(2*b*x + 2*a) + 2*I*b*x*sin(4*b*x + 4*a) - 4*I*b*x*sin(2*b*x + 2*a) + 2*b*x)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (2*b*x*cos(4*b*x + 4*a) - 4*b*x*cos(2*b*x + 2*a) + 2*I*b*x*sin(4*b*x + 4*a) - 4*I*b*x*sin(2*b*x + 2*a) + 2*b*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 2*(b^2*x^2 + 2*I*b*x + 1)*cos(2*b*x + 2*a) + (2*cos(4*b*x + 4*a) - 4*cos(2*b*x + 2*a) + 2*I*sin(4*b*x + 4*a) - 4*I*sin(2*b*x + 2*a) + 2)*dilog(-e^(I*b*x + I*a)) + (2*cos(4*b*x + 4*a) - 4*cos(2*b*x + 2*a) + 2*I*sin(4*b*x + 4*a) - 4*I*sin(2*b*x + 2*a) + 2)*dilog(e^(I*b*x + I*a)) - (-I*b*x*cos(4*b*x + 4*a) + 2*I*b*x*cos(2*b*x + 2*a) + b*x*sin(4*b*x + 4*a) - 2*b*x*sin(2*b*x + 2*a) - I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (-I*b*x*cos(4*b*x + 4*a) + 2*I*b*x*cos(2*b*x + 2*a) + b*x*sin(4*b*x + 4*a) - 2*b*x*sin(2*b*x + 2*a) - I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (2*I*b^2*x^2 - 4*b*x + 2*I)*sin(2*b*x + 2*a) + 2)/(-2*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
14,0,0,0,0.000000," ","integrate(cot(b*x+a)^3/x,x, algorithm=""maxima"")","-\frac{4 \, b x \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, b x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, b x \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \frac{{\left(b^{2} x^{2} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{2} - 2 \, {\left(2 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)\right)} {\left(b^{2} \int \frac{x^{2} \sin\left(b x + a\right)}{x^{3} \cos\left(b x + a\right)^{2} + x^{3} \sin\left(b x + a\right)^{2} + 2 \, x^{3} \cos\left(b x + a\right) + x^{3}}\,{d x} - \int \frac{\sin\left(b x + a\right)}{x^{3} \cos\left(b x + a\right)^{2} + x^{3} \sin\left(b x + a\right)^{2} + 2 \, x^{3} \cos\left(b x + a\right) + x^{3}}\,{d x}\right)}}{b^{2}} + \frac{{\left(b^{2} x^{2} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{2} - 2 \, {\left(2 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)\right)} {\left(b^{2} \int \frac{x^{2} \sin\left(b x + a\right)}{x^{3} \cos\left(b x + a\right)^{2} + x^{3} \sin\left(b x + a\right)^{2} - 2 \, x^{3} \cos\left(b x + a\right) + x^{3}}\,{d x} - \int \frac{\sin\left(b x + a\right)}{x^{3} \cos\left(b x + a\right)^{2} + x^{3} \sin\left(b x + a\right)^{2} - 2 \, x^{3} \cos\left(b x + a\right) + x^{3}}\,{d x}\right)}}{b^{2}} - \sin\left(2 \, b x + 2 \, a\right)}{b^{2} x^{2} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{2} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{2} - 2 \, {\left(2 \, b^{2} x^{2} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)}"," ",0,"-(4*b*x*cos(2*b*x + 2*a)^2 + 4*b*x*sin(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a) - (2*b*x*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (b^2*x^2*cos(4*b*x + 4*a)^2 + 4*b^2*x^2*cos(2*b*x + 2*a)^2 + b^2*x^2*sin(4*b*x + 4*a)^2 - 4*b^2*x^2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^2*sin(2*b*x + 2*a)^2 - 4*b^2*x^2*cos(2*b*x + 2*a) + b^2*x^2 - 2*(2*b^2*x^2*cos(2*b*x + 2*a) - b^2*x^2)*cos(4*b*x + 4*a))*integrate((b^2*x^2 - 1)*sin(b*x + a)/(b^2*x^3*cos(b*x + a)^2 + b^2*x^3*sin(b*x + a)^2 + 2*b^2*x^3*cos(b*x + a) + b^2*x^3), x) + (b^2*x^2*cos(4*b*x + 4*a)^2 + 4*b^2*x^2*cos(2*b*x + 2*a)^2 + b^2*x^2*sin(4*b*x + 4*a)^2 - 4*b^2*x^2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^2*sin(2*b*x + 2*a)^2 - 4*b^2*x^2*cos(2*b*x + 2*a) + b^2*x^2 - 2*(2*b^2*x^2*cos(2*b*x + 2*a) - b^2*x^2)*cos(4*b*x + 4*a))*integrate((b^2*x^2 - 1)*sin(b*x + a)/(b^2*x^3*cos(b*x + a)^2 + b^2*x^3*sin(b*x + a)^2 - 2*b^2*x^3*cos(b*x + a) + b^2*x^3), x) - (2*b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))/(b^2*x^2*cos(4*b*x + 4*a)^2 + 4*b^2*x^2*cos(2*b*x + 2*a)^2 + b^2*x^2*sin(4*b*x + 4*a)^2 - 4*b^2*x^2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^2*sin(2*b*x + 2*a)^2 - 4*b^2*x^2*cos(2*b*x + 2*a) + b^2*x^2 - 2*(2*b^2*x^2*cos(2*b*x + 2*a) - b^2*x^2)*cos(4*b*x + 4*a))","F",0
15,0,0,0,0.000000," ","integrate(cot(b*x+a)^3/x^2,x, algorithm=""maxima"")","-\frac{4 \, b x \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, b x \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \frac{{\left(b^{2} x^{3} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{3} - 2 \, {\left(2 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)\right)} {\left(b^{2} \int \frac{x^{2} \sin\left(b x + a\right)}{x^{4} \cos\left(b x + a\right)^{2} + x^{4} \sin\left(b x + a\right)^{2} + 2 \, x^{4} \cos\left(b x + a\right) + x^{4}}\,{d x} - 3 \, \int \frac{\sin\left(b x + a\right)}{x^{4} \cos\left(b x + a\right)^{2} + x^{4} \sin\left(b x + a\right)^{2} + 2 \, x^{4} \cos\left(b x + a\right) + x^{4}}\,{d x}\right)}}{b^{2}} + \frac{{\left(b^{2} x^{3} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{3} - 2 \, {\left(2 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)\right)} {\left(b^{2} \int \frac{x^{2} \sin\left(b x + a\right)}{x^{4} \cos\left(b x + a\right)^{2} + x^{4} \sin\left(b x + a\right)^{2} - 2 \, x^{4} \cos\left(b x + a\right) + x^{4}}\,{d x} - 3 \, \int \frac{\sin\left(b x + a\right)}{x^{4} \cos\left(b x + a\right)^{2} + x^{4} \sin\left(b x + a\right)^{2} - 2 \, x^{4} \cos\left(b x + a\right) + x^{4}}\,{d x}\right)}}{b^{2}} - 2 \, \sin\left(2 \, b x + 2 \, a\right)}{b^{2} x^{3} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b^{2} x^{3} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) + b^{2} x^{3} - 2 \, {\left(2 \, b^{2} x^{3} \cos\left(2 \, b x + 2 \, a\right) - b^{2} x^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)}"," ",0,"-(4*b*x*cos(2*b*x + 2*a)^2 + 4*b*x*sin(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a) - 2*(b*x*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (b^2*x^3*cos(4*b*x + 4*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a)^2 + b^2*x^3*sin(4*b*x + 4*a)^2 - 4*b^2*x^3*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^3*sin(2*b*x + 2*a)^2 - 4*b^2*x^3*cos(2*b*x + 2*a) + b^2*x^3 - 2*(2*b^2*x^3*cos(2*b*x + 2*a) - b^2*x^3)*cos(4*b*x + 4*a))*integrate((b^2*x^2 - 3)*sin(b*x + a)/(b^2*x^4*cos(b*x + a)^2 + b^2*x^4*sin(b*x + a)^2 + 2*b^2*x^4*cos(b*x + a) + b^2*x^4), x) + (b^2*x^3*cos(4*b*x + 4*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a)^2 + b^2*x^3*sin(4*b*x + 4*a)^2 - 4*b^2*x^3*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^3*sin(2*b*x + 2*a)^2 - 4*b^2*x^3*cos(2*b*x + 2*a) + b^2*x^3 - 2*(2*b^2*x^3*cos(2*b*x + 2*a) - b^2*x^3)*cos(4*b*x + 4*a))*integrate((b^2*x^2 - 3)*sin(b*x + a)/(b^2*x^4*cos(b*x + a)^2 + b^2*x^4*sin(b*x + a)^2 - 2*b^2*x^4*cos(b*x + a) + b^2*x^4), x) - 2*(b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))/(b^2*x^3*cos(4*b*x + 4*a)^2 + 4*b^2*x^3*cos(2*b*x + 2*a)^2 + b^2*x^3*sin(4*b*x + 4*a)^2 - 4*b^2*x^3*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b^2*x^3*sin(2*b*x + 2*a)^2 - 4*b^2*x^3*cos(2*b*x + 2*a) + b^2*x^3 - 2*(2*b^2*x^3*cos(2*b*x + 2*a) - b^2*x^3)*cos(4*b*x + 4*a))","F",0
16,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
17,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
18,-2,0,0,0.000000," ","integrate((d*x+c)/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
19,1,111,0,0.449044," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\frac{f \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - i \, f E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f \log\left({\left(f x + e\right)} d - d e + c f\right)}{2 \, a d f}"," ",0,"1/2*(f*cos(-2*(d*e - c*f)/d)*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - I*f*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) + f*log((f*x + e)*d - d*e + c*f))/(a*d*f)","A",0
20,1,122,0,0.790756," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\frac{8 \, f^{2} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 8 i \, f^{2} E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 8 \, f^{2}}{16 \, {\left({\left(f x + e\right)} a d^{2} - a d^{2} e + a c d f\right)} f}"," ",0,"1/16*(8*f^2*cos(-2*(d*e - c*f)/d)*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 8*I*f^2*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) - 8*f^2)/(((f*x + e)*a*d^2 - a*d^2*e + a*c*d*f)*f)","A",0
21,1,160,0,0.910230," ","integrate(1/(d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, f^{3} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 2 i \, f^{3} E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - f^{3}}{4 \, {\left({\left(f x + e\right)}^{2} a d^{3} + a d^{3} e^{2} - 2 \, a c d^{2} e f + a c^{2} d f^{2} - 2 \, {\left(a d^{3} e - a c d^{2} f\right)} {\left(f x + e\right)}\right)} f}"," ",0,"1/4*(2*f^3*cos(-2*(d*e - c*f)/d)*exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 2*I*f^3*exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) - f^3)/(((f*x + e)^2*a*d^3 + a*d^3*e^2 - 2*a*c*d^2*e*f + a*c^2*d*f^2 - 2*(a*d^3*e - a*c*d^2*f)*(f*x + e))*f)","A",0
22,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
23,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
24,-2,0,0,0.000000," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
25,1,194,0,0.962813," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","-\frac{f \cos\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) - 2 \, f \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + 2 i \, f E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - i \, f E_{1}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) \sin\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - f \log\left({\left(f x + e\right)} d - d e + c f\right)}{4 \, a^{2} d f}"," ",0,"-1/4*(f*cos(-4*(d*e - c*f)/d)*exp_integral_e(1, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d) - 2*f*cos(-2*(d*e - c*f)/d)*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + 2*I*f*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) - I*f*exp_integral_e(1, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d)*sin(-4*(d*e - c*f)/d) - f*log((f*x + e)*d - d*e + c*f))/(a^2*d*f)","A",0
26,1,214,0,0.809408," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","-\frac{64 \, f^{2} \cos\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) - 128 \, f^{2} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + 128 i \, f^{2} E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 64 i \, f^{2} E_{2}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) \sin\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 64 \, f^{2}}{256 \, {\left({\left(f x + e\right)} a^{2} d^{2} - a^{2} d^{2} e + a^{2} c d f\right)} f}"," ",0,"-1/256*(64*f^2*cos(-4*(d*e - c*f)/d)*exp_integral_e(2, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d) - 128*f^2*cos(-2*(d*e - c*f)/d)*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + 128*I*f^2*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) - 64*I*f^2*exp_integral_e(2, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d)*sin(-4*(d*e - c*f)/d) + 64*f^2)/(((f*x + e)*a^2*d^2 - a^2*d^2*e + a^2*c*d*f)*f)","A",0
27,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
28,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
29,-2,0,0,0.000000," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
30,1,275,0,0.902055," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","\frac{f \cos\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{6 i \, {\left(f x + e\right)} d - 6 i \, d e + 6 i \, c f}{d}\right) - 3 \, f \cos\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) + 3 \, f \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 3 i \, f E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 3 i \, f E_{1}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) \sin\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - i \, f E_{1}\left(-\frac{6 i \, {\left(f x + e\right)} d - 6 i \, d e + 6 i \, c f}{d}\right) \sin\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + f \log\left({\left(f x + e\right)} d - d e + c f\right)}{8 \, a^{3} d f}"," ",0,"1/8*(f*cos(-6*(d*e - c*f)/d)*exp_integral_e(1, -(6*I*(f*x + e)*d - 6*I*d*e + 6*I*c*f)/d) - 3*f*cos(-4*(d*e - c*f)/d)*exp_integral_e(1, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d) + 3*f*cos(-2*(d*e - c*f)/d)*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 3*I*f*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) + 3*I*f*exp_integral_e(1, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d)*sin(-4*(d*e - c*f)/d) - I*f*exp_integral_e(1, -(6*I*(f*x + e)*d - 6*I*d*e + 6*I*c*f)/d)*sin(-6*(d*e - c*f)/d) + f*log((f*x + e)*d - d*e + c*f))/(a^3*d*f)","A",0
31,1,300,0,1.651645," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","\frac{8192 \, f^{2} \cos\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{6 i \, {\left(f x + e\right)} d - 6 i \, d e + 6 i \, c f}{d}\right) - 24576 \, f^{2} \cos\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) + 24576 \, f^{2} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 24576 i \, f^{2} E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 24576 i \, f^{2} E_{2}\left(-\frac{4 i \, {\left(f x + e\right)} d - 4 i \, d e + 4 i \, c f}{d}\right) \sin\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - 8192 i \, f^{2} E_{2}\left(-\frac{6 i \, {\left(f x + e\right)} d - 6 i \, d e + 6 i \, c f}{d}\right) \sin\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) - 8192 \, f^{2}}{65536 \, {\left({\left(f x + e\right)} a^{3} d^{2} - a^{3} d^{2} e + a^{3} c d f\right)} f}"," ",0,"1/65536*(8192*f^2*cos(-6*(d*e - c*f)/d)*exp_integral_e(2, -(6*I*(f*x + e)*d - 6*I*d*e + 6*I*c*f)/d) - 24576*f^2*cos(-4*(d*e - c*f)/d)*exp_integral_e(2, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d) + 24576*f^2*cos(-2*(d*e - c*f)/d)*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 24576*I*f^2*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d)*sin(-2*(d*e - c*f)/d) + 24576*I*f^2*exp_integral_e(2, -(4*I*(f*x + e)*d - 4*I*d*e + 4*I*c*f)/d)*sin(-4*(d*e - c*f)/d) - 8192*I*f^2*exp_integral_e(2, -(6*I*(f*x + e)*d - 6*I*d*e + 6*I*c*f)/d)*sin(-6*(d*e - c*f)/d) - 8192*f^2)/(((f*x + e)*a^3*d^2 - a^3*d^2*e + a^3*c*d*f)*f)","A",0
32,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(d x + c\right)}^{m} a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d x + c\right)}^{m} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d x + c\right)}^{m} a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d x + c\right)}^{m} a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d x + c\right)}^{m} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(d x + c\right)}^{m} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(d x + c\right)}^{m} a^{2} - 2 \, {\left(2 \, {\left(d x + c\right)}^{m} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(d x + c\right)}^{m} a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)}{2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} - 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1}\,{d x} - i \, \int -\frac{4 \, {\left({\left(d x + c\right)}^{m} a^{2} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(d x + c\right)}^{m} a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)}}{2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \cos\left(4 \, f x + 4 \, e\right) - \cos\left(4 \, f x + 4 \, e\right)^{2} - 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) - 1}\,{d x}"," ",0,"(d*x + c)^(m + 1)*a^2/(d*(m + 1)) - integrate(-((d*x + c)^m*a^2*cos(4*f*x + 4*e)^2 + 4*(d*x + c)^m*a^2*cos(2*f*x + 2*e)^2 + (d*x + c)^m*a^2*sin(4*f*x + 4*e)^2 - 4*(d*x + c)^m*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d*x + c)^m*a^2*sin(2*f*x + 2*e)^2 + 4*(d*x + c)^m*a^2*cos(2*f*x + 2*e) - 3*(d*x + c)^m*a^2 - 2*(2*(d*x + c)^m*a^2*cos(2*f*x + 2*e) + (d*x + c)^m*a^2)*cos(4*f*x + 4*e))/(2*(2*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - 4*cos(2*f*x + 2*e)^2 - sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) - 1), x) - I*integrate(-4*((d*x + c)^m*a^2*sin(4*f*x + 4*e) - 2*(d*x + c)^m*a^2*sin(2*f*x + 2*e))/(2*(2*cos(2*f*x + 2*e) - 1)*cos(4*f*x + 4*e) - cos(4*f*x + 4*e)^2 - 4*cos(2*f*x + 2*e)^2 - sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) - 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) - 1), x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","2 i \, a \int \frac{{\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, 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*I*a*integrate((d*x + c)^m*sin(2*f*x + 2*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
34,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e)),x, algorithm=""maxima"")","-\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} + {\left(i \, d m + i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, e\right)\,{d x} - e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{2 \, {\left(a d m + a d\right)}}"," ",0,"-1/2*((d*m + d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) + (I*d*m + I*d)*integrate((d*x + c)^m*sin(2*f*x + 2*e), x) - e^(m*log(d*x + c) + log(d*x + c)))/(a*d*m + a*d)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(4 \, f x + 4 \, e\right)\,{d x} - 2 \, {\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} + {\left(i \, d m + i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(4 \, f x + 4 \, e\right)\,{d x} + {\left(-2 i \, d m - 2 i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, e\right)\,{d x} + e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{4 \, {\left(a^{2} d m + a^{2} d\right)}}"," ",0,"1/4*((d*m + d)*integrate((d*x + c)^m*cos(4*f*x + 4*e), x) - 2*(d*m + d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) + (I*d*m + I*d)*integrate((d*x + c)^m*sin(4*f*x + 4*e), x) + (-2*I*d*m - 2*I*d)*integrate((d*x + c)^m*sin(2*f*x + 2*e), x) + e^(m*log(d*x + c) + log(d*x + c)))/(a^2*d*m + a^2*d)","F",0
36,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^3,x, algorithm=""maxima"")","-\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(6 \, f x + 6 \, e\right)\,{d x} - 3 \, {\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(4 \, f x + 4 \, e\right)\,{d x} + 3 \, {\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} + {\left(i \, d m + i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(6 \, f x + 6 \, e\right)\,{d x} + {\left(-3 i \, d m - 3 i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(4 \, f x + 4 \, e\right)\,{d x} + {\left(3 i \, d m + 3 i \, d\right)} \int {\left(d x + c\right)}^{m} \sin\left(2 \, f x + 2 \, e\right)\,{d x} - e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{8 \, {\left(a^{3} d m + a^{3} d\right)}}"," ",0,"-1/8*((d*m + d)*integrate((d*x + c)^m*cos(6*f*x + 6*e), x) - 3*(d*m + d)*integrate((d*x + c)^m*cos(4*f*x + 4*e), x) + 3*(d*m + d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) + (I*d*m + I*d)*integrate((d*x + c)^m*sin(6*f*x + 6*e), x) + (-3*I*d*m - 3*I*d)*integrate((d*x + c)^m*sin(4*f*x + 4*e), x) + (3*I*d*m + 3*I*d)*integrate((d*x + c)^m*sin(2*f*x + 2*e), x) - e^(m*log(d*x + c) + log(d*x + c)))/(a^3*d*m + a^3*d)","F",0
37,1,966,0,1.163653," ","integrate((d*x+c)^3*(a+b*cot(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(\sin\left(f x + e\right)\right) - \frac{4 \, b d^{3} e^{3} \log\left(\sin\left(f x + e\right)\right)}{f^{3}} + \frac{12 \, b c d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, b c^{2} d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{-i \, {\left(f x + e\right)}^{4} b d^{3} + 24 i \, b d^{3} {\rm Li}_{4}(-e^{\left(i \, f x + i \, e\right)}) + 24 i \, b d^{3} {\rm Li}_{4}(e^{\left(i \, f x + i \, e\right)}) + {\left(4 i \, b d^{3} e - 4 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\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)}^{2} + {\left(4 i \, {\left(f x + e\right)}^{3} b d^{3} + {\left(-12 i \, b d^{3} e + 12 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(12 i \, b d^{3} e^{2} - 24 i \, b c d^{2} e f + 12 i \, b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(-4 i \, {\left(f x + e\right)}^{3} b d^{3} + {\left(12 i \, b d^{3} e - 12 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b d^{3} e^{2} + 24 i \, b c d^{2} e f - 12 i \, b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + {\left(-12 i \, {\left(f x + e\right)}^{2} b d^{3} - 12 i \, b d^{3} e^{2} + 24 i \, b c d^{2} e f - 12 i \, b c^{2} d f^{2} + {\left(24 i \, b d^{3} e - 24 i \, b c d^{2} f\right)} {\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} b d^{3} - 12 i \, b d^{3} e^{2} + 24 i \, b c d^{2} e f - 12 i \, b c^{2} d f^{2} + {\left(24 i \, b d^{3} e - 24 i \, b c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + 2 \, {\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 \, \cos\left(f x + e\right) + 1\right) + 2 \, {\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 \, \cos\left(f x + e\right) + 1\right) + 24 \, {\left({\left(f x + e\right)} b d^{3} - b d^{3} e + b c d^{2} f\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) + 24 \, {\left({\left(f x + e\right)} b d^{3} - b d^{3} e + b c d^{2} f\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\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(sin(f*x + e)) - 4*b*d^3*e^3*log(sin(f*x + e))/f^3 + 12*b*c*d^2*e^2*log(sin(f*x + e))/f^2 - 12*b*c^2*d*e*log(sin(f*x + e))/f + (-I*(f*x + e)^4*b*d^3 + 24*I*b*d^3*polylog(4, -e^(I*f*x + I*e)) + 24*I*b*d^3*polylog(4, e^(I*f*x + I*e)) + (4*I*b*d^3*e - 4*I*b*c*d^2*f)*(f*x + e)^3 + (-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)^2 + (4*I*(f*x + e)^3*b*d^3 + (-12*I*b*d^3*e + 12*I*b*c*d^2*f)*(f*x + e)^2 + (12*I*b*d^3*e^2 - 24*I*b*c*d^2*e*f + 12*I*b*c^2*d*f^2)*(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (-4*I*(f*x + e)^3*b*d^3 + (12*I*b*d^3*e - 12*I*b*c*d^2*f)*(f*x + e)^2 + (-12*I*b*d^3*e^2 + 24*I*b*c*d^2*e*f - 12*I*b*c^2*d*f^2)*(f*x + e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + (-12*I*(f*x + e)^2*b*d^3 - 12*I*b*d^3*e^2 + 24*I*b*c*d^2*e*f - 12*I*b*c^2*d*f^2 + (24*I*b*d^3*e - 24*I*b*c*d^2*f)*(f*x + e))*dilog(-e^(I*f*x + I*e)) + (-12*I*(f*x + e)^2*b*d^3 - 12*I*b*d^3*e^2 + 24*I*b*c*d^2*e*f - 12*I*b*c^2*d*f^2 + (24*I*b*d^3*e - 24*I*b*c*d^2*f)*(f*x + e))*dilog(e^(I*f*x + I*e)) + 2*((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*cos(f*x + e) + 1) + 2*((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*cos(f*x + e) + 1) + 24*((f*x + e)*b*d^3 - b*d^3*e + b*c*d^2*f)*polylog(3, -e^(I*f*x + I*e)) + 24*((f*x + e)*b*d^3 - b*d^3*e + b*c*d^2*f)*polylog(3, e^(I*f*x + I*e)))/f^3)/f","B",0
38,1,520,0,1.753039," ","integrate((d*x+c)^2*(a+b*cot(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(\sin\left(f x + e\right)\right) + \frac{6 \, b d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, b c d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{-2 i \, {\left(f x + e\right)}^{3} b d^{2} + 12 \, b d^{2} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) + 12 \, b d^{2} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) + {\left(6 i \, b d^{2} e - 6 i \, b c d f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, {\left(f x + e\right)}^{2} b d^{2} + {\left(-12 i \, b d^{2} e + 12 i \, b c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} b d^{2} + {\left(12 i \, b d^{2} e - 12 i \, b c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + {\left(-12 i \, {\left(f x + e\right)} b d^{2} + 12 i \, b d^{2} e - 12 i \, b c d f\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-12 i \, {\left(f x + e\right)} b d^{2} + 12 i \, b d^{2} e - 12 i \, b c d f\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + 3 \, {\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 \, \cos\left(f x + e\right) + 1\right) + 3 \, {\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 \, \cos\left(f x + e\right) + 1\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(sin(f*x + e)) + 6*b*d^2*e^2*log(sin(f*x + e))/f^2 - 12*b*c*d*e*log(sin(f*x + e))/f + (-2*I*(f*x + e)^3*b*d^2 + 12*b*d^2*polylog(3, -e^(I*f*x + I*e)) + 12*b*d^2*polylog(3, e^(I*f*x + I*e)) + (6*I*b*d^2*e - 6*I*b*c*d*f)*(f*x + e)^2 + (6*I*(f*x + e)^2*b*d^2 + (-12*I*b*d^2*e + 12*I*b*c*d*f)*(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (-6*I*(f*x + e)^2*b*d^2 + (12*I*b*d^2*e - 12*I*b*c*d*f)*(f*x + e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + (-12*I*(f*x + e)*b*d^2 + 12*I*b*d^2*e - 12*I*b*c*d*f)*dilog(-e^(I*f*x + I*e)) + (-12*I*(f*x + e)*b*d^2 + 12*I*b*d^2*e - 12*I*b*c*d*f)*dilog(e^(I*f*x + I*e)) + 3*((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*cos(f*x + e) + 1) + 3*((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*cos(f*x + e) + 1))/f^2)/f","B",0
39,1,208,0,0.929534," ","integrate((d*x+c)*(a+b*cot(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(a - i \, b\right)} d f^{2} x^{2} + 2 \, {\left(a - i \, b\right)} c f^{2} x - 2 i \, b d f x \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + 2 i \, b c f \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - 2 i \, b d {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - 2 i \, b d {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(2 i \, b d f x + 2 i \, b c f\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(b d f x + b c f\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(b d f x + b c f\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 \, f^{2}}"," ",0,"1/2*((a - I*b)*d*f^2*x^2 + 2*(a - I*b)*c*f^2*x - 2*I*b*d*f*x*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + 2*I*b*c*f*arctan2(sin(f*x + e), cos(f*x + e) - 1) - 2*I*b*d*dilog(-e^(I*f*x + I*e)) - 2*I*b*d*dilog(e^(I*f*x + I*e)) + (2*I*b*d*f*x + 2*I*b*c*f)*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (b*d*f*x + b*c*f)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (b*d*f*x + b*c*f)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1))/f^2","B",0
40,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))/(d*x+c),x, algorithm=""maxima"")","-\frac{b d \int \frac{\sin\left(f x + e\right)}{{\left(d x + c\right)} {\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} - b d \int \frac{\sin\left(f x + e\right)}{{\left(d x + c\right)} {\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 \log\left(d x + c\right)}{d}"," ",0,"-(b*d*integrate(sin(f*x + e)/((d*x + c)*cos(f*x + e)^2 + (d*x + c)*sin(f*x + e)^2 + d*x + 2*(d*x + c)*cos(f*x + e) + c), x) - b*d*integrate(sin(f*x + e)/((d*x + c)*cos(f*x + e)^2 + (d*x + c)*sin(f*x + e)^2 + d*x - 2*(d*x + c)*cos(f*x + e) + c), x) - a*log(d*x + c))/d","F",0
41,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b d^{2} x + b c d\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} - {\left(b d^{2} x + b c d\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}{d^{2} x + c d}"," ",0,"-((b*d^2*x + b*c*d)*integrate(sin(f*x + e)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(f*x + e)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(f*x + e)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(f*x + e)), x) - (b*d^2*x + b*c*d)*integrate(sin(f*x + e)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(f*x + e)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(f*x + e)^2 + c^2 - 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(f*x + e)), x) + a)/(d^2*x + c*d)","F",0
42,1,4012,0,4.351837," ","integrate((d*x+c)^3*(a+b*cot(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(\sin\left(f x + e\right)\right) - \frac{8 \, a b d^{3} e^{3} \log\left(\sin\left(f x + e\right)\right)}{f^{3}} + \frac{24 \, a b c d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{24 \, a b c^{2} d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{4 \, {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{4} d^{3} + 8 \, b^{2} d^{3} e^{3} - 24 \, b^{2} c d^{2} e^{2} f + 24 \, b^{2} c^{2} d e f^{2} - 8 \, b^{2} c^{3} f^{3} - {\left({\left(8 \, a b - 4 i \, b^{2}\right)} d^{3} e - {\left(8 \, a b - 4 i \, b^{2}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\left({\left(12 \, a b - 6 i \, b^{2}\right)} d^{3} e^{2} - {\left(24 \, a b - 12 i \, b^{2}\right)} c d^{2} e f + {\left(12 \, a b - 6 i \, b^{2}\right)} c^{2} d f^{2}\right)} {\left(f x + e\right)}^{2} + {\left(4 i \, b^{2} d^{3} e^{3} - 12 i \, b^{2} c d^{2} e^{2} f + 12 i \, b^{2} c^{2} d e f^{2} - 4 i \, b^{2} c^{3} f^{3}\right)} {\left(f x + e\right)} - {\left(8 \, {\left(f x + e\right)}^{3} a b d^{3} + 12 \, b^{2} d^{3} e^{2} - 24 \, b^{2} c d^{2} e f + 12 \, b^{2} c^{2} d f^{2} - 12 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 24 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)} - 4 \, {\left(2 \, {\left(f x + e\right)}^{3} a b d^{3} + 3 \, b^{2} d^{3} e^{2} - 6 \, b^{2} c d^{2} e f + 3 \, b^{2} c^{2} d f^{2} - 3 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 6 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(8 i \, {\left(f x + e\right)}^{3} a b d^{3} + 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} + {\left(-24 i \, a b d^{3} e + 24 i \, a b c d^{2} f + 12 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(24 i \, a b d^{3} e^{2} + 24 i \, a b c^{2} d f^{2} - 24 i \, b^{2} d^{3} e + {\left(-48 i \, a b c d^{2} e + 24 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(12 \, b^{2} d^{3} e^{2} - 24 \, b^{2} c d^{2} e f + 12 \, b^{2} c^{2} d f^{2} - 12 \, {\left(b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f + b^{2} c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\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)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(8 \, {\left(f x + e\right)}^{3} a b d^{3} - 12 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 24 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)} - 4 \, {\left(2 \, {\left(f x + e\right)}^{3} a b d^{3} - 3 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 6 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-8 i \, {\left(f x + e\right)}^{3} a b d^{3} + {\left(24 i \, a b d^{3} e - 24 i \, a b c d^{2} f - 12 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-24 i \, a b d^{3} e^{2} - 24 i \, a b c^{2} d f^{2} + 24 i \, b^{2} d^{3} e + {\left(48 i \, a b c d^{2} e - 24 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) - {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{4} d^{3} + {\left(8 \, b^{2} d^{3} - {\left(8 \, a b - 4 i \, b^{2}\right)} d^{3} e + {\left(8 \, a b - 4 i \, b^{2}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} - {\left(24 \, b^{2} d^{3} e - {\left(12 \, a b - 6 i \, b^{2}\right)} d^{3} e^{2} - {\left(12 \, a b - 6 i \, b^{2}\right)} c^{2} d f^{2} - {\left(24 \, b^{2} c d^{2} - {\left(24 \, a b - 12 i \, b^{2}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}^{2} - {\left(-4 i \, b^{2} d^{3} e^{3} + 4 i \, b^{2} c^{3} f^{3} - 24 \, b^{2} d^{3} e^{2} - 12 \, {\left(i \, b^{2} c^{2} d e + 2 \, b^{2} c^{2} d\right)} f^{2} - 12 \, {\left(-i \, b^{2} c d^{2} e^{2} - 4 \, b^{2} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(24 \, {\left(f x + e\right)}^{2} a b d^{3} + 24 \, a b d^{3} e^{2} + 24 \, a b c^{2} d f^{2} - 24 \, b^{2} d^{3} e - 24 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)} - 24 \, {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f - 24 \, {\left({\left(f x + e\right)}^{2} a b d^{3} + a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)} - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-24 i \, {\left(f x + e\right)}^{2} a b d^{3} - 24 i \, a b d^{3} e^{2} - 24 i \, a b c^{2} d f^{2} + 24 i \, b^{2} d^{3} e + {\left(48 i \, a b d^{3} e - 48 i \, a b c d^{2} f - 24 i \, b^{2} d^{3}\right)} {\left(f x + e\right)} + {\left(48 i \, a b c d^{2} e - 24 i \, b^{2} c d^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(24 \, {\left(f x + e\right)}^{2} a b d^{3} + 24 \, a b d^{3} e^{2} + 24 \, a b c^{2} d f^{2} - 24 \, b^{2} d^{3} e - 24 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)} - 24 \, {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f - 24 \, {\left({\left(f x + e\right)}^{2} a b d^{3} + a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)} - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-24 i \, {\left(f x + e\right)}^{2} a b d^{3} - 24 i \, a b d^{3} e^{2} - 24 i \, a b c^{2} d f^{2} + 24 i \, b^{2} d^{3} e + {\left(48 i \, a b d^{3} e - 48 i \, a b c d^{2} f - 24 i \, b^{2} d^{3}\right)} {\left(f x + e\right)} + {\left(48 i \, a b c d^{2} e - 24 i \, b^{2} c d^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(4 i \, {\left(f x + e\right)}^{3} a b 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 \, a b d^{3} e + 12 i \, a b c d^{2} f + 6 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(12 i \, a b d^{3} e^{2} + 12 i \, a b c^{2} d f^{2} - 12 i \, b^{2} d^{3} e + {\left(-24 i \, a b c d^{2} e + 12 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)} + {\left(-4 i \, {\left(f x + e\right)}^{3} a b 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 \, a b d^{3} e - 12 i \, a b c d^{2} f - 6 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a b d^{3} e^{2} - 12 i \, a b c^{2} d f^{2} + 12 i \, b^{2} d^{3} e + {\left(24 i \, a b c d^{2} e - 12 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)}^{3} a b d^{3} + 3 \, b^{2} d^{3} e^{2} - 6 \, b^{2} c d^{2} e f + 3 \, b^{2} c^{2} d f^{2} - 3 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 6 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} 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 \, \cos\left(f x + e\right) + 1\right) + {\left(4 i \, {\left(f x + e\right)}^{3} a b 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 \, a b d^{3} e + 12 i \, a b c d^{2} f + 6 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(12 i \, a b d^{3} e^{2} + 12 i \, a b c^{2} d f^{2} - 12 i \, b^{2} d^{3} e + {\left(-24 i \, a b c d^{2} e + 12 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)} + {\left(-4 i \, {\left(f x + e\right)}^{3} a b 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 \, a b d^{3} e - 12 i \, a b c d^{2} f - 6 i \, b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, a b d^{3} e^{2} - 12 i \, a b c^{2} d f^{2} + 12 i \, b^{2} d^{3} e + {\left(24 i \, a b c d^{2} e - 12 i \, b^{2} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)}^{3} a b d^{3} + 3 \, b^{2} d^{3} e^{2} - 6 \, b^{2} c d^{2} e f + 3 \, b^{2} c^{2} d f^{2} - 3 \, {\left(2 \, a b d^{3} e - 2 \, a b c d^{2} f - b^{2} d^{3}\right)} {\left(f x + e\right)}^{2} + 6 \, {\left(a b d^{3} e^{2} + a b c^{2} d f^{2} - b^{2} d^{3} e - {\left(2 \, a b c d^{2} e - b^{2} c d^{2}\right)} 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 \, \cos\left(f x + e\right) + 1\right) + 48 \, {\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}(-e^{\left(i \, f x + i \, e\right)}) + 48 \, {\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}(e^{\left(i \, f x + i \, e\right)}) + {\left(48 i \, {\left(f x + e\right)} a b d^{3} - 48 i \, a b d^{3} e + 48 i \, a b c d^{2} f + 24 i \, b^{2} d^{3} + {\left(-48 i \, {\left(f x + e\right)} a b d^{3} + 48 i \, a b d^{3} e - 48 i \, a b c d^{2} f - 24 i \, b^{2} d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 24 \, {\left(2 \, {\left(f x + e\right)} a b d^{3} - 2 \, a b d^{3} e + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) + {\left(48 i \, {\left(f x + e\right)} a b d^{3} - 48 i \, a b d^{3} e + 48 i \, a b c d^{2} f + 24 i \, b^{2} d^{3} + {\left(-48 i \, {\left(f x + e\right)} a b d^{3} + 48 i \, a b d^{3} e - 48 i \, a b c d^{2} f - 24 i \, b^{2} d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 24 \, {\left(2 \, {\left(f x + e\right)} a b d^{3} - 2 \, a b d^{3} e + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) + {\left({\left(-2 i \, a b - b^{2}\right)} {\left(f x + e\right)}^{4} d^{3} + {\left(-8 i \, b^{2} d^{3} - 4 \, {\left(-2 i \, a b - b^{2}\right)} d^{3} e - 4 \, {\left(2 i \, a b + b^{2}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\left(24 i \, b^{2} d^{3} e - 6 \, {\left(2 i \, a b + b^{2}\right)} d^{3} e^{2} - 6 \, {\left(2 i \, a b + b^{2}\right)} c^{2} d f^{2} + {\left(-24 i \, b^{2} c d^{2} - 12 \, {\left(-2 i \, a b - b^{2}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}^{2} + {\left(4 \, b^{2} d^{3} e^{3} - 4 \, b^{2} c^{3} f^{3} - 24 i \, b^{2} d^{3} e^{2} + {\left(12 \, b^{2} c^{2} d e - 24 i \, b^{2} c^{2} d\right)} f^{2} - {\left(12 \, b^{2} c d^{2} e^{2} - 48 i \, b^{2} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-4 i \, f^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, f^{3} \sin\left(2 \, f x + 2 \, e\right) + 4 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(sin(f*x + e)) - 8*a*b*d^3*e^3*log(sin(f*x + e))/f^3 + 24*a*b*c*d^2*e^2*log(sin(f*x + e))/f^2 - 24*a*b*c^2*d*e*log(sin(f*x + e))/f + 4*((2*a*b - I*b^2)*(f*x + e)^4*d^3 + 8*b^2*d^3*e^3 - 24*b^2*c*d^2*e^2*f + 24*b^2*c^2*d*e*f^2 - 8*b^2*c^3*f^3 - ((8*a*b - 4*I*b^2)*d^3*e - (8*a*b - 4*I*b^2)*c*d^2*f)*(f*x + e)^3 + ((12*a*b - 6*I*b^2)*d^3*e^2 - (24*a*b - 12*I*b^2)*c*d^2*e*f + (12*a*b - 6*I*b^2)*c^2*d*f^2)*(f*x + e)^2 + (4*I*b^2*d^3*e^3 - 12*I*b^2*c*d^2*e^2*f + 12*I*b^2*c^2*d*e*f^2 - 4*I*b^2*c^3*f^3)*(f*x + e) - (8*(f*x + e)^3*a*b*d^3 + 12*b^2*d^3*e^2 - 24*b^2*c*d^2*e*f + 12*b^2*c^2*d*f^2 - 12*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 24*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e) - 4*(2*(f*x + e)^3*a*b*d^3 + 3*b^2*d^3*e^2 - 6*b^2*c*d^2*e*f + 3*b^2*c^2*d*f^2 - 3*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 6*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) - (8*I*(f*x + e)^3*a*b*d^3 + 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 + (-24*I*a*b*d^3*e + 24*I*a*b*c*d^2*f + 12*I*b^2*d^3)*(f*x + e)^2 + (24*I*a*b*d^3*e^2 + 24*I*a*b*c^2*d*f^2 - 24*I*b^2*d^3*e + (-48*I*a*b*c*d^2*e + 24*I*b^2*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (12*b^2*d^3*e^2 - 24*b^2*c*d^2*e*f + 12*b^2*c^2*d*f^2 - 12*(b^2*d^3*e^2 - 2*b^2*c*d^2*e*f + b^2*c^2*d*f^2)*cos(2*f*x + 2*e) - (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)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (8*(f*x + e)^3*a*b*d^3 - 12*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 24*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e) - 4*(2*(f*x + e)^3*a*b*d^3 - 3*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 6*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) + (-8*I*(f*x + e)^3*a*b*d^3 + (24*I*a*b*d^3*e - 24*I*a*b*c*d^2*f - 12*I*b^2*d^3)*(f*x + e)^2 + (-24*I*a*b*d^3*e^2 - 24*I*a*b*c^2*d*f^2 + 24*I*b^2*d^3*e + (48*I*a*b*c*d^2*e - 24*I*b^2*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) - ((2*a*b - I*b^2)*(f*x + e)^4*d^3 + (8*b^2*d^3 - (8*a*b - 4*I*b^2)*d^3*e + (8*a*b - 4*I*b^2)*c*d^2*f)*(f*x + e)^3 - (24*b^2*d^3*e - (12*a*b - 6*I*b^2)*d^3*e^2 - (12*a*b - 6*I*b^2)*c^2*d*f^2 - (24*b^2*c*d^2 - (24*a*b - 12*I*b^2)*c*d^2*e)*f)*(f*x + e)^2 - (-4*I*b^2*d^3*e^3 + 4*I*b^2*c^3*f^3 - 24*b^2*d^3*e^2 - 12*(I*b^2*c^2*d*e + 2*b^2*c^2*d)*f^2 - 12*(-I*b^2*c*d^2*e^2 - 4*b^2*c*d^2*e)*f)*(f*x + e))*cos(2*f*x + 2*e) + (24*(f*x + e)^2*a*b*d^3 + 24*a*b*d^3*e^2 + 24*a*b*c^2*d*f^2 - 24*b^2*d^3*e - 24*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e) - 24*(2*a*b*c*d^2*e - b^2*c*d^2)*f - 24*((f*x + e)^2*a*b*d^3 + a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e) - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*cos(2*f*x + 2*e) + (-24*I*(f*x + e)^2*a*b*d^3 - 24*I*a*b*d^3*e^2 - 24*I*a*b*c^2*d*f^2 + 24*I*b^2*d^3*e + (48*I*a*b*d^3*e - 48*I*a*b*c*d^2*f - 24*I*b^2*d^3)*(f*x + e) + (48*I*a*b*c*d^2*e - 24*I*b^2*c*d^2)*f)*sin(2*f*x + 2*e))*dilog(-e^(I*f*x + I*e)) + (24*(f*x + e)^2*a*b*d^3 + 24*a*b*d^3*e^2 + 24*a*b*c^2*d*f^2 - 24*b^2*d^3*e - 24*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e) - 24*(2*a*b*c*d^2*e - b^2*c*d^2)*f - 24*((f*x + e)^2*a*b*d^3 + a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e) - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*cos(2*f*x + 2*e) + (-24*I*(f*x + e)^2*a*b*d^3 - 24*I*a*b*d^3*e^2 - 24*I*a*b*c^2*d*f^2 + 24*I*b^2*d^3*e + (48*I*a*b*d^3*e - 48*I*a*b*c*d^2*f - 24*I*b^2*d^3)*(f*x + e) + (48*I*a*b*c*d^2*e - 24*I*b^2*c*d^2)*f)*sin(2*f*x + 2*e))*dilog(e^(I*f*x + I*e)) + (4*I*(f*x + e)^3*a*b*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*a*b*d^3*e + 12*I*a*b*c*d^2*f + 6*I*b^2*d^3)*(f*x + e)^2 + (12*I*a*b*d^3*e^2 + 12*I*a*b*c^2*d*f^2 - 12*I*b^2*d^3*e + (-24*I*a*b*c*d^2*e + 12*I*b^2*c*d^2)*f)*(f*x + e) + (-4*I*(f*x + e)^3*a*b*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*a*b*d^3*e - 12*I*a*b*c*d^2*f - 6*I*b^2*d^3)*(f*x + e)^2 + (-12*I*a*b*d^3*e^2 - 12*I*a*b*c^2*d*f^2 + 12*I*b^2*d^3*e + (24*I*a*b*c*d^2*e - 12*I*b^2*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) + 2*(2*(f*x + e)^3*a*b*d^3 + 3*b^2*d^3*e^2 - 6*b^2*c*d^2*e*f + 3*b^2*c^2*d*f^2 - 3*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 6*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (4*I*(f*x + e)^3*a*b*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*a*b*d^3*e + 12*I*a*b*c*d^2*f + 6*I*b^2*d^3)*(f*x + e)^2 + (12*I*a*b*d^3*e^2 + 12*I*a*b*c^2*d*f^2 - 12*I*b^2*d^3*e + (-24*I*a*b*c*d^2*e + 12*I*b^2*c*d^2)*f)*(f*x + e) + (-4*I*(f*x + e)^3*a*b*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*a*b*d^3*e - 12*I*a*b*c*d^2*f - 6*I*b^2*d^3)*(f*x + e)^2 + (-12*I*a*b*d^3*e^2 - 12*I*a*b*c^2*d*f^2 + 12*I*b^2*d^3*e + (24*I*a*b*c*d^2*e - 12*I*b^2*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) + 2*(2*(f*x + e)^3*a*b*d^3 + 3*b^2*d^3*e^2 - 6*b^2*c*d^2*e*f + 3*b^2*c^2*d*f^2 - 3*(2*a*b*d^3*e - 2*a*b*c*d^2*f - b^2*d^3)*(f*x + e)^2 + 6*(a*b*d^3*e^2 + a*b*c^2*d*f^2 - b^2*d^3*e - (2*a*b*c*d^2*e - b^2*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) + 48*(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, -e^(I*f*x + I*e)) + 48*(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, e^(I*f*x + I*e)) + (48*I*(f*x + e)*a*b*d^3 - 48*I*a*b*d^3*e + 48*I*a*b*c*d^2*f + 24*I*b^2*d^3 + (-48*I*(f*x + e)*a*b*d^3 + 48*I*a*b*d^3*e - 48*I*a*b*c*d^2*f - 24*I*b^2*d^3)*cos(2*f*x + 2*e) + 24*(2*(f*x + e)*a*b*d^3 - 2*a*b*d^3*e + 2*a*b*c*d^2*f + b^2*d^3)*sin(2*f*x + 2*e))*polylog(3, -e^(I*f*x + I*e)) + (48*I*(f*x + e)*a*b*d^3 - 48*I*a*b*d^3*e + 48*I*a*b*c*d^2*f + 24*I*b^2*d^3 + (-48*I*(f*x + e)*a*b*d^3 + 48*I*a*b*d^3*e - 48*I*a*b*c*d^2*f - 24*I*b^2*d^3)*cos(2*f*x + 2*e) + 24*(2*(f*x + e)*a*b*d^3 - 2*a*b*d^3*e + 2*a*b*c*d^2*f + b^2*d^3)*sin(2*f*x + 2*e))*polylog(3, e^(I*f*x + I*e)) + ((-2*I*a*b - b^2)*(f*x + e)^4*d^3 + (-8*I*b^2*d^3 - 4*(-2*I*a*b - b^2)*d^3*e - 4*(2*I*a*b + b^2)*c*d^2*f)*(f*x + e)^3 + (24*I*b^2*d^3*e - 6*(2*I*a*b + b^2)*d^3*e^2 - 6*(2*I*a*b + b^2)*c^2*d*f^2 + (-24*I*b^2*c*d^2 - 12*(-2*I*a*b - b^2)*c*d^2*e)*f)*(f*x + e)^2 + (4*b^2*d^3*e^3 - 4*b^2*c^3*f^3 - 24*I*b^2*d^3*e^2 + (12*b^2*c^2*d*e - 24*I*b^2*c^2*d)*f^2 - (12*b^2*c*d^2*e^2 - 48*I*b^2*c*d^2*e)*f)*(f*x + e))*sin(2*f*x + 2*e))/(-4*I*f^3*cos(2*f*x + 2*e) + 4*f^3*sin(2*f*x + 2*e) + 4*I*f^3))/f","B",0
43,1,1945,0,1.992508," ","integrate((d*x+c)^2*(a+b*cot(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(\sin\left(f x + e\right)\right) + \frac{6 \, a b d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{12 \, a b c d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{3 \, {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{3} d^{2} - 6 \, b^{2} d^{2} e^{2} + 12 \, b^{2} c d e f - 6 \, b^{2} c^{2} f^{2} - {\left({\left(6 \, a b - 3 i \, b^{2}\right)} d^{2} e - {\left(6 \, a b - 3 i \, b^{2}\right)} c d f\right)} {\left(f x + e\right)}^{2} + {\left(-3 i \, b^{2} d^{2} e^{2} + 6 i \, b^{2} c d e f - 3 i \, b^{2} c^{2} f^{2}\right)} {\left(f x + e\right)} - {\left(6 \, {\left(f x + e\right)}^{2} a b d^{2} - 6 \, b^{2} d^{2} e + 6 \, b^{2} c d f - 6 \, {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{2}\right)} {\left(f x + e\right)} - 6 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - b^{2} d^{2} e + b^{2} c d f - {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{2}\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 b d^{2} - 6 i \, b^{2} d^{2} e + 6 i \, b^{2} c d f + {\left(-12 i \, a b d^{2} e + 12 i \, a b c d f + 6 i \, b^{2} d^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + {\left(6 \, b^{2} d^{2} e - 6 \, b^{2} c d f - 6 \, {\left(b^{2} d^{2} e - b^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-6 i \, b^{2} d^{2} e + 6 i \, b^{2} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(6 \, {\left(f x + e\right)}^{2} a b d^{2} - 6 \, {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{2}\right)} {\left(f x + e\right)} - 6 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{2}\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 b d^{2} + {\left(12 i \, a b d^{2} e - 12 i \, a b c d f - 6 i \, b^{2} d^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) - {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{3} d^{2} + {\left(6 \, b^{2} d^{2} - {\left(6 \, a b - 3 i \, b^{2}\right)} d^{2} e + {\left(6 \, a b - 3 i \, b^{2}\right)} c d f\right)} {\left(f x + e\right)}^{2} - {\left(3 i \, b^{2} d^{2} e^{2} + 3 i \, b^{2} c^{2} f^{2} + 12 \, b^{2} d^{2} e - 6 \, {\left(i \, b^{2} c d e + 2 \, b^{2} c d\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(12 \, {\left(f x + e\right)} a b d^{2} - 12 \, a b d^{2} e + 12 \, a b c d f + 6 \, b^{2} d^{2} - 6 \, {\left(2 \, {\left(f x + e\right)} a b d^{2} - 2 \, a b d^{2} e + 2 \, a b c d f + b^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-12 i \, {\left(f x + e\right)} a b d^{2} + 12 i \, a b d^{2} e - 12 i \, a b c d f - 6 i \, b^{2} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(12 \, {\left(f x + e\right)} a b d^{2} - 12 \, a b d^{2} e + 12 \, a b c d f + 6 \, b^{2} d^{2} - 6 \, {\left(2 \, {\left(f x + e\right)} a b d^{2} - 2 \, a b d^{2} e + 2 \, a b c d f + b^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-12 i \, {\left(f x + e\right)} a b d^{2} + 12 i \, a b d^{2} e - 12 i \, a b c d f - 6 i \, b^{2} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(3 i \, {\left(f x + e\right)}^{2} a b d^{2} - 3 i \, b^{2} d^{2} e + 3 i \, b^{2} c d f + {\left(-6 i \, a b d^{2} e + 6 i \, a b c d f + 3 i \, b^{2} d^{2}\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} a b d^{2} + 3 i \, b^{2} d^{2} e - 3 i \, b^{2} c d f + {\left(6 i \, a b d^{2} e - 6 i \, a b c d f - 3 i \, b^{2} d^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - b^{2} d^{2} e + b^{2} c d f - {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{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 \, \cos\left(f x + e\right) + 1\right) + {\left(3 i \, {\left(f x + e\right)}^{2} a b d^{2} - 3 i \, b^{2} d^{2} e + 3 i \, b^{2} c d f + {\left(-6 i \, a b d^{2} e + 6 i \, a b c d f + 3 i \, b^{2} d^{2}\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} a b d^{2} + 3 i \, b^{2} d^{2} e - 3 i \, b^{2} c d f + {\left(6 i \, a b d^{2} e - 6 i \, a b c d f - 3 i \, b^{2} d^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left({\left(f x + e\right)}^{2} a b d^{2} - b^{2} d^{2} e + b^{2} c d f - {\left(2 \, a b d^{2} e - 2 \, a b c d f - b^{2} d^{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 \, \cos\left(f x + e\right) + 1\right) + {\left(-12 i \, a b d^{2} \cos\left(2 \, f x + 2 \, e\right) + 12 \, a b d^{2} \sin\left(2 \, f x + 2 \, e\right) + 12 i \, a b d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) + {\left(-12 i \, a b d^{2} \cos\left(2 \, f x + 2 \, e\right) + 12 \, a b d^{2} \sin\left(2 \, f x + 2 \, e\right) + 12 i \, a b d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) + {\left({\left(-2 i \, a b - b^{2}\right)} {\left(f x + e\right)}^{3} d^{2} + {\left(-6 i \, b^{2} d^{2} - 3 \, {\left(-2 i \, a b - b^{2}\right)} d^{2} e - 3 \, {\left(2 i \, a b + b^{2}\right)} c d f\right)} {\left(f x + e\right)}^{2} - {\left(3 \, b^{2} d^{2} e^{2} + 3 \, b^{2} c^{2} f^{2} - 12 i \, b^{2} d^{2} e - {\left(6 \, b^{2} c d e - 12 i \, b^{2} c d\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-3 i \, f^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, f^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 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(sin(f*x + e)) + 6*a*b*d^2*e^2*log(sin(f*x + e))/f^2 - 12*a*b*c*d*e*log(sin(f*x + e))/f + 3*((2*a*b - I*b^2)*(f*x + e)^3*d^2 - 6*b^2*d^2*e^2 + 12*b^2*c*d*e*f - 6*b^2*c^2*f^2 - ((6*a*b - 3*I*b^2)*d^2*e - (6*a*b - 3*I*b^2)*c*d*f)*(f*x + e)^2 + (-3*I*b^2*d^2*e^2 + 6*I*b^2*c*d*e*f - 3*I*b^2*c^2*f^2)*(f*x + e) - (6*(f*x + e)^2*a*b*d^2 - 6*b^2*d^2*e + 6*b^2*c*d*f - 6*(2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e) - 6*((f*x + e)^2*a*b*d^2 - b^2*d^2*e + b^2*c*d*f - (2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e))*cos(2*f*x + 2*e) - (6*I*(f*x + e)^2*a*b*d^2 - 6*I*b^2*d^2*e + 6*I*b^2*c*d*f + (-12*I*a*b*d^2*e + 12*I*a*b*c*d*f + 6*I*b^2*d^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + (6*b^2*d^2*e - 6*b^2*c*d*f - 6*(b^2*d^2*e - b^2*c*d*f)*cos(2*f*x + 2*e) + (-6*I*b^2*d^2*e + 6*I*b^2*c*d*f)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (6*(f*x + e)^2*a*b*d^2 - 6*(2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e) - 6*((f*x + e)^2*a*b*d^2 - (2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e))*cos(2*f*x + 2*e) + (-6*I*(f*x + e)^2*a*b*d^2 + (12*I*a*b*d^2*e - 12*I*a*b*c*d*f - 6*I*b^2*d^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) - ((2*a*b - I*b^2)*(f*x + e)^3*d^2 + (6*b^2*d^2 - (6*a*b - 3*I*b^2)*d^2*e + (6*a*b - 3*I*b^2)*c*d*f)*(f*x + e)^2 - (3*I*b^2*d^2*e^2 + 3*I*b^2*c^2*f^2 + 12*b^2*d^2*e - 6*(I*b^2*c*d*e + 2*b^2*c*d)*f)*(f*x + e))*cos(2*f*x + 2*e) + (12*(f*x + e)*a*b*d^2 - 12*a*b*d^2*e + 12*a*b*c*d*f + 6*b^2*d^2 - 6*(2*(f*x + e)*a*b*d^2 - 2*a*b*d^2*e + 2*a*b*c*d*f + b^2*d^2)*cos(2*f*x + 2*e) + (-12*I*(f*x + e)*a*b*d^2 + 12*I*a*b*d^2*e - 12*I*a*b*c*d*f - 6*I*b^2*d^2)*sin(2*f*x + 2*e))*dilog(-e^(I*f*x + I*e)) + (12*(f*x + e)*a*b*d^2 - 12*a*b*d^2*e + 12*a*b*c*d*f + 6*b^2*d^2 - 6*(2*(f*x + e)*a*b*d^2 - 2*a*b*d^2*e + 2*a*b*c*d*f + b^2*d^2)*cos(2*f*x + 2*e) + (-12*I*(f*x + e)*a*b*d^2 + 12*I*a*b*d^2*e - 12*I*a*b*c*d*f - 6*I*b^2*d^2)*sin(2*f*x + 2*e))*dilog(e^(I*f*x + I*e)) + (3*I*(f*x + e)^2*a*b*d^2 - 3*I*b^2*d^2*e + 3*I*b^2*c*d*f + (-6*I*a*b*d^2*e + 6*I*a*b*c*d*f + 3*I*b^2*d^2)*(f*x + e) + (-3*I*(f*x + e)^2*a*b*d^2 + 3*I*b^2*d^2*e - 3*I*b^2*c*d*f + (6*I*a*b*d^2*e - 6*I*a*b*c*d*f - 3*I*b^2*d^2)*(f*x + e))*cos(2*f*x + 2*e) + 3*((f*x + e)^2*a*b*d^2 - b^2*d^2*e + b^2*c*d*f - (2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (3*I*(f*x + e)^2*a*b*d^2 - 3*I*b^2*d^2*e + 3*I*b^2*c*d*f + (-6*I*a*b*d^2*e + 6*I*a*b*c*d*f + 3*I*b^2*d^2)*(f*x + e) + (-3*I*(f*x + e)^2*a*b*d^2 + 3*I*b^2*d^2*e - 3*I*b^2*c*d*f + (6*I*a*b*d^2*e - 6*I*a*b*c*d*f - 3*I*b^2*d^2)*(f*x + e))*cos(2*f*x + 2*e) + 3*((f*x + e)^2*a*b*d^2 - b^2*d^2*e + b^2*c*d*f - (2*a*b*d^2*e - 2*a*b*c*d*f - b^2*d^2)*(f*x + e))*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) + (-12*I*a*b*d^2*cos(2*f*x + 2*e) + 12*a*b*d^2*sin(2*f*x + 2*e) + 12*I*a*b*d^2)*polylog(3, -e^(I*f*x + I*e)) + (-12*I*a*b*d^2*cos(2*f*x + 2*e) + 12*a*b*d^2*sin(2*f*x + 2*e) + 12*I*a*b*d^2)*polylog(3, e^(I*f*x + I*e)) + ((-2*I*a*b - b^2)*(f*x + e)^3*d^2 + (-6*I*b^2*d^2 - 3*(-2*I*a*b - b^2)*d^2*e - 3*(2*I*a*b + b^2)*c*d*f)*(f*x + e)^2 - (3*b^2*d^2*e^2 + 3*b^2*c^2*f^2 - 12*I*b^2*d^2*e - (6*b^2*c*d*e - 12*I*b^2*c*d)*f)*(f*x + e))*sin(2*f*x + 2*e))/(-3*I*f^2*cos(2*f*x + 2*e) + 3*f^2*sin(2*f*x + 2*e) + 3*I*f^2))/f","B",0
44,1,776,0,1.446625," ","integrate((d*x+c)*(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a^{2} c + \frac{{\left(f x + e\right)}^{2} a^{2} d}{f} - \frac{2 \, {\left(f x + e\right)} a^{2} d e}{f} + 4 \, a b c \log\left(\sin\left(f x + e\right)\right) - \frac{4 \, a b d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{2 \, {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{2} d + 4 \, b^{2} d e - 4 \, b^{2} c f + {\left(2 i \, b^{2} d e - 2 i \, b^{2} c f\right)} {\left(f x + e\right)} - {\left(4 \, {\left(f x + e\right)} a b d + 2 \, b^{2} d - 2 \, {\left(2 \, {\left(f x + e\right)} a b d + b^{2} d\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(4 i \, {\left(f x + e\right)} a b d + 2 i \, b^{2} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + 2 \, {\left(b^{2} d \cos\left(2 \, f x + 2 \, e\right) + i \, b^{2} d \sin\left(2 \, f x + 2 \, e\right) - b^{2} d\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - {\left(4 \, {\left(f x + e\right)} a b d \cos\left(2 \, f x + 2 \, e\right) + 4 i \, {\left(f x + e\right)} a b d \sin\left(2 \, f x + 2 \, e\right) - 4 \, {\left(f x + e\right)} a b d\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) - {\left({\left(2 \, a b - i \, b^{2}\right)} {\left(f x + e\right)}^{2} d - {\left(-2 i \, b^{2} d e + 2 i \, b^{2} c f - 4 \, b^{2} d\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(a b d \cos\left(2 \, f x + 2 \, e\right) + i \, a b d \sin\left(2 \, f x + 2 \, e\right) - a b d\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - 4 \, {\left(a b d \cos\left(2 \, f x + 2 \, e\right) + i \, a b d \sin\left(2 \, f x + 2 \, e\right) - a b d\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(2 i \, {\left(f x + e\right)} a b d + i \, b^{2} d + {\left(-2 i \, {\left(f x + e\right)} a b d - i \, b^{2} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, {\left(f x + e\right)} a b d + b^{2} d\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 \, \cos\left(f x + e\right) + 1\right) + {\left(2 i \, {\left(f x + e\right)} a b d + i \, b^{2} d + {\left(-2 i \, {\left(f x + e\right)} a b d - i \, b^{2} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, {\left(f x + e\right)} a b d + b^{2} d\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 \, \cos\left(f x + e\right) + 1\right) + {\left({\left(-2 i \, a b - b^{2}\right)} {\left(f x + e\right)}^{2} d + {\left(2 \, b^{2} d e - 2 \, b^{2} c f - 4 i \, b^{2} d\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-2 i \, f \cos\left(2 \, f x + 2 \, e\right) + 2 \, f \sin\left(2 \, f x + 2 \, e\right) + 2 i \, f}}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*a^2*c + (f*x + e)^2*a^2*d/f - 2*(f*x + e)*a^2*d*e/f + 4*a*b*c*log(sin(f*x + e)) - 4*a*b*d*e*log(sin(f*x + e))/f + 2*((2*a*b - I*b^2)*(f*x + e)^2*d + 4*b^2*d*e - 4*b^2*c*f + (2*I*b^2*d*e - 2*I*b^2*c*f)*(f*x + e) - (4*(f*x + e)*a*b*d + 2*b^2*d - 2*(2*(f*x + e)*a*b*d + b^2*d)*cos(2*f*x + 2*e) - (4*I*(f*x + e)*a*b*d + 2*I*b^2*d)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + 2*(b^2*d*cos(2*f*x + 2*e) + I*b^2*d*sin(2*f*x + 2*e) - b^2*d)*arctan2(sin(f*x + e), cos(f*x + e) - 1) - (4*(f*x + e)*a*b*d*cos(2*f*x + 2*e) + 4*I*(f*x + e)*a*b*d*sin(2*f*x + 2*e) - 4*(f*x + e)*a*b*d)*arctan2(sin(f*x + e), -cos(f*x + e) + 1) - ((2*a*b - I*b^2)*(f*x + e)^2*d - (-2*I*b^2*d*e + 2*I*b^2*c*f - 4*b^2*d)*(f*x + e))*cos(2*f*x + 2*e) - 4*(a*b*d*cos(2*f*x + 2*e) + I*a*b*d*sin(2*f*x + 2*e) - a*b*d)*dilog(-e^(I*f*x + I*e)) - 4*(a*b*d*cos(2*f*x + 2*e) + I*a*b*d*sin(2*f*x + 2*e) - a*b*d)*dilog(e^(I*f*x + I*e)) + (2*I*(f*x + e)*a*b*d + I*b^2*d + (-2*I*(f*x + e)*a*b*d - I*b^2*d)*cos(2*f*x + 2*e) + (2*(f*x + e)*a*b*d + b^2*d)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (2*I*(f*x + e)*a*b*d + I*b^2*d + (-2*I*(f*x + e)*a*b*d - I*b^2*d)*cos(2*f*x + 2*e) + (2*(f*x + e)*a*b*d + b^2*d)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) + ((-2*I*a*b - b^2)*(f*x + e)^2*d + (2*b^2*d*e - 2*b^2*c*f - 4*I*b^2*d)*(f*x + e))*sin(2*f*x + 2*e))/(-2*I*f*cos(2*f*x + 2*e) + 2*f*sin(2*f*x + 2*e) + 2*I*f))/f","B",0
45,-1,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} - b^{2}\right)} d f x + 2 \, b^{2} d \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} c f + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c 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 + {\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 - b^{2} d\right)} \sin\left(f x + 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(f x + 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(f x + 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(f x + e\right)}\,{d x} - 2 \, {\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 - b^{2} d\right)} \sin\left(f x + 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(f x + 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(f x + 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(f x + 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 - b^2)*d*f*x + 2*b^2*d*sin(2*f*x + 2*e) + (a^2 - b^2)*c*f + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*cos(2*f*x + 2*e)^2 + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*sin(2*f*x + 2*e)^2 - 2*((a^2 - b^2)*d*f*x + (a^2 - b^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(2*(a*b*d*f*x + a*b*c*f - b^2*d)*sin(f*x + 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(f*x + e)^2 + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*sin(f*x + 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(f*x + 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))*integrate(2*(a*b*d*f*x + a*b*c*f - b^2*d)*sin(f*x + 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(f*x + e)^2 + (d^3*f*x^3 + 3*c*d^2*f*x^2 + 3*c^2*d*f*x + c^3*f)*sin(f*x + 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(f*x + 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
47,1,11204,0,35.800228," ","integrate((d*x+c)^3*(a+b*cot(f*x+e))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a^{3} c^{3} + \frac{{\left(f x + e\right)}^{4} a^{3} d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a^{3} d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{3} d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a^{3} d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a^{3} c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a^{3} c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a^{3} c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a^{3} c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a^{3} c^{2} d e}{f} + 12 \, a^{2} b c^{3} \log\left(\sin\left(f x + e\right)\right) - \frac{12 \, a^{2} b d^{3} e^{3} \log\left(\sin\left(f x + e\right)\right)}{f^{3}} + \frac{36 \, a^{2} b c d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{36 \, a^{2} b c^{2} d e \log\left(\sin\left(f x + e\right)\right)}{f} - \frac{4 \, {\left(24 \, a b^{2} d^{3} e^{3} - 24 \, a b^{2} c^{3} f^{3} + {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} - 12 \, b^{3} d^{3} e^{2} - 4 \, {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + 6 \, {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} e f + {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c^{2} d f^{2}\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(6 \, a b^{2} c^{2} d e - b^{3} c^{2} d\right)} f^{2} - 4 \, {\left({\left(-3 i \, a b^{2} - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 i \, a b^{2} + b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c^{2} d e f^{2} + {\left(3 i \, a b^{2} + b^{3}\right)} c^{3} f^{3}\right)} {\left(f x + e\right)} - 24 \, {\left(3 \, a b^{2} c d^{2} e^{2} - b^{3} c d^{2} e\right)} f - {\left(4 \, b^{3} d^{3} e^{3} - 4 \, b^{3} c^{3} f^{3} + 36 \, a b^{2} d^{3} e^{2} + 4 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 12 \, b^{3} d^{3} e + 12 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 12 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 12 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 12 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f + 4 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, b^{3} d^{3} e^{3} + 4 i \, b^{3} c^{3} f^{3} - 36 i \, a b^{2} d^{3} e^{2} + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 12 i \, b^{3} d^{3} e + {\left(-36 i \, a b^{2} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b^{3} c^{2} d e - 36 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(72 i \, a b^{2} d^{3} e - 12 i \, b^{3} d^{3} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-72 i \, a b^{2} c d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(12 i \, b^{3} c d^{2} e^{2} + 72 i \, a b^{2} c d^{2} e - 12 i \, b^{3} c d^{2}\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(8 i \, b^{3} d^{3} e^{3} - 8 i \, b^{3} c^{3} f^{3} + 72 i \, a b^{2} d^{3} e^{2} + {\left(24 i \, a^{2} b - 8 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 24 i \, b^{3} d^{3} e + {\left(72 i \, a b^{2} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(24 i \, b^{3} c^{2} d e + 72 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-144 i \, a b^{2} d^{3} e + 24 i \, b^{3} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} d^{3} e^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c^{2} d f^{2} + {\left(144 i \, a b^{2} c d^{2} + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-24 i \, b^{3} c d^{2} e^{2} - 144 i \, a b^{2} c d^{2} e + 24 i \, b^{3} c d^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(4 \, b^{3} d^{3} e^{3} - 4 \, b^{3} c^{3} f^{3} + 36 \, a b^{2} d^{3} e^{2} - 12 \, b^{3} d^{3} e + 12 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 12 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f + 4 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, b^{3} d^{3} e^{3} + 4 i \, b^{3} c^{3} f^{3} - 36 i \, a b^{2} d^{3} e^{2} + 12 i \, b^{3} d^{3} e + {\left(-12 i \, b^{3} c^{2} d e - 36 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(12 i \, b^{3} c d^{2} e^{2} + 72 i \, a b^{2} c d^{2} e - 12 i \, b^{3} c d^{2}\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(8 i \, b^{3} d^{3} e^{3} - 8 i \, b^{3} c^{3} f^{3} + 72 i \, a b^{2} d^{3} e^{2} - 24 i \, b^{3} d^{3} e + {\left(24 i \, b^{3} c^{2} d e + 72 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-24 i \, b^{3} c d^{2} e^{2} - 144 i \, a b^{2} c d^{2} e + 24 i \, b^{3} c d^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(4 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 12 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} - 12 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + 4 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(4 \, f x + 4 \, e\right) - 8 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(12 i \, a^{2} b - 4 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + {\left(36 i \, a b^{2} d^{3} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{3} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-72 i \, a b^{2} d^{3} e + 12 i \, b^{3} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(72 i \, a b^{2} c d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left({\left(-24 i \, a^{2} b + 8 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + {\left(-72 i \, a b^{2} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} d^{3} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(144 i \, a b^{2} d^{3} e - 24 i \, b^{3} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-144 i \, a b^{2} c d^{2} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} + 4 \, {\left(6 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} - 6 \, {\left(12 \, a b^{2} d^{3} e - 2 \, b^{3} d^{3} - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(6 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}^{2} + 4 \, {\left(18 \, a b^{2} d^{3} e^{2} - 6 \, b^{3} d^{3} e - {\left(-3 i \, a b^{2} - b^{3}\right)} d^{3} e^{3} - {\left(3 i \, a b^{2} + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(6 \, a b^{2} c^{2} d - {\left(-3 i \, a b^{2} - b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(12 \, a b^{2} c d^{2} e - 2 \, b^{3} c d^{2} + {\left(3 i \, a b^{2} + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(2 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} - 12 \, b^{3} d^{3} e^{2} + {\left(24 \, a b^{2} + 8 i \, b^{3}\right)} d^{3} e^{3} - {\left(24 \, a b^{2} + 8 i \, b^{3}\right)} c^{3} f^{3} - {\left(8 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e - 8 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} f - {\left(24 \, a b^{2} - 8 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(12 \, b^{3} d^{3} + 12 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{3} e^{2} + 12 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c^{2} d f^{2} - {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} d^{3} e - {\left(24 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d^{2} e - {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}^{2} - {\left(12 \, b^{3} c^{2} d - {\left(72 \, a b^{2} + 24 i \, b^{3}\right)} c^{2} d e\right)} f^{2} - {\left(24 \, b^{3} d^{3} e - 8 \, {\left(3 i \, a b^{2} + b^{3}\right)} d^{3} e^{3} - 8 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c^{3} f^{3} - {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} d^{3} e^{2} - {\left(24 \, {\left(3 i \, a b^{2} + b^{3}\right)} c^{2} d e + {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c^{2} d\right)} f^{2} - {\left(24 \, b^{3} c d^{2} + 24 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c d^{2} e^{2} - {\left(144 \, a b^{2} - 48 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(24 \, b^{3} c d^{2} e - {\left(72 \, a b^{2} + 24 i \, b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(72 \, a b^{2} d^{3} e - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - 12 \, b^{3} d^{3} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 24 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 24 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f + 12 \, {\left(6 \, a b^{2} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 24 \, {\left(6 \, a b^{2} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72 i \, a b^{2} d^{3} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} + 12 i \, b^{3} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(72 i \, a b^{2} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} + {\left(72 i \, a b^{2} c d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(144 i \, a b^{2} d^{3} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - 24 i \, b^{3} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-144 i \, a b^{2} d^{3} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} e + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} + {\left(-144 i \, a b^{2} c d^{2} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - {\left(72 \, a b^{2} d^{3} e - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - 12 \, b^{3} d^{3} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 24 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 24 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f + 12 \, {\left(6 \, a b^{2} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 24 \, {\left(6 \, a b^{2} d^{3} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72 i \, a b^{2} d^{3} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} + 12 i \, b^{3} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(72 i \, a b^{2} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} + {\left(72 i \, a b^{2} c d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(144 i \, a b^{2} d^{3} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{3} - 24 i \, b^{3} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-144 i \, a b^{2} d^{3} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} e + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)} + {\left(-144 i \, a b^{2} c d^{2} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(2 i \, b^{3} d^{3} e^{3} - 2 i \, b^{3} c^{3} f^{3} + 18 i \, a b^{2} d^{3} e^{2} + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 6 i \, b^{3} d^{3} e + {\left(18 i \, a b^{2} d^{3} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{3} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, b^{3} c^{2} d e + 18 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-36 i \, a b^{2} d^{3} e + 6 i \, b^{3} d^{3} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c^{2} d f^{2} + {\left(36 i \, a b^{2} c d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-6 i \, b^{3} c d^{2} e^{2} - 36 i \, a b^{2} c d^{2} e + 6 i \, b^{3} c d^{2}\right)} f + {\left(2 i \, b^{3} d^{3} e^{3} - 2 i \, b^{3} c^{3} f^{3} + 18 i \, a b^{2} d^{3} e^{2} + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 6 i \, b^{3} d^{3} e + {\left(18 i \, a b^{2} d^{3} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{3} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, b^{3} c^{2} d e + 18 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-36 i \, a b^{2} d^{3} e + 6 i \, b^{3} d^{3} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c^{2} d f^{2} + {\left(36 i \, a b^{2} c d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-6 i \, b^{3} c d^{2} e^{2} - 36 i \, a b^{2} c d^{2} e + 6 i \, b^{3} c d^{2}\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-4 i \, b^{3} d^{3} e^{3} + 4 i \, b^{3} c^{3} f^{3} - 36 i \, a b^{2} d^{3} e^{2} + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 12 i \, b^{3} d^{3} e + {\left(-36 i \, a b^{2} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b^{3} c^{2} d e - 36 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(72 i \, a b^{2} d^{3} e - 12 i \, b^{3} d^{3} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-72 i \, a b^{2} c d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(12 i \, b^{3} c d^{2} e^{2} + 72 i \, a b^{2} c d^{2} e - 12 i \, b^{3} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\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 \, \cos\left(f x + e\right) + 1\right) + {\left(2 i \, b^{3} d^{3} e^{3} - 2 i \, b^{3} c^{3} f^{3} + 18 i \, a b^{2} d^{3} e^{2} + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 6 i \, b^{3} d^{3} e + {\left(18 i \, a b^{2} d^{3} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{3} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, b^{3} c^{2} d e + 18 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-36 i \, a b^{2} d^{3} e + 6 i \, b^{3} d^{3} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c^{2} d f^{2} + {\left(36 i \, a b^{2} c d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-6 i \, b^{3} c d^{2} e^{2} - 36 i \, a b^{2} c d^{2} e + 6 i \, b^{3} c d^{2}\right)} f + {\left(2 i \, b^{3} d^{3} e^{3} - 2 i \, b^{3} c^{3} f^{3} + 18 i \, a b^{2} d^{3} e^{2} + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 6 i \, b^{3} d^{3} e + {\left(18 i \, a b^{2} d^{3} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{3} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(6 i \, b^{3} c^{2} d e + 18 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(-36 i \, a b^{2} d^{3} e + 6 i \, b^{3} d^{3} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c^{2} d f^{2} + {\left(36 i \, a b^{2} c d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-6 i \, b^{3} c d^{2} e^{2} - 36 i \, a b^{2} c d^{2} e + 6 i \, b^{3} c d^{2}\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-4 i \, b^{3} d^{3} e^{3} + 4 i \, b^{3} c^{3} f^{3} - 36 i \, a b^{2} d^{3} e^{2} + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} + 12 i \, b^{3} d^{3} e + {\left(-36 i \, a b^{2} d^{3} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{3} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b^{3} c^{2} d e - 36 i \, a b^{2} c^{2} d\right)} f^{2} + {\left(72 i \, a b^{2} d^{3} e - 12 i \, b^{3} d^{3} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c^{2} d f^{2} + {\left(-72 i \, a b^{2} c d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(12 i \, b^{3} c d^{2} e^{2} + 72 i \, a b^{2} c d^{2} e - 12 i \, b^{3} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(b^{3} d^{3} e^{3} - b^{3} c^{3} f^{3} + 9 \, a b^{2} d^{3} e^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{3} d^{3} - 3 \, b^{3} d^{3} e + 3 \, {\left(3 \, a b^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(b^{3} c^{2} d e + 3 \, a b^{2} c^{2} d\right)} f^{2} - 3 \, {\left(6 \, a b^{2} d^{3} e - b^{3} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d f^{2} - 2 \, {\left(3 \, a b^{2} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} - 3 \, {\left(b^{3} c d^{2} e^{2} + 6 \, a b^{2} c d^{2} e - b^{3} c d^{2}\right)} f\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 \, \cos\left(f x + e\right) + 1\right) - {\left(24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(4 \, f x + 4 \, e\right) - 48 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} \sin\left(2 \, f x + 2 \, e\right) + 24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, f x + i \, e\right)}) - {\left(24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(4 \, f x + 4 \, e\right) - 48 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} \sin\left(2 \, f x + 2 \, e\right) + 24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, f x + i \, e\right)}) + {\left(72 i \, a b^{2} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f + {\left(72 i \, a b^{2} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-144 i \, a b^{2} d^{3} + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} e + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 24 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(4 \, f x + 4 \, e\right) + 48 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) + {\left(72 i \, a b^{2} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f + {\left(72 i \, a b^{2} d^{3} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{3} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d^{2} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-144 i \, a b^{2} d^{3} + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} {\left(f x + e\right)} d^{3} + {\left(144 i \, a^{2} b - 48 i \, b^{3}\right)} d^{3} e + {\left(-144 i \, a^{2} b + 48 i \, b^{3}\right)} c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) - 24 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(4 \, f x + 4 \, e\right) + 48 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3} e + {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) + {\left({\left(3 i \, a^{2} b + 3 \, a b^{2} - i \, b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} + {\left(24 i \, a b^{2} d^{3} + {\left(-12 i \, a^{2} b - 12 \, a b^{2} + 4 i \, b^{3}\right)} d^{3} e + {\left(12 i \, a^{2} b + 12 \, a b^{2} - 4 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\left(-72 i \, a b^{2} d^{3} e + 12 i \, b^{3} d^{3} + {\left(18 i \, a^{2} b + 18 \, a b^{2} - 6 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{2} b + 18 \, a b^{2} - 6 i \, b^{3}\right)} c^{2} d f^{2} + {\left(72 i \, a b^{2} c d^{2} + {\left(-36 i \, a^{2} b - 36 \, a b^{2} + 12 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}^{2} + {\left(72 i \, a b^{2} d^{3} e^{2} - 24 i \, b^{3} d^{3} e - {\left(12 \, a b^{2} - 4 i \, b^{3}\right)} d^{3} e^{3} + {\left(12 \, a b^{2} - 4 i \, b^{3}\right)} c^{3} f^{3} + {\left(72 i \, a b^{2} c^{2} d - {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} c^{2} d e\right)} f^{2} + {\left(-144 i \, a b^{2} c d^{2} e + 24 i \, b^{3} c d^{2} + {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} c d^{2} e^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left({\left(-6 i \, a^{2} b - 6 \, a b^{2} + 2 i \, b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} + 12 i \, b^{3} d^{3} e^{2} - 8 \, {\left(3 i \, a b^{2} - b^{3}\right)} d^{3} e^{3} - 8 \, {\left(-3 i \, a b^{2} + b^{3}\right)} c^{3} f^{3} + {\left({\left(24 i \, a^{2} b + 24 \, a b^{2} - 8 i \, b^{3}\right)} d^{3} e + {\left(-24 i \, a^{2} b - 24 \, a b^{2} + 8 i \, b^{3}\right)} c d^{2} f - 8 \, {\left(3 i \, a b^{2} + b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{3} + {\left(-12 i \, b^{3} d^{3} + {\left(-36 i \, a^{2} b - 36 \, a b^{2} + 12 i \, b^{3}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b - 36 \, a b^{2} + 12 i \, b^{3}\right)} c^{2} d f^{2} - 24 \, {\left(-3 i \, a b^{2} - b^{3}\right)} d^{3} e + {\left({\left(72 i \, a^{2} b + 72 \, a b^{2} - 24 i \, b^{3}\right)} c d^{2} e - 24 \, {\left(3 i \, a b^{2} + b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}^{2} - 12 \, {\left(-i \, b^{3} c^{2} d + 2 \, {\left(3 i \, a b^{2} - b^{3}\right)} c^{2} d e\right)} f^{2} + {\left(24 i \, b^{3} d^{3} e + {\left(24 \, a b^{2} - 8 i \, b^{3}\right)} d^{3} e^{3} - {\left(24 \, a b^{2} - 8 i \, b^{3}\right)} c^{3} f^{3} - 24 \, {\left(3 i \, a b^{2} + b^{3}\right)} d^{3} e^{2} + {\left({\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c^{2} d e - 24 \, {\left(3 i \, a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} + {\left(-24 i \, b^{3} c d^{2} - {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c d^{2} e^{2} - 48 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)} + {\left(-24 i \, b^{3} c d^{2} e - 24 \, {\left(-3 i \, a b^{2} + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-4 i \, f^{3} \cos\left(4 \, f x + 4 \, e\right) + 8 i \, f^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 \, f^{3} \sin\left(4 \, f x + 4 \, e\right) - 8 \, f^{3} \sin\left(2 \, f x + 2 \, e\right) - 4 i \, f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a^3*c^3 + (f*x + e)^4*a^3*d^3/f^3 - 4*(f*x + e)^3*a^3*d^3*e/f^3 + 6*(f*x + e)^2*a^3*d^3*e^2/f^3 - 4*(f*x + e)*a^3*d^3*e^3/f^3 + 4*(f*x + e)^3*a^3*c*d^2/f^2 - 12*(f*x + e)^2*a^3*c*d^2*e/f^2 + 12*(f*x + e)*a^3*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a^3*c^2*d/f - 12*(f*x + e)*a^3*c^2*d*e/f + 12*a^2*b*c^3*log(sin(f*x + e)) - 12*a^2*b*d^3*e^3*log(sin(f*x + e))/f^3 + 36*a^2*b*c*d^2*e^2*log(sin(f*x + e))/f^2 - 36*a^2*b*c^2*d*e*log(sin(f*x + e))/f - 4*(24*a*b^2*d^3*e^3 - 24*a*b^2*c^3*f^3 + (3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^4*d^3 - 12*b^3*d^3*e^2 - 4*((3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e - (3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*f)*(f*x + e)^3 + 6*((3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e^2 - 2*(3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*e*f + (3*a^2*b - 3*I*a*b^2 - b^3)*c^2*d*f^2)*(f*x + e)^2 + 12*(6*a*b^2*c^2*d*e - b^3*c^2*d)*f^2 - 4*((-3*I*a*b^2 - b^3)*d^3*e^3 + 3*(3*I*a*b^2 + b^3)*c*d^2*e^2*f + 3*(-3*I*a*b^2 - b^3)*c^2*d*e*f^2 + (3*I*a*b^2 + b^3)*c^3*f^3)*(f*x + e) - 24*(3*a*b^2*c*d^2*e^2 - b^3*c*d^2*e)*f - (4*b^3*d^3*e^3 - 4*b^3*c^3*f^3 + 36*a*b^2*d^3*e^2 + 4*(3*a^2*b - b^3)*(f*x + e)^3*d^3 - 12*b^3*d^3*e + 12*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 12*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 12*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 12*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f + 4*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*cos(4*f*x + 4*e) - 8*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*cos(2*f*x + 2*e) - (-4*I*b^3*d^3*e^3 + 4*I*b^3*c^3*f^3 - 36*I*a*b^2*d^3*e^2 + (-12*I*a^2*b + 4*I*b^3)*(f*x + e)^3*d^3 + 12*I*b^3*d^3*e + (-36*I*a*b^2*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e + (-36*I*a^2*b + 12*I*b^3)*c*d^2*f)*(f*x + e)^2 + (-12*I*b^3*c^2*d*e - 36*I*a*b^2*c^2*d)*f^2 + (72*I*a*b^2*d^3*e - 12*I*b^3*d^3 + (-36*I*a^2*b + 12*I*b^3)*d^3*e^2 + (-36*I*a^2*b + 12*I*b^3)*c^2*d*f^2 + (-72*I*a*b^2*c*d^2 + (72*I*a^2*b - 24*I*b^3)*c*d^2*e)*f)*(f*x + e) + (12*I*b^3*c*d^2*e^2 + 72*I*a*b^2*c*d^2*e - 12*I*b^3*c*d^2)*f)*sin(4*f*x + 4*e) - (8*I*b^3*d^3*e^3 - 8*I*b^3*c^3*f^3 + 72*I*a*b^2*d^3*e^2 + (24*I*a^2*b - 8*I*b^3)*(f*x + e)^3*d^3 - 24*I*b^3*d^3*e + (72*I*a*b^2*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f)*(f*x + e)^2 + (24*I*b^3*c^2*d*e + 72*I*a*b^2*c^2*d)*f^2 + (-144*I*a*b^2*d^3*e + 24*I*b^3*d^3 + (72*I*a^2*b - 24*I*b^3)*d^3*e^2 + (72*I*a^2*b - 24*I*b^3)*c^2*d*f^2 + (144*I*a*b^2*c*d^2 + (-144*I*a^2*b + 48*I*b^3)*c*d^2*e)*f)*(f*x + e) + (-24*I*b^3*c*d^2*e^2 - 144*I*a*b^2*c*d^2*e + 24*I*b^3*c*d^2)*f)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (4*b^3*d^3*e^3 - 4*b^3*c^3*f^3 + 36*a*b^2*d^3*e^2 - 12*b^3*d^3*e + 12*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 12*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f + 4*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 - 3*b^3*d^3*e + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*cos(4*f*x + 4*e) - 8*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 - 3*b^3*d^3*e + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*cos(2*f*x + 2*e) - (-4*I*b^3*d^3*e^3 + 4*I*b^3*c^3*f^3 - 36*I*a*b^2*d^3*e^2 + 12*I*b^3*d^3*e + (-12*I*b^3*c^2*d*e - 36*I*a*b^2*c^2*d)*f^2 + (12*I*b^3*c*d^2*e^2 + 72*I*a*b^2*c*d^2*e - 12*I*b^3*c*d^2)*f)*sin(4*f*x + 4*e) - (8*I*b^3*d^3*e^3 - 8*I*b^3*c^3*f^3 + 72*I*a*b^2*d^3*e^2 - 24*I*b^3*d^3*e + (24*I*b^3*c^2*d*e + 72*I*a*b^2*c^2*d)*f^2 + (-24*I*b^3*c*d^2*e^2 - 144*I*a*b^2*c*d^2*e + 24*I*b^3*c*d^2)*f)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (4*(3*a^2*b - b^3)*(f*x + e)^3*d^3 + 12*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 - 12*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) + 4*((3*a^2*b - b^3)*(f*x + e)^3*d^3 + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e))*cos(4*f*x + 4*e) - 8*((3*a^2*b - b^3)*(f*x + e)^3*d^3 + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e))*cos(2*f*x + 2*e) + ((12*I*a^2*b - 4*I*b^3)*(f*x + e)^3*d^3 + (36*I*a*b^2*d^3 + (-36*I*a^2*b + 12*I*b^3)*d^3*e + (36*I*a^2*b - 12*I*b^3)*c*d^2*f)*(f*x + e)^2 + (-72*I*a*b^2*d^3*e + 12*I*b^3*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e^2 + (36*I*a^2*b - 12*I*b^3)*c^2*d*f^2 + (72*I*a*b^2*c*d^2 + (-72*I*a^2*b + 24*I*b^3)*c*d^2*e)*f)*(f*x + e))*sin(4*f*x + 4*e) + ((-24*I*a^2*b + 8*I*b^3)*(f*x + e)^3*d^3 + (-72*I*a*b^2*d^3 + (72*I*a^2*b - 24*I*b^3)*d^3*e + (-72*I*a^2*b + 24*I*b^3)*c*d^2*f)*(f*x + e)^2 + (144*I*a*b^2*d^3*e - 24*I*b^3*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e^2 + (-72*I*a^2*b + 24*I*b^3)*c^2*d*f^2 + (-144*I*a*b^2*c*d^2 + (144*I*a^2*b - 48*I*b^3)*c*d^2*e)*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + ((3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^4*d^3 + 4*(6*a*b^2*d^3 - (3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e + (3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*f)*(f*x + e)^3 - 6*(12*a*b^2*d^3*e - 2*b^3*d^3 - (3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e^2 - (3*a^2*b - 3*I*a*b^2 - b^3)*c^2*d*f^2 - 2*(6*a*b^2*c*d^2 - (3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*e)*f)*(f*x + e)^2 + 4*(18*a*b^2*d^3*e^2 - 6*b^3*d^3*e - (-3*I*a*b^2 - b^3)*d^3*e^3 - (3*I*a*b^2 + b^3)*c^3*f^3 + 3*(6*a*b^2*c^2*d - (-3*I*a*b^2 - b^3)*c^2*d*e)*f^2 - 3*(12*a*b^2*c*d^2*e - 2*b^3*c*d^2 + (3*I*a*b^2 + b^3)*c*d^2*e^2)*f)*(f*x + e))*cos(4*f*x + 4*e) - (2*(3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^4*d^3 - 12*b^3*d^3*e^2 + (24*a*b^2 + 8*I*b^3)*d^3*e^3 - (24*a*b^2 + 8*I*b^3)*c^3*f^3 - (8*(3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e - 8*(3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*f - (24*a*b^2 - 8*I*b^3)*d^3)*(f*x + e)^3 + (12*b^3*d^3 + 12*(3*a^2*b - 3*I*a*b^2 - b^3)*d^3*e^2 + 12*(3*a^2*b - 3*I*a*b^2 - b^3)*c^2*d*f^2 - (72*a*b^2 - 24*I*b^3)*d^3*e - (24*(3*a^2*b - 3*I*a*b^2 - b^3)*c*d^2*e - (72*a*b^2 - 24*I*b^3)*c*d^2)*f)*(f*x + e)^2 - (12*b^3*c^2*d - (72*a*b^2 + 24*I*b^3)*c^2*d*e)*f^2 - (24*b^3*d^3*e - 8*(3*I*a*b^2 + b^3)*d^3*e^3 - 8*(-3*I*a*b^2 - b^3)*c^3*f^3 - (72*a*b^2 - 24*I*b^3)*d^3*e^2 - (24*(3*I*a*b^2 + b^3)*c^2*d*e + (72*a*b^2 - 24*I*b^3)*c^2*d)*f^2 - (24*b^3*c*d^2 + 24*(-3*I*a*b^2 - b^3)*c*d^2*e^2 - (144*a*b^2 - 48*I*b^3)*c*d^2*e)*f)*(f*x + e) + (24*b^3*c*d^2*e - (72*a*b^2 + 24*I*b^3)*c*d^2*e^2)*f)*cos(2*f*x + 2*e) - (72*a*b^2*d^3*e - 12*(3*a^2*b - b^3)*(f*x + e)^2*d^3 - 12*b^3*d^3 - 12*(3*a^2*b - b^3)*d^3*e^2 - 12*(3*a^2*b - b^3)*c^2*d*f^2 - 24*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 24*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f + 12*(6*a*b^2*d^3*e - (3*a^2*b - b^3)*(f*x + e)^2*d^3 - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*cos(4*f*x + 4*e) - 24*(6*a*b^2*d^3*e - (3*a^2*b - b^3)*(f*x + e)^2*d^3 - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*cos(2*f*x + 2*e) - (-72*I*a*b^2*d^3*e + (36*I*a^2*b - 12*I*b^3)*(f*x + e)^2*d^3 + 12*I*b^3*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e^2 + (36*I*a^2*b - 12*I*b^3)*c^2*d*f^2 + (72*I*a*b^2*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f)*(f*x + e) + (72*I*a*b^2*c*d^2 + (-72*I*a^2*b + 24*I*b^3)*c*d^2*e)*f)*sin(4*f*x + 4*e) - (144*I*a*b^2*d^3*e + (-72*I*a^2*b + 24*I*b^3)*(f*x + e)^2*d^3 - 24*I*b^3*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e^2 + (-72*I*a^2*b + 24*I*b^3)*c^2*d*f^2 + (-144*I*a*b^2*d^3 + (144*I*a^2*b - 48*I*b^3)*d^3*e + (-144*I*a^2*b + 48*I*b^3)*c*d^2*f)*(f*x + e) + (-144*I*a*b^2*c*d^2 + (144*I*a^2*b - 48*I*b^3)*c*d^2*e)*f)*sin(2*f*x + 2*e))*dilog(-e^(I*f*x + I*e)) - (72*a*b^2*d^3*e - 12*(3*a^2*b - b^3)*(f*x + e)^2*d^3 - 12*b^3*d^3 - 12*(3*a^2*b - b^3)*d^3*e^2 - 12*(3*a^2*b - b^3)*c^2*d*f^2 - 24*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 24*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f + 12*(6*a*b^2*d^3*e - (3*a^2*b - b^3)*(f*x + e)^2*d^3 - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*cos(4*f*x + 4*e) - 24*(6*a*b^2*d^3*e - (3*a^2*b - b^3)*(f*x + e)^2*d^3 - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e) - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*cos(2*f*x + 2*e) - (-72*I*a*b^2*d^3*e + (36*I*a^2*b - 12*I*b^3)*(f*x + e)^2*d^3 + 12*I*b^3*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e^2 + (36*I*a^2*b - 12*I*b^3)*c^2*d*f^2 + (72*I*a*b^2*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f)*(f*x + e) + (72*I*a*b^2*c*d^2 + (-72*I*a^2*b + 24*I*b^3)*c*d^2*e)*f)*sin(4*f*x + 4*e) - (144*I*a*b^2*d^3*e + (-72*I*a^2*b + 24*I*b^3)*(f*x + e)^2*d^3 - 24*I*b^3*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e^2 + (-72*I*a^2*b + 24*I*b^3)*c^2*d*f^2 + (-144*I*a*b^2*d^3 + (144*I*a^2*b - 48*I*b^3)*d^3*e + (-144*I*a^2*b + 48*I*b^3)*c*d^2*f)*(f*x + e) + (-144*I*a*b^2*c*d^2 + (144*I*a^2*b - 48*I*b^3)*c*d^2*e)*f)*sin(2*f*x + 2*e))*dilog(e^(I*f*x + I*e)) + (2*I*b^3*d^3*e^3 - 2*I*b^3*c^3*f^3 + 18*I*a*b^2*d^3*e^2 + (6*I*a^2*b - 2*I*b^3)*(f*x + e)^3*d^3 - 6*I*b^3*d^3*e + (18*I*a*b^2*d^3 + (-18*I*a^2*b + 6*I*b^3)*d^3*e + (18*I*a^2*b - 6*I*b^3)*c*d^2*f)*(f*x + e)^2 + (6*I*b^3*c^2*d*e + 18*I*a*b^2*c^2*d)*f^2 + (-36*I*a*b^2*d^3*e + 6*I*b^3*d^3 + (18*I*a^2*b - 6*I*b^3)*d^3*e^2 + (18*I*a^2*b - 6*I*b^3)*c^2*d*f^2 + (36*I*a*b^2*c*d^2 + (-36*I*a^2*b + 12*I*b^3)*c*d^2*e)*f)*(f*x + e) + (-6*I*b^3*c*d^2*e^2 - 36*I*a*b^2*c*d^2*e + 6*I*b^3*c*d^2)*f + (2*I*b^3*d^3*e^3 - 2*I*b^3*c^3*f^3 + 18*I*a*b^2*d^3*e^2 + (6*I*a^2*b - 2*I*b^3)*(f*x + e)^3*d^3 - 6*I*b^3*d^3*e + (18*I*a*b^2*d^3 + (-18*I*a^2*b + 6*I*b^3)*d^3*e + (18*I*a^2*b - 6*I*b^3)*c*d^2*f)*(f*x + e)^2 + (6*I*b^3*c^2*d*e + 18*I*a*b^2*c^2*d)*f^2 + (-36*I*a*b^2*d^3*e + 6*I*b^3*d^3 + (18*I*a^2*b - 6*I*b^3)*d^3*e^2 + (18*I*a^2*b - 6*I*b^3)*c^2*d*f^2 + (36*I*a*b^2*c*d^2 + (-36*I*a^2*b + 12*I*b^3)*c*d^2*e)*f)*(f*x + e) + (-6*I*b^3*c*d^2*e^2 - 36*I*a*b^2*c*d^2*e + 6*I*b^3*c*d^2)*f)*cos(4*f*x + 4*e) + (-4*I*b^3*d^3*e^3 + 4*I*b^3*c^3*f^3 - 36*I*a*b^2*d^3*e^2 + (-12*I*a^2*b + 4*I*b^3)*(f*x + e)^3*d^3 + 12*I*b^3*d^3*e + (-36*I*a*b^2*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e + (-36*I*a^2*b + 12*I*b^3)*c*d^2*f)*(f*x + e)^2 + (-12*I*b^3*c^2*d*e - 36*I*a*b^2*c^2*d)*f^2 + (72*I*a*b^2*d^3*e - 12*I*b^3*d^3 + (-36*I*a^2*b + 12*I*b^3)*d^3*e^2 + (-36*I*a^2*b + 12*I*b^3)*c^2*d*f^2 + (-72*I*a*b^2*c*d^2 + (72*I*a^2*b - 24*I*b^3)*c*d^2*e)*f)*(f*x + e) + (12*I*b^3*c*d^2*e^2 + 72*I*a*b^2*c*d^2*e - 12*I*b^3*c*d^2)*f)*cos(2*f*x + 2*e) - 2*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*sin(4*f*x + 4*e) + 4*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (2*I*b^3*d^3*e^3 - 2*I*b^3*c^3*f^3 + 18*I*a*b^2*d^3*e^2 + (6*I*a^2*b - 2*I*b^3)*(f*x + e)^3*d^3 - 6*I*b^3*d^3*e + (18*I*a*b^2*d^3 + (-18*I*a^2*b + 6*I*b^3)*d^3*e + (18*I*a^2*b - 6*I*b^3)*c*d^2*f)*(f*x + e)^2 + (6*I*b^3*c^2*d*e + 18*I*a*b^2*c^2*d)*f^2 + (-36*I*a*b^2*d^3*e + 6*I*b^3*d^3 + (18*I*a^2*b - 6*I*b^3)*d^3*e^2 + (18*I*a^2*b - 6*I*b^3)*c^2*d*f^2 + (36*I*a*b^2*c*d^2 + (-36*I*a^2*b + 12*I*b^3)*c*d^2*e)*f)*(f*x + e) + (-6*I*b^3*c*d^2*e^2 - 36*I*a*b^2*c*d^2*e + 6*I*b^3*c*d^2)*f + (2*I*b^3*d^3*e^3 - 2*I*b^3*c^3*f^3 + 18*I*a*b^2*d^3*e^2 + (6*I*a^2*b - 2*I*b^3)*(f*x + e)^3*d^3 - 6*I*b^3*d^3*e + (18*I*a*b^2*d^3 + (-18*I*a^2*b + 6*I*b^3)*d^3*e + (18*I*a^2*b - 6*I*b^3)*c*d^2*f)*(f*x + e)^2 + (6*I*b^3*c^2*d*e + 18*I*a*b^2*c^2*d)*f^2 + (-36*I*a*b^2*d^3*e + 6*I*b^3*d^3 + (18*I*a^2*b - 6*I*b^3)*d^3*e^2 + (18*I*a^2*b - 6*I*b^3)*c^2*d*f^2 + (36*I*a*b^2*c*d^2 + (-36*I*a^2*b + 12*I*b^3)*c*d^2*e)*f)*(f*x + e) + (-6*I*b^3*c*d^2*e^2 - 36*I*a*b^2*c*d^2*e + 6*I*b^3*c*d^2)*f)*cos(4*f*x + 4*e) + (-4*I*b^3*d^3*e^3 + 4*I*b^3*c^3*f^3 - 36*I*a*b^2*d^3*e^2 + (-12*I*a^2*b + 4*I*b^3)*(f*x + e)^3*d^3 + 12*I*b^3*d^3*e + (-36*I*a*b^2*d^3 + (36*I*a^2*b - 12*I*b^3)*d^3*e + (-36*I*a^2*b + 12*I*b^3)*c*d^2*f)*(f*x + e)^2 + (-12*I*b^3*c^2*d*e - 36*I*a*b^2*c^2*d)*f^2 + (72*I*a*b^2*d^3*e - 12*I*b^3*d^3 + (-36*I*a^2*b + 12*I*b^3)*d^3*e^2 + (-36*I*a^2*b + 12*I*b^3)*c^2*d*f^2 + (-72*I*a*b^2*c*d^2 + (72*I*a^2*b - 24*I*b^3)*c*d^2*e)*f)*(f*x + e) + (12*I*b^3*c*d^2*e^2 + 72*I*a*b^2*c*d^2*e - 12*I*b^3*c*d^2)*f)*cos(2*f*x + 2*e) - 2*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*sin(4*f*x + 4*e) + 4*(b^3*d^3*e^3 - b^3*c^3*f^3 + 9*a*b^2*d^3*e^2 + (3*a^2*b - b^3)*(f*x + e)^3*d^3 - 3*b^3*d^3*e + 3*(3*a*b^2*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*(f*x + e)^2 + 3*(b^3*c^2*d*e + 3*a*b^2*c^2*d)*f^2 - 3*(6*a*b^2*d^3*e - b^3*d^3 - (3*a^2*b - b^3)*d^3*e^2 - (3*a^2*b - b^3)*c^2*d*f^2 - 2*(3*a*b^2*c*d^2 - (3*a^2*b - b^3)*c*d^2*e)*f)*(f*x + e) - 3*(b^3*c*d^2*e^2 + 6*a*b^2*c*d^2*e - b^3*c*d^2)*f)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - (24*(3*a^2*b - b^3)*d^3*cos(4*f*x + 4*e) - 48*(3*a^2*b - b^3)*d^3*cos(2*f*x + 2*e) - (-72*I*a^2*b + 24*I*b^3)*d^3*sin(4*f*x + 4*e) - (144*I*a^2*b - 48*I*b^3)*d^3*sin(2*f*x + 2*e) + 24*(3*a^2*b - b^3)*d^3)*polylog(4, -e^(I*f*x + I*e)) - (24*(3*a^2*b - b^3)*d^3*cos(4*f*x + 4*e) - 48*(3*a^2*b - b^3)*d^3*cos(2*f*x + 2*e) - (-72*I*a^2*b + 24*I*b^3)*d^3*sin(4*f*x + 4*e) - (144*I*a^2*b - 48*I*b^3)*d^3*sin(2*f*x + 2*e) + 24*(3*a^2*b - b^3)*d^3)*polylog(4, e^(I*f*x + I*e)) + (72*I*a*b^2*d^3 + (72*I*a^2*b - 24*I*b^3)*(f*x + e)*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f + (72*I*a*b^2*d^3 + (72*I*a^2*b - 24*I*b^3)*(f*x + e)*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f)*cos(4*f*x + 4*e) + (-144*I*a*b^2*d^3 + (-144*I*a^2*b + 48*I*b^3)*(f*x + e)*d^3 + (144*I*a^2*b - 48*I*b^3)*d^3*e + (-144*I*a^2*b + 48*I*b^3)*c*d^2*f)*cos(2*f*x + 2*e) - 24*(3*a*b^2*d^3 + (3*a^2*b - b^3)*(f*x + e)*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*sin(4*f*x + 4*e) + 48*(3*a*b^2*d^3 + (3*a^2*b - b^3)*(f*x + e)*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, -e^(I*f*x + I*e)) + (72*I*a*b^2*d^3 + (72*I*a^2*b - 24*I*b^3)*(f*x + e)*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f + (72*I*a*b^2*d^3 + (72*I*a^2*b - 24*I*b^3)*(f*x + e)*d^3 + (-72*I*a^2*b + 24*I*b^3)*d^3*e + (72*I*a^2*b - 24*I*b^3)*c*d^2*f)*cos(4*f*x + 4*e) + (-144*I*a*b^2*d^3 + (-144*I*a^2*b + 48*I*b^3)*(f*x + e)*d^3 + (144*I*a^2*b - 48*I*b^3)*d^3*e + (-144*I*a^2*b + 48*I*b^3)*c*d^2*f)*cos(2*f*x + 2*e) - 24*(3*a*b^2*d^3 + (3*a^2*b - b^3)*(f*x + e)*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*sin(4*f*x + 4*e) + 48*(3*a*b^2*d^3 + (3*a^2*b - b^3)*(f*x + e)*d^3 - (3*a^2*b - b^3)*d^3*e + (3*a^2*b - b^3)*c*d^2*f)*sin(2*f*x + 2*e))*polylog(3, e^(I*f*x + I*e)) + ((3*I*a^2*b + 3*a*b^2 - I*b^3)*(f*x + e)^4*d^3 + (24*I*a*b^2*d^3 + (-12*I*a^2*b - 12*a*b^2 + 4*I*b^3)*d^3*e + (12*I*a^2*b + 12*a*b^2 - 4*I*b^3)*c*d^2*f)*(f*x + e)^3 + (-72*I*a*b^2*d^3*e + 12*I*b^3*d^3 + (18*I*a^2*b + 18*a*b^2 - 6*I*b^3)*d^3*e^2 + (18*I*a^2*b + 18*a*b^2 - 6*I*b^3)*c^2*d*f^2 + (72*I*a*b^2*c*d^2 + (-36*I*a^2*b - 36*a*b^2 + 12*I*b^3)*c*d^2*e)*f)*(f*x + e)^2 + (72*I*a*b^2*d^3*e^2 - 24*I*b^3*d^3*e - (12*a*b^2 - 4*I*b^3)*d^3*e^3 + (12*a*b^2 - 4*I*b^3)*c^3*f^3 + (72*I*a*b^2*c^2*d - (36*a*b^2 - 12*I*b^3)*c^2*d*e)*f^2 + (-144*I*a*b^2*c*d^2*e + 24*I*b^3*c*d^2 + (36*a*b^2 - 12*I*b^3)*c*d^2*e^2)*f)*(f*x + e))*sin(4*f*x + 4*e) + ((-6*I*a^2*b - 6*a*b^2 + 2*I*b^3)*(f*x + e)^4*d^3 + 12*I*b^3*d^3*e^2 - 8*(3*I*a*b^2 - b^3)*d^3*e^3 - 8*(-3*I*a*b^2 + b^3)*c^3*f^3 + ((24*I*a^2*b + 24*a*b^2 - 8*I*b^3)*d^3*e + (-24*I*a^2*b - 24*a*b^2 + 8*I*b^3)*c*d^2*f - 8*(3*I*a*b^2 + b^3)*d^3)*(f*x + e)^3 + (-12*I*b^3*d^3 + (-36*I*a^2*b - 36*a*b^2 + 12*I*b^3)*d^3*e^2 + (-36*I*a^2*b - 36*a*b^2 + 12*I*b^3)*c^2*d*f^2 - 24*(-3*I*a*b^2 - b^3)*d^3*e + ((72*I*a^2*b + 72*a*b^2 - 24*I*b^3)*c*d^2*e - 24*(3*I*a*b^2 + b^3)*c*d^2)*f)*(f*x + e)^2 - 12*(-I*b^3*c^2*d + 2*(3*I*a*b^2 - b^3)*c^2*d*e)*f^2 + (24*I*b^3*d^3*e + (24*a*b^2 - 8*I*b^3)*d^3*e^3 - (24*a*b^2 - 8*I*b^3)*c^3*f^3 - 24*(3*I*a*b^2 + b^3)*d^3*e^2 + ((72*a*b^2 - 24*I*b^3)*c^2*d*e - 24*(3*I*a*b^2 + b^3)*c^2*d)*f^2 + (-24*I*b^3*c*d^2 - (72*a*b^2 - 24*I*b^3)*c*d^2*e^2 - 48*(-3*I*a*b^2 - b^3)*c*d^2*e)*f)*(f*x + e) + (-24*I*b^3*c*d^2*e - 24*(-3*I*a*b^2 + b^3)*c*d^2*e^2)*f)*sin(2*f*x + 2*e))/(-4*I*f^3*cos(4*f*x + 4*e) + 8*I*f^3*cos(2*f*x + 2*e) + 4*f^3*sin(4*f*x + 4*e) - 8*f^3*sin(2*f*x + 2*e) - 4*I*f^3))/f","B",0
48,1,5411,0,3.976677," ","integrate((d*x+c)^2*(a+b*cot(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a^{3} c^{2} + \frac{{\left(f x + e\right)}^{3} a^{3} d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a^{3} d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a^{3} d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a^{3} c d}{f} - \frac{6 \, {\left(f x + e\right)} a^{3} c d e}{f} + 9 \, a^{2} b c^{2} \log\left(\sin\left(f x + e\right)\right) + \frac{9 \, a^{2} b d^{2} e^{2} \log\left(\sin\left(f x + e\right)\right)}{f^{2}} - \frac{18 \, a^{2} b c d e \log\left(\sin\left(f x + e\right)\right)}{f} + \frac{3 \, {\left(36 \, a b^{2} d^{2} e^{2} + 36 \, a b^{2} c^{2} f^{2} - 2 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} - 12 \, b^{3} d^{2} e + 6 \, {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{2} e - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d f\right)} {\left(f x + e\right)}^{2} + 6 \, {\left({\left(3 i \, a b^{2} + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c d e f + {\left(3 i \, a b^{2} + b^{3}\right)} c^{2} f^{2}\right)} {\left(f x + e\right)} - 12 \, {\left(6 \, a b^{2} c d e - b^{3} c d\right)} f - {\left(6 \, b^{3} d^{2} e^{2} + 6 \, b^{3} c^{2} f^{2} + 36 \, a b^{2} d^{2} e - 6 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - 6 \, b^{3} d^{2} - 12 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 12 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f + 6 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, b^{3} d^{2} e^{2} + 6 i \, b^{3} c^{2} f^{2} + 36 i \, a b^{2} d^{2} e + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - 6 i \, b^{3} d^{2} + {\left(-36 i \, a b^{2} d^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(-12 i \, b^{3} c d e - 36 i \, a b^{2} c d\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left(-12 i \, b^{3} d^{2} e^{2} - 12 i \, b^{3} c^{2} f^{2} - 72 i \, a b^{2} d^{2} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 12 i \, b^{3} d^{2} + {\left(72 i \, a b^{2} d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{2} e + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(24 i \, b^{3} c d e + 72 i \, a b^{2} c d\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(6 \, b^{3} d^{2} e^{2} + 6 \, b^{3} c^{2} f^{2} + 36 \, a b^{2} d^{2} e - 6 \, b^{3} d^{2} - 12 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f + 6 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - b^{3} d^{2} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - b^{3} d^{2} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, b^{3} d^{2} e^{2} + 6 i \, b^{3} c^{2} f^{2} + 36 i \, a b^{2} d^{2} e - 6 i \, b^{3} d^{2} + {\left(-12 i \, b^{3} c d e - 36 i \, a b^{2} c d\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left(-12 i \, b^{3} d^{2} e^{2} - 12 i \, b^{3} c^{2} f^{2} - 72 i \, a b^{2} d^{2} e + 12 i \, b^{3} d^{2} + {\left(24 i \, b^{3} c d e + 72 i \, a b^{2} c d\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) - {\left(6 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 12 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(4 \, f x + 4 \, e\right) - 12 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + {\left(36 i \, a b^{2} d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{2} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left({\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + {\left(-72 i \, a b^{2} d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} d^{2} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) - 2 \, {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} + 3 \, {\left(6 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d f\right)} {\left(f x + e\right)}^{2} - 3 \, {\left(12 \, a b^{2} d^{2} e - 2 \, b^{3} d^{2} + {\left(3 i \, a b^{2} + b^{3}\right)} d^{2} e^{2} + {\left(3 i \, a b^{2} + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(6 \, a b^{2} c d - {\left(-3 i \, a b^{2} - b^{3}\right)} c d e\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(4 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} + 12 \, b^{3} d^{2} e - {\left(36 \, a b^{2} + 12 i \, b^{3}\right)} d^{2} e^{2} - {\left(36 \, a b^{2} + 12 i \, b^{3}\right)} c^{2} f^{2} - {\left(12 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{2} e - 12 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} c d f - {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}^{2} + {\left(12 \, b^{3} d^{2} + 12 \, {\left(-3 i \, a b^{2} - b^{3}\right)} d^{2} e^{2} + 12 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c^{2} f^{2} - {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} d^{2} e + {\left(24 \, {\left(3 i \, a b^{2} + b^{3}\right)} c d e + {\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c d\right)} f\right)} {\left(f x + e\right)} - {\left(12 \, b^{3} c d - {\left(72 \, a b^{2} + 24 i \, b^{3}\right)} c d e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(36 \, a b^{2} d^{2} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c d f + 12 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} \cos\left(4 \, f x + 4 \, e\right) - 24 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(36 i \, a b^{2} d^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} {\left(f x + e\right)} d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{2} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c d f\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left(-72 i \, a b^{2} d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} d^{2} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - {\left(36 \, a b^{2} d^{2} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c d f + 12 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} \cos\left(4 \, f x + 4 \, e\right) - 24 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(36 i \, a b^{2} d^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} {\left(f x + e\right)} d^{2} + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} d^{2} e + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} c d f\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left(-72 i \, a b^{2} d^{2} + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} {\left(f x + e\right)} d^{2} + {\left(72 i \, a^{2} b - 24 i \, b^{3}\right)} d^{2} e + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) - {\left(-3 i \, b^{3} d^{2} e^{2} - 3 i \, b^{3} c^{2} f^{2} - 18 i \, a b^{2} d^{2} e + {\left(9 i \, a^{2} b - 3 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 3 i \, b^{3} d^{2} + {\left(18 i \, a b^{2} d^{2} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{2} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(6 i \, b^{3} c d e + 18 i \, a b^{2} c d\right)} f + {\left(-3 i \, b^{3} d^{2} e^{2} - 3 i \, b^{3} c^{2} f^{2} - 18 i \, a b^{2} d^{2} e + {\left(9 i \, a^{2} b - 3 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 3 i \, b^{3} d^{2} + {\left(18 i \, a b^{2} d^{2} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{2} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(6 i \, b^{3} c d e + 18 i \, a b^{2} c d\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(6 i \, b^{3} d^{2} e^{2} + 6 i \, b^{3} c^{2} f^{2} + 36 i \, a b^{2} d^{2} e + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - 6 i \, b^{3} d^{2} + {\left(-36 i \, a b^{2} d^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(-12 i \, b^{3} c d e - 36 i \, a b^{2} c d\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - 6 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\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 \, \cos\left(f x + e\right) + 1\right) - {\left(-3 i \, b^{3} d^{2} e^{2} - 3 i \, b^{3} c^{2} f^{2} - 18 i \, a b^{2} d^{2} e + {\left(9 i \, a^{2} b - 3 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 3 i \, b^{3} d^{2} + {\left(18 i \, a b^{2} d^{2} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{2} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(6 i \, b^{3} c d e + 18 i \, a b^{2} c d\right)} f + {\left(-3 i \, b^{3} d^{2} e^{2} - 3 i \, b^{3} c^{2} f^{2} - 18 i \, a b^{2} d^{2} e + {\left(9 i \, a^{2} b - 3 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} + 3 i \, b^{3} d^{2} + {\left(18 i \, a b^{2} d^{2} + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} d^{2} e + {\left(18 i \, a^{2} b - 6 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(6 i \, b^{3} c d e + 18 i \, a b^{2} c d\right)} f\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(6 i \, b^{3} d^{2} e^{2} + 6 i \, b^{3} c^{2} f^{2} + 36 i \, a b^{2} d^{2} e + {\left(-18 i \, a^{2} b + 6 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - 6 i \, b^{3} d^{2} + {\left(-36 i \, a b^{2} d^{2} + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2} e + {\left(-36 i \, a^{2} b + 12 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)} + {\left(-12 i \, b^{3} c d e - 36 i \, a b^{2} c d\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\right)} \sin\left(4 \, f x + 4 \, e\right) - 6 \, {\left(b^{3} d^{2} e^{2} + b^{3} c^{2} f^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)}^{2} d^{2} - b^{3} d^{2} - 2 \, {\left(3 \, a b^{2} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{2} e + {\left(3 \, a^{2} b - b^{3}\right)} c d f\right)} {\left(f x + e\right)} - 2 \, {\left(b^{3} c d e + 3 \, a b^{2} c d\right)} f\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 \, \cos\left(f x + e\right) + 1\right) - {\left({\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{2} \cos\left(2 \, f x + 2 \, e\right) - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) - {\left({\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-72 i \, a^{2} b + 24 i \, b^{3}\right)} d^{2} \cos\left(2 \, f x + 2 \, e\right) - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(3 \, a^{2} b - b^{3}\right)} d^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(36 i \, a^{2} b - 12 i \, b^{3}\right)} d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) - {\left({\left(6 i \, a^{2} b + 6 \, a b^{2} - 2 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} + {\left(36 i \, a b^{2} d^{2} + {\left(-18 i \, a^{2} b - 18 \, a b^{2} + 6 i \, b^{3}\right)} d^{2} e + {\left(18 i \, a^{2} b + 18 \, a b^{2} - 6 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)}^{2} + {\left(-72 i \, a b^{2} d^{2} e + 12 i \, b^{3} d^{2} + {\left(18 \, a b^{2} - 6 i \, b^{3}\right)} d^{2} e^{2} + {\left(18 \, a b^{2} - 6 i \, b^{3}\right)} c^{2} f^{2} + {\left(72 i \, a b^{2} c d - {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} c d e\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left({\left(-12 i \, a^{2} b - 12 \, a b^{2} + 4 i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} - 12 i \, b^{3} d^{2} e - 12 \, {\left(-3 i \, a b^{2} + b^{3}\right)} d^{2} e^{2} - 12 \, {\left(-3 i \, a b^{2} + b^{3}\right)} c^{2} f^{2} + {\left({\left(36 i \, a^{2} b + 36 \, a b^{2} - 12 i \, b^{3}\right)} d^{2} e + {\left(-36 i \, a^{2} b - 36 \, a b^{2} + 12 i \, b^{3}\right)} c d f - 12 \, {\left(3 i \, a b^{2} + b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}^{2} + {\left(-12 i \, b^{3} d^{2} - {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} d^{2} e^{2} - {\left(36 \, a b^{2} - 12 i \, b^{3}\right)} c^{2} f^{2} - 24 \, {\left(-3 i \, a b^{2} - b^{3}\right)} d^{2} e + {\left({\left(72 \, a b^{2} - 24 i \, b^{3}\right)} c d e - 24 \, {\left(3 i \, a b^{2} + b^{3}\right)} c d\right)} f\right)} {\left(f x + e\right)} - 12 \, {\left(-i \, b^{3} c d + 2 \, {\left(3 i \, a b^{2} - b^{3}\right)} c d e\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-6 i \, f^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 i \, f^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 \, f^{2} \sin\left(4 \, f x + 4 \, e\right) - 12 \, f^{2} \sin\left(2 \, f x + 2 \, e\right) - 6 i \, f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a^3*c^2 + (f*x + e)^3*a^3*d^2/f^2 - 3*(f*x + e)^2*a^3*d^2*e/f^2 + 3*(f*x + e)*a^3*d^2*e^2/f^2 + 3*(f*x + e)^2*a^3*c*d/f - 6*(f*x + e)*a^3*c*d*e/f + 9*a^2*b*c^2*log(sin(f*x + e)) + 9*a^2*b*d^2*e^2*log(sin(f*x + e))/f^2 - 18*a^2*b*c*d*e*log(sin(f*x + e))/f + 3*(36*a*b^2*d^2*e^2 + 36*a*b^2*c^2*f^2 - 2*(3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^3*d^2 - 12*b^3*d^2*e + 6*((3*a^2*b - 3*I*a*b^2 - b^3)*d^2*e - (3*a^2*b - 3*I*a*b^2 - b^3)*c*d*f)*(f*x + e)^2 + 6*((3*I*a*b^2 + b^3)*d^2*e^2 + 2*(-3*I*a*b^2 - b^3)*c*d*e*f + (3*I*a*b^2 + b^3)*c^2*f^2)*(f*x + e) - 12*(6*a*b^2*c*d*e - b^3*c*d)*f - (6*b^3*d^2*e^2 + 6*b^3*c^2*f^2 + 36*a*b^2*d^2*e - 6*(3*a^2*b - b^3)*(f*x + e)^2*d^2 - 6*b^3*d^2 - 12*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 12*(b^3*c*d*e + 3*a*b^2*c*d)*f + 6*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*cos(4*f*x + 4*e) - 12*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*cos(2*f*x + 2*e) + (6*I*b^3*d^2*e^2 + 6*I*b^3*c^2*f^2 + 36*I*a*b^2*d^2*e + (-18*I*a^2*b + 6*I*b^3)*(f*x + e)^2*d^2 - 6*I*b^3*d^2 + (-36*I*a*b^2*d^2 + (36*I*a^2*b - 12*I*b^3)*d^2*e + (-36*I*a^2*b + 12*I*b^3)*c*d*f)*(f*x + e) + (-12*I*b^3*c*d*e - 36*I*a*b^2*c*d)*f)*sin(4*f*x + 4*e) + (-12*I*b^3*d^2*e^2 - 12*I*b^3*c^2*f^2 - 72*I*a*b^2*d^2*e + (36*I*a^2*b - 12*I*b^3)*(f*x + e)^2*d^2 + 12*I*b^3*d^2 + (72*I*a*b^2*d^2 + (-72*I*a^2*b + 24*I*b^3)*d^2*e + (72*I*a^2*b - 24*I*b^3)*c*d*f)*(f*x + e) + (24*I*b^3*c*d*e + 72*I*a*b^2*c*d)*f)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (6*b^3*d^2*e^2 + 6*b^3*c^2*f^2 + 36*a*b^2*d^2*e - 6*b^3*d^2 - 12*(b^3*c*d*e + 3*a*b^2*c*d)*f + 6*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - b^3*d^2 - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*cos(4*f*x + 4*e) - 12*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - b^3*d^2 - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*cos(2*f*x + 2*e) + (6*I*b^3*d^2*e^2 + 6*I*b^3*c^2*f^2 + 36*I*a*b^2*d^2*e - 6*I*b^3*d^2 + (-12*I*b^3*c*d*e - 36*I*a*b^2*c*d)*f)*sin(4*f*x + 4*e) + (-12*I*b^3*d^2*e^2 - 12*I*b^3*c^2*f^2 - 72*I*a*b^2*d^2*e + 12*I*b^3*d^2 + (24*I*b^3*c*d*e + 72*I*a*b^2*c*d)*f)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) - 1) - (6*(3*a^2*b - b^3)*(f*x + e)^2*d^2 + 12*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) + 6*((3*a^2*b - b^3)*(f*x + e)^2*d^2 + 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e))*cos(4*f*x + 4*e) - 12*((3*a^2*b - b^3)*(f*x + e)^2*d^2 + 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) + ((18*I*a^2*b - 6*I*b^3)*(f*x + e)^2*d^2 + (36*I*a*b^2*d^2 + (-36*I*a^2*b + 12*I*b^3)*d^2*e + (36*I*a^2*b - 12*I*b^3)*c*d*f)*(f*x + e))*sin(4*f*x + 4*e) + ((-36*I*a^2*b + 12*I*b^3)*(f*x + e)^2*d^2 + (-72*I*a*b^2*d^2 + (72*I*a^2*b - 24*I*b^3)*d^2*e + (-72*I*a^2*b + 24*I*b^3)*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) - 2*((3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^3*d^2 + 3*(6*a*b^2*d^2 - (3*a^2*b - 3*I*a*b^2 - b^3)*d^2*e + (3*a^2*b - 3*I*a*b^2 - b^3)*c*d*f)*(f*x + e)^2 - 3*(12*a*b^2*d^2*e - 2*b^3*d^2 + (3*I*a*b^2 + b^3)*d^2*e^2 + (3*I*a*b^2 + b^3)*c^2*f^2 - 2*(6*a*b^2*c*d - (-3*I*a*b^2 - b^3)*c*d*e)*f)*(f*x + e))*cos(4*f*x + 4*e) + (4*(3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^3*d^2 + 12*b^3*d^2*e - (36*a*b^2 + 12*I*b^3)*d^2*e^2 - (36*a*b^2 + 12*I*b^3)*c^2*f^2 - (12*(3*a^2*b - 3*I*a*b^2 - b^3)*d^2*e - 12*(3*a^2*b - 3*I*a*b^2 - b^3)*c*d*f - (36*a*b^2 - 12*I*b^3)*d^2)*(f*x + e)^2 + (12*b^3*d^2 + 12*(-3*I*a*b^2 - b^3)*d^2*e^2 + 12*(-3*I*a*b^2 - b^3)*c^2*f^2 - (72*a*b^2 - 24*I*b^3)*d^2*e + (24*(3*I*a*b^2 + b^3)*c*d*e + (72*a*b^2 - 24*I*b^3)*c*d)*f)*(f*x + e) - (12*b^3*c*d - (72*a*b^2 + 24*I*b^3)*c*d*e)*f)*cos(2*f*x + 2*e) - (36*a*b^2*d^2 + 12*(3*a^2*b - b^3)*(f*x + e)*d^2 - 12*(3*a^2*b - b^3)*d^2*e + 12*(3*a^2*b - b^3)*c*d*f + 12*(3*a*b^2*d^2 + (3*a^2*b - b^3)*(f*x + e)*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*cos(4*f*x + 4*e) - 24*(3*a*b^2*d^2 + (3*a^2*b - b^3)*(f*x + e)*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*cos(2*f*x + 2*e) + (36*I*a*b^2*d^2 + (36*I*a^2*b - 12*I*b^3)*(f*x + e)*d^2 + (-36*I*a^2*b + 12*I*b^3)*d^2*e + (36*I*a^2*b - 12*I*b^3)*c*d*f)*sin(4*f*x + 4*e) + (-72*I*a*b^2*d^2 + (-72*I*a^2*b + 24*I*b^3)*(f*x + e)*d^2 + (72*I*a^2*b - 24*I*b^3)*d^2*e + (-72*I*a^2*b + 24*I*b^3)*c*d*f)*sin(2*f*x + 2*e))*dilog(-e^(I*f*x + I*e)) - (36*a*b^2*d^2 + 12*(3*a^2*b - b^3)*(f*x + e)*d^2 - 12*(3*a^2*b - b^3)*d^2*e + 12*(3*a^2*b - b^3)*c*d*f + 12*(3*a*b^2*d^2 + (3*a^2*b - b^3)*(f*x + e)*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*cos(4*f*x + 4*e) - 24*(3*a*b^2*d^2 + (3*a^2*b - b^3)*(f*x + e)*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*cos(2*f*x + 2*e) + (36*I*a*b^2*d^2 + (36*I*a^2*b - 12*I*b^3)*(f*x + e)*d^2 + (-36*I*a^2*b + 12*I*b^3)*d^2*e + (36*I*a^2*b - 12*I*b^3)*c*d*f)*sin(4*f*x + 4*e) + (-72*I*a*b^2*d^2 + (-72*I*a^2*b + 24*I*b^3)*(f*x + e)*d^2 + (72*I*a^2*b - 24*I*b^3)*d^2*e + (-72*I*a^2*b + 24*I*b^3)*c*d*f)*sin(2*f*x + 2*e))*dilog(e^(I*f*x + I*e)) - (-3*I*b^3*d^2*e^2 - 3*I*b^3*c^2*f^2 - 18*I*a*b^2*d^2*e + (9*I*a^2*b - 3*I*b^3)*(f*x + e)^2*d^2 + 3*I*b^3*d^2 + (18*I*a*b^2*d^2 + (-18*I*a^2*b + 6*I*b^3)*d^2*e + (18*I*a^2*b - 6*I*b^3)*c*d*f)*(f*x + e) + (6*I*b^3*c*d*e + 18*I*a*b^2*c*d)*f + (-3*I*b^3*d^2*e^2 - 3*I*b^3*c^2*f^2 - 18*I*a*b^2*d^2*e + (9*I*a^2*b - 3*I*b^3)*(f*x + e)^2*d^2 + 3*I*b^3*d^2 + (18*I*a*b^2*d^2 + (-18*I*a^2*b + 6*I*b^3)*d^2*e + (18*I*a^2*b - 6*I*b^3)*c*d*f)*(f*x + e) + (6*I*b^3*c*d*e + 18*I*a*b^2*c*d)*f)*cos(4*f*x + 4*e) + (6*I*b^3*d^2*e^2 + 6*I*b^3*c^2*f^2 + 36*I*a*b^2*d^2*e + (-18*I*a^2*b + 6*I*b^3)*(f*x + e)^2*d^2 - 6*I*b^3*d^2 + (-36*I*a*b^2*d^2 + (36*I*a^2*b - 12*I*b^3)*d^2*e + (-36*I*a^2*b + 12*I*b^3)*c*d*f)*(f*x + e) + (-12*I*b^3*c*d*e - 36*I*a*b^2*c*d)*f)*cos(2*f*x + 2*e) + 3*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*sin(4*f*x + 4*e) - 6*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - (-3*I*b^3*d^2*e^2 - 3*I*b^3*c^2*f^2 - 18*I*a*b^2*d^2*e + (9*I*a^2*b - 3*I*b^3)*(f*x + e)^2*d^2 + 3*I*b^3*d^2 + (18*I*a*b^2*d^2 + (-18*I*a^2*b + 6*I*b^3)*d^2*e + (18*I*a^2*b - 6*I*b^3)*c*d*f)*(f*x + e) + (6*I*b^3*c*d*e + 18*I*a*b^2*c*d)*f + (-3*I*b^3*d^2*e^2 - 3*I*b^3*c^2*f^2 - 18*I*a*b^2*d^2*e + (9*I*a^2*b - 3*I*b^3)*(f*x + e)^2*d^2 + 3*I*b^3*d^2 + (18*I*a*b^2*d^2 + (-18*I*a^2*b + 6*I*b^3)*d^2*e + (18*I*a^2*b - 6*I*b^3)*c*d*f)*(f*x + e) + (6*I*b^3*c*d*e + 18*I*a*b^2*c*d)*f)*cos(4*f*x + 4*e) + (6*I*b^3*d^2*e^2 + 6*I*b^3*c^2*f^2 + 36*I*a*b^2*d^2*e + (-18*I*a^2*b + 6*I*b^3)*(f*x + e)^2*d^2 - 6*I*b^3*d^2 + (-36*I*a*b^2*d^2 + (36*I*a^2*b - 12*I*b^3)*d^2*e + (-36*I*a^2*b + 12*I*b^3)*c*d*f)*(f*x + e) + (-12*I*b^3*c*d*e - 36*I*a*b^2*c*d)*f)*cos(2*f*x + 2*e) + 3*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*sin(4*f*x + 4*e) - 6*(b^3*d^2*e^2 + b^3*c^2*f^2 + 6*a*b^2*d^2*e - (3*a^2*b - b^3)*(f*x + e)^2*d^2 - b^3*d^2 - 2*(3*a*b^2*d^2 - (3*a^2*b - b^3)*d^2*e + (3*a^2*b - b^3)*c*d*f)*(f*x + e) - 2*(b^3*c*d*e + 3*a*b^2*c*d)*f)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - ((36*I*a^2*b - 12*I*b^3)*d^2*cos(4*f*x + 4*e) + (-72*I*a^2*b + 24*I*b^3)*d^2*cos(2*f*x + 2*e) - 12*(3*a^2*b - b^3)*d^2*sin(4*f*x + 4*e) + 24*(3*a^2*b - b^3)*d^2*sin(2*f*x + 2*e) + (36*I*a^2*b - 12*I*b^3)*d^2)*polylog(3, -e^(I*f*x + I*e)) - ((36*I*a^2*b - 12*I*b^3)*d^2*cos(4*f*x + 4*e) + (-72*I*a^2*b + 24*I*b^3)*d^2*cos(2*f*x + 2*e) - 12*(3*a^2*b - b^3)*d^2*sin(4*f*x + 4*e) + 24*(3*a^2*b - b^3)*d^2*sin(2*f*x + 2*e) + (36*I*a^2*b - 12*I*b^3)*d^2)*polylog(3, e^(I*f*x + I*e)) - ((6*I*a^2*b + 6*a*b^2 - 2*I*b^3)*(f*x + e)^3*d^2 + (36*I*a*b^2*d^2 + (-18*I*a^2*b - 18*a*b^2 + 6*I*b^3)*d^2*e + (18*I*a^2*b + 18*a*b^2 - 6*I*b^3)*c*d*f)*(f*x + e)^2 + (-72*I*a*b^2*d^2*e + 12*I*b^3*d^2 + (18*a*b^2 - 6*I*b^3)*d^2*e^2 + (18*a*b^2 - 6*I*b^3)*c^2*f^2 + (72*I*a*b^2*c*d - (36*a*b^2 - 12*I*b^3)*c*d*e)*f)*(f*x + e))*sin(4*f*x + 4*e) - ((-12*I*a^2*b - 12*a*b^2 + 4*I*b^3)*(f*x + e)^3*d^2 - 12*I*b^3*d^2*e - 12*(-3*I*a*b^2 + b^3)*d^2*e^2 - 12*(-3*I*a*b^2 + b^3)*c^2*f^2 + ((36*I*a^2*b + 36*a*b^2 - 12*I*b^3)*d^2*e + (-36*I*a^2*b - 36*a*b^2 + 12*I*b^3)*c*d*f - 12*(3*I*a*b^2 + b^3)*d^2)*(f*x + e)^2 + (-12*I*b^3*d^2 - (36*a*b^2 - 12*I*b^3)*d^2*e^2 - (36*a*b^2 - 12*I*b^3)*c^2*f^2 - 24*(-3*I*a*b^2 - b^3)*d^2*e + ((72*a*b^2 - 24*I*b^3)*c*d*e - 24*(3*I*a*b^2 + b^3)*c*d)*f)*(f*x + e) - 12*(-I*b^3*c*d + 2*(3*I*a*b^2 - b^3)*c*d*e)*f)*sin(2*f*x + 2*e))/(-6*I*f^2*cos(4*f*x + 4*e) + 12*I*f^2*cos(2*f*x + 2*e) + 6*f^2*sin(4*f*x + 4*e) - 12*f^2*sin(2*f*x + 2*e) - 6*I*f^2))/f","B",0
49,1,2017,0,1.211715," ","integrate((d*x+c)*(a+b*cot(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a^{3} c + \frac{{\left(f x + e\right)}^{2} a^{3} d}{f} - \frac{2 \, {\left(f x + e\right)} a^{3} d e}{f} + 6 \, a^{2} b c \log\left(\sin\left(f x + e\right)\right) - \frac{6 \, a^{2} b d e \log\left(\sin\left(f x + e\right)\right)}{f} - \frac{2 \, {\left(12 \, a b^{2} d e - 12 \, a b^{2} c f + {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{2} d - 2 \, b^{3} d - 2 \, {\left({\left(-3 i \, a b^{2} - b^{3}\right)} d e + {\left(3 i \, a b^{2} + b^{3}\right)} c f\right)} {\left(f x + e\right)} - {\left(2 \, b^{3} d e - 2 \, b^{3} c f + 6 \, a b^{2} d + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, b^{3} d e + 2 i \, b^{3} c f - 6 i \, a b^{2} d + {\left(-6 i \, a^{2} b + 2 i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(4 i \, b^{3} d e - 4 i \, b^{3} c f + 12 i \, a b^{2} d + {\left(12 i \, a^{2} b - 4 i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - {\left(2 \, b^{3} d e - 2 \, b^{3} c f + 6 \, a b^{2} d + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, b^{3} d e + 2 i \, b^{3} c f - 6 i \, a b^{2} d\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(4 i \, b^{3} d e - 4 i \, b^{3} c f + 12 i \, a b^{2} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} {\left(f x + e\right)} d \sin\left(4 \, f x + 4 \, e\right) + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} {\left(f x + e\right)} d \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + {\left({\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{2} d + 2 \, {\left(6 \, a b^{2} d - {\left(-3 i \, a b^{2} - b^{3}\right)} d e - {\left(3 i \, a b^{2} + b^{3}\right)} c f\right)} {\left(f x + e\right)}\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(2 \, {\left(3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(f x + e\right)}^{2} d - 2 \, b^{3} d + {\left(12 \, a b^{2} + 4 i \, b^{3}\right)} d e - {\left(12 \, a b^{2} + 4 i \, b^{3}\right)} c f + {\left(4 \, {\left(3 i \, a b^{2} + b^{3}\right)} d e + 4 \, {\left(-3 i \, a b^{2} - b^{3}\right)} c f + {\left(12 \, a b^{2} - 4 i \, b^{3}\right)} d\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} d \sin\left(4 \, f x + 4 \, e\right) + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} d \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(2 \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(3 \, a^{2} b - b^{3}\right)} d \cos\left(2 \, f x + 2 \, e\right) + {\left(6 i \, a^{2} b - 2 i \, b^{3}\right)} d \sin\left(4 \, f x + 4 \, e\right) + {\left(-12 i \, a^{2} b + 4 i \, b^{3}\right)} d \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(i \, b^{3} d e - i \, b^{3} c f + 3 i \, a b^{2} d + {\left(3 i \, a^{2} b - i \, b^{3}\right)} {\left(f x + e\right)} d + {\left(i \, b^{3} d e - i \, b^{3} c f + 3 i \, a b^{2} d + {\left(3 i \, a^{2} b - i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-2 i \, b^{3} d e + 2 i \, b^{3} c f - 6 i \, a b^{2} d + {\left(-6 i \, a^{2} b + 2 i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\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 \, \cos\left(f x + e\right) + 1\right) + {\left(i \, b^{3} d e - i \, b^{3} c f + 3 i \, a b^{2} d + {\left(3 i \, a^{2} b - i \, b^{3}\right)} {\left(f x + e\right)} d + {\left(i \, b^{3} d e - i \, b^{3} c f + 3 i \, a b^{2} d + {\left(3 i \, a^{2} b - i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-2 i \, b^{3} d e + 2 i \, b^{3} c f - 6 i \, a b^{2} d + {\left(-6 i \, a^{2} b + 2 i \, b^{3}\right)} {\left(f x + e\right)} d\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, a b^{2} d + {\left(3 \, a^{2} b - b^{3}\right)} {\left(f x + e\right)} d\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 \, \cos\left(f x + e\right) + 1\right) + {\left({\left(3 i \, a^{2} b + 3 \, a b^{2} - i \, b^{3}\right)} {\left(f x + e\right)}^{2} d + {\left(12 i \, a b^{2} d - {\left(6 \, a b^{2} - 2 i \, b^{3}\right)} d e + {\left(6 \, a b^{2} - 2 i \, b^{3}\right)} c f\right)} {\left(f x + e\right)}\right)} \sin\left(4 \, f x + 4 \, e\right) + {\left({\left(-6 i \, a^{2} b - 6 \, a b^{2} + 2 i \, b^{3}\right)} {\left(f x + e\right)}^{2} d + 2 i \, b^{3} d - 4 \, {\left(3 i \, a b^{2} - b^{3}\right)} d e - 4 \, {\left(-3 i \, a b^{2} + b^{3}\right)} c f + {\left({\left(12 \, a b^{2} - 4 i \, b^{3}\right)} d e - {\left(12 \, a b^{2} - 4 i \, b^{3}\right)} c f - 4 \, {\left(3 i \, a b^{2} + b^{3}\right)} d\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{-2 i \, f \cos\left(4 \, f x + 4 \, e\right) + 4 i \, f \cos\left(2 \, f x + 2 \, e\right) + 2 \, f \sin\left(4 \, f x + 4 \, e\right) - 4 \, f \sin\left(2 \, f x + 2 \, e\right) - 2 i \, f}}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*a^3*c + (f*x + e)^2*a^3*d/f - 2*(f*x + e)*a^3*d*e/f + 6*a^2*b*c*log(sin(f*x + e)) - 6*a^2*b*d*e*log(sin(f*x + e))/f - 2*(12*a*b^2*d*e - 12*a*b^2*c*f + (3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^2*d - 2*b^3*d - 2*((-3*I*a*b^2 - b^3)*d*e + (3*I*a*b^2 + b^3)*c*f)*(f*x + e) - (2*b^3*d*e - 2*b^3*c*f + 6*a*b^2*d + 2*(3*a^2*b - b^3)*(f*x + e)*d + 2*(b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*cos(4*f*x + 4*e) - 4*(b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*cos(2*f*x + 2*e) - (-2*I*b^3*d*e + 2*I*b^3*c*f - 6*I*a*b^2*d + (-6*I*a^2*b + 2*I*b^3)*(f*x + e)*d)*sin(4*f*x + 4*e) - (4*I*b^3*d*e - 4*I*b^3*c*f + 12*I*a*b^2*d + (12*I*a^2*b - 4*I*b^3)*(f*x + e)*d)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - (2*b^3*d*e - 2*b^3*c*f + 6*a*b^2*d + 2*(b^3*d*e - b^3*c*f + 3*a*b^2*d)*cos(4*f*x + 4*e) - 4*(b^3*d*e - b^3*c*f + 3*a*b^2*d)*cos(2*f*x + 2*e) - (-2*I*b^3*d*e + 2*I*b^3*c*f - 6*I*a*b^2*d)*sin(4*f*x + 4*e) - (4*I*b^3*d*e - 4*I*b^3*c*f + 12*I*a*b^2*d)*sin(2*f*x + 2*e))*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (2*(3*a^2*b - b^3)*(f*x + e)*d*cos(4*f*x + 4*e) - 4*(3*a^2*b - b^3)*(f*x + e)*d*cos(2*f*x + 2*e) + (6*I*a^2*b - 2*I*b^3)*(f*x + e)*d*sin(4*f*x + 4*e) + (-12*I*a^2*b + 4*I*b^3)*(f*x + e)*d*sin(2*f*x + 2*e) + 2*(3*a^2*b - b^3)*(f*x + e)*d)*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + ((3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^2*d + 2*(6*a*b^2*d - (-3*I*a*b^2 - b^3)*d*e - (3*I*a*b^2 + b^3)*c*f)*(f*x + e))*cos(4*f*x + 4*e) - (2*(3*a^2*b - 3*I*a*b^2 - b^3)*(f*x + e)^2*d - 2*b^3*d + (12*a*b^2 + 4*I*b^3)*d*e - (12*a*b^2 + 4*I*b^3)*c*f + (4*(3*I*a*b^2 + b^3)*d*e + 4*(-3*I*a*b^2 - b^3)*c*f + (12*a*b^2 - 4*I*b^3)*d)*(f*x + e))*cos(2*f*x + 2*e) + (2*(3*a^2*b - b^3)*d*cos(4*f*x + 4*e) - 4*(3*a^2*b - b^3)*d*cos(2*f*x + 2*e) + (6*I*a^2*b - 2*I*b^3)*d*sin(4*f*x + 4*e) + (-12*I*a^2*b + 4*I*b^3)*d*sin(2*f*x + 2*e) + 2*(3*a^2*b - b^3)*d)*dilog(-e^(I*f*x + I*e)) + (2*(3*a^2*b - b^3)*d*cos(4*f*x + 4*e) - 4*(3*a^2*b - b^3)*d*cos(2*f*x + 2*e) + (6*I*a^2*b - 2*I*b^3)*d*sin(4*f*x + 4*e) + (-12*I*a^2*b + 4*I*b^3)*d*sin(2*f*x + 2*e) + 2*(3*a^2*b - b^3)*d)*dilog(e^(I*f*x + I*e)) + (I*b^3*d*e - I*b^3*c*f + 3*I*a*b^2*d + (3*I*a^2*b - I*b^3)*(f*x + e)*d + (I*b^3*d*e - I*b^3*c*f + 3*I*a*b^2*d + (3*I*a^2*b - I*b^3)*(f*x + e)*d)*cos(4*f*x + 4*e) + (-2*I*b^3*d*e + 2*I*b^3*c*f - 6*I*a*b^2*d + (-6*I*a^2*b + 2*I*b^3)*(f*x + e)*d)*cos(2*f*x + 2*e) - (b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*sin(4*f*x + 4*e) + 2*(b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (I*b^3*d*e - I*b^3*c*f + 3*I*a*b^2*d + (3*I*a^2*b - I*b^3)*(f*x + e)*d + (I*b^3*d*e - I*b^3*c*f + 3*I*a*b^2*d + (3*I*a^2*b - I*b^3)*(f*x + e)*d)*cos(4*f*x + 4*e) + (-2*I*b^3*d*e + 2*I*b^3*c*f - 6*I*a*b^2*d + (-6*I*a^2*b + 2*I*b^3)*(f*x + e)*d)*cos(2*f*x + 2*e) - (b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*sin(4*f*x + 4*e) + 2*(b^3*d*e - b^3*c*f + 3*a*b^2*d + (3*a^2*b - b^3)*(f*x + e)*d)*sin(2*f*x + 2*e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) + ((3*I*a^2*b + 3*a*b^2 - I*b^3)*(f*x + e)^2*d + (12*I*a*b^2*d - (6*a*b^2 - 2*I*b^3)*d*e + (6*a*b^2 - 2*I*b^3)*c*f)*(f*x + e))*sin(4*f*x + 4*e) + ((-6*I*a^2*b - 6*a*b^2 + 2*I*b^3)*(f*x + e)^2*d + 2*I*b^3*d - 4*(3*I*a*b^2 - b^3)*d*e - 4*(-3*I*a*b^2 + b^3)*c*f + ((12*a*b^2 - 4*I*b^3)*d*e - (12*a*b^2 - 4*I*b^3)*c*f - 4*(3*I*a*b^2 + b^3)*d)*(f*x + e))*sin(2*f*x + 2*e))/(-2*I*f*cos(4*f*x + 4*e) + 4*I*f*cos(2*f*x + 2*e) + 2*f*sin(4*f*x + 4*e) - 4*f*sin(2*f*x + 2*e) - 2*I*f))/f","B",0
50,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^3/(d*x+c),x, algorithm=""maxima"")","\frac{{\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} \log\left(d x + c\right) + {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right) \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(b^{3} d^{2} f x + b^{3} c d f - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, {\left(b^{3} d^{2} f x + b^{3} c d f - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(2 \, {\left(b^{3} d^{2} f x + b^{3} c d f - 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} f x + 6 \, a b^{2} c d f - b^{3} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 2 \, {\left(b^{3} d^{2} f x + b^{3} c d f - 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 3 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - {\left(3 \, a b^{2} d^{2} f - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \sin\left(f x + e\right)}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} + {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \cos\left(f x + e\right)}\,{d x} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 3 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - {\left(3 \, a b^{2} d^{2} f - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \sin\left(f x + e\right)}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} + {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2}\right)} \cos\left(f x + e\right)}\,{d x} + {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} f x + 6 \, a b^{2} c d f - b^{3} d^{2} - {\left(6 \, a b^{2} d^{2} f x + 6 \, a b^{2} c d f - b^{3} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(b^{3} d^{2} f x + b^{3} c d f - 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \log\left(d x + c\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(6 \, a b^{2} d^{2} f x + 6 \, a b^{2} c d f - b^{3} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"(((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*cos(4*f*x + 4*e)^2*log(d*x + c) + ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c)*sin(4*f*x + 4*e)^2 - 4*(b^3*d^2*f*x + b^3*c*d*f - ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c))*cos(2*f*x + 2*e)^2 - 4*(b^3*d^2*f*x + b^3*c*d*f - ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c))*sin(2*f*x + 2*e)^2 + (2*(b^3*d^2*f*x + b^3*c*d*f - 2*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c))*cos(2*f*x + 2*e) + 2*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c) + (6*a*b^2*d^2*f*x + 6*a*b^2*c*d*f - b^3*d^2)*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) + 2*(b^3*d^2*f*x + b^3*c*d*f - 2*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c))*cos(2*f*x + 2*e) + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e)^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))*integrate(-((3*a^2*b - b^3)*d^2*f^2*x^2 - 3*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - (3*a*b^2*d^2*f - 2*(3*a^2*b - b^3)*c*d*f^2)*x)*sin(f*x + e)/(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 + (d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*cos(f*x + e)^2 + (d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*sin(f*x + e)^2 + 2*(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*cos(f*x + e)), x) - (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e)^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))*integrate(-((3*a^2*b - b^3)*d^2*f^2*x^2 - 3*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - (3*a*b^2*d^2*f - 2*(3*a^2*b - b^3)*c*d*f^2)*x)*sin(f*x + e)/(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 + (d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*cos(f*x + e)^2 + (d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*sin(f*x + e)^2 - 2*(d^3*f^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2)*cos(f*x + e)), x) + ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c) + (6*a*b^2*d^2*f*x + 6*a*b^2*c*d*f - b^3*d^2 - (6*a*b^2*d^2*f*x + 6*a*b^2*c*d*f - b^3*d^2)*cos(2*f*x + 2*e) + 2*(b^3*d^2*f*x + b^3*c*d*f - 2*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*log(d*x + c))*sin(2*f*x + 2*e))*sin(4*f*x + 4*e) - (6*a*b^2*d^2*f*x + 6*a*b^2*c*d*f - b^3*d^2)*sin(2*f*x + 2*e))/(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e)^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(2*f*x + 2*e))","F",0
51,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^3/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + b^{3} c d f + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(b^{3} d^{2} f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2}\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + b^{3} c d f + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(b^{3} d^{2} f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2}\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2} x + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} - {\left(2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + b^{3} c d f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(b^{3} d^{2} f + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2}\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(3 \, a b^{2} d^{2} f x + 3 \, a b^{2} c d f - b^{3} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 2 \, {\left(2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + b^{3} c d f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(b^{3} d^{2} f + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2}\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} - 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 6 \, a b^{2} c d f + 3 \, b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} d^{2} f - {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \sin\left(f x + e\right)}{d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2} + {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \cos\left(f x + e\right)}\,{d x} - {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} - 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \int \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 6 \, a b^{2} c d f + 3 \, b^{3} d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} d^{2} f - {\left(3 \, a^{2} b - b^{3}\right)} c d f^{2}\right)} x\right)} \sin\left(f x + e\right)}{d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2} + {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2}\right)} \cos\left(f x + e\right)}\,{d x} - 2 \, {\left(3 \, a b^{2} d^{2} f x + 3 \, a b^{2} c d f - b^{3} d^{2} - {\left(3 \, a b^{2} d^{2} f x + 3 \, a b^{2} c d f - b^{3} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + b^{3} c d f + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(b^{3} d^{2} f + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d f^{2}\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 2 \, {\left(3 \, a b^{2} d^{2} f x + 3 \, a b^{2} c d f - b^{3} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} - 2 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 \, {\left(d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}"," ",0,"-((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2 + ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*cos(4*f*x + 4*e)^2 + 4*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + b^3*c*d*f + (a^3 - 3*a*b^2)*c^2*f^2 + (b^3*d^2*f + 2*(a^3 - 3*a*b^2)*c*d*f^2)*x)*cos(2*f*x + 2*e)^2 + ((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2)*sin(4*f*x + 4*e)^2 + 4*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + b^3*c*d*f + (a^3 - 3*a*b^2)*c^2*f^2 + (b^3*d^2*f + 2*(a^3 - 3*a*b^2)*c*d*f^2)*x)*sin(2*f*x + 2*e)^2 + 2*((a^3 - 3*a*b^2)*d^2*f^2*x^2 + 2*(a^3 - 3*a*b^2)*c*d*f^2*x + (a^3 - 3*a*b^2)*c^2*f^2 - (2*(a^3 - 3*a*b^2)*d^2*f^2*x^2 + b^3*c*d*f + 2*(a^3 - 3*a*b^2)*c^2*f^2 + (b^3*d^2*f + 4*(a^3 - 3*a*b^2)*c*d*f^2)*x)*cos(2*f*x + 2*e) - (3*a*b^2*d^2*f*x + 3*a*b^2*c*d*f - b^3*d^2)*sin(2*f*x + 2*e))*cos(4*f*x + 4*e) - 2*(2*(a^3 - 3*a*b^2)*d^2*f^2*x^2 + b^3*c*d*f + 2*(a^3 - 3*a*b^2)*c^2*f^2 + (b^3*d^2*f + 4*(a^3 - 3*a*b^2)*c*d*f^2)*x)*cos(2*f*x + 2*e) - (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e)^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 - 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))*integrate(-((3*a^2*b - b^3)*d^2*f^2*x^2 - 6*a*b^2*c*d*f + 3*b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*d^2*f - (3*a^2*b - b^3)*c*d*f^2)*x)*sin(f*x + e)/(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2 + (d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*cos(f*x + e)^2 + (d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*sin(f*x + e)^2 + 2*(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*cos(f*x + e)), x) + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e)^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 - 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))*integrate(-((3*a^2*b - b^3)*d^2*f^2*x^2 - 6*a*b^2*c*d*f + 3*b^3*d^2 + (3*a^2*b - b^3)*c^2*f^2 - 2*(3*a*b^2*d^2*f - (3*a^2*b - b^3)*c*d*f^2)*x)*sin(f*x + e)/(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2 + (d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*cos(f*x + e)^2 + (d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*sin(f*x + e)^2 - 2*(d^4*f^2*x^4 + 4*c*d^3*f^2*x^3 + 6*c^2*d^2*f^2*x^2 + 4*c^3*d*f^2*x + c^4*f^2)*cos(f*x + e)), x) - 2*(3*a*b^2*d^2*f*x + 3*a*b^2*c*d*f - b^3*d^2 - (3*a*b^2*d^2*f*x + 3*a*b^2*c*d*f - b^3*d^2)*cos(2*f*x + 2*e) + (2*(a^3 - 3*a*b^2)*d^2*f^2*x^2 + b^3*c*d*f + 2*(a^3 - 3*a*b^2)*c^2*f^2 + (b^3*d^2*f + 4*(a^3 - 3*a*b^2)*c*d*f^2)*x)*sin(2*f*x + 2*e))*sin(4*f*x + 4*e) + 2*(3*a*b^2*d^2*f*x + 3*a*b^2*c*d*f - b^3*d^2)*sin(2*f*x + 2*e))/(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(4*f*x + 4*e)^2 + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e)^2 + (d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)^2 - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*sin(2*f*x + 2*e)^2 + 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2 - 2*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))*cos(4*f*x + 4*e) - 4*(d^4*f^2*x^3 + 3*c*d^3*f^2*x^2 + 3*c^2*d^2*f^2*x + c^3*d*f^2)*cos(2*f*x + 2*e))","F",0
52,1,987,0,0.846363," ","integrate((d*x+c)^3/(a+b*cot(f*x+e)),x, algorithm=""maxima"")","-\frac{18 \, c^{2} d e {\left(\frac{2 \, {\left(f x + e\right)} a}{{\left(a^{2} + b^{2}\right)} f} - \frac{2 \, b \log\left(a \tan\left(f x + e\right) + b\right)}{{\left(a^{2} + b^{2}\right)} f} + \frac{b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} f}\right)} - 6 \, {\left(\frac{2 \, {\left(f x + e\right)} a}{a^{2} + b^{2}} - \frac{2 \, b \log\left(a \tan\left(f x + e\right) + b\right)}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{3} - \frac{3 \, {\left(f x + e\right)}^{4} {\left(a + i \, b\right)} d^{3} - 12 i \, b d^{3} {\rm Li}_{4}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}) - 12 \, {\left({\left(a + i \, b\right)} d^{3} e - {\left(a + i \, b\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + 18 \, {\left({\left(a + i \, b\right)} d^{3} e^{2} - 2 \, {\left(a + i \, b\right)} c d^{2} e f + {\left(a + i \, b\right)} c^{2} d f^{2}\right)} {\left(f x + e\right)}^{2} - 12 \, {\left({\left(a + i \, b\right)} d^{3} e^{3} - 3 \, {\left(a + i \, b\right)} c d^{2} e^{2} f\right)} {\left(f x + e\right)} - {\left(-12 i \, b d^{3} e^{3} + 36 i \, b c d^{2} e^{2} f\right)} \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - {\left(16 i \, {\left(f x + e\right)}^{3} b d^{3} + {\left(-36 i \, b d^{3} e + 36 i \, b c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(36 i \, b d^{3} e^{2} - 72 i \, b c d^{2} e f + 36 i \, b c^{2} d f^{2}\right)} {\left(f x + e\right)}\right)} \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left(-24 i \, {\left(f x + e\right)}^{2} b d^{3} - 18 i \, b d^{3} e^{2} + 36 i \, b c d^{2} e f - 18 i \, b c^{2} d f^{2} + {\left(36 i \, b d^{3} e - 36 i \, b c d^{2} f\right)} {\left(f x + e\right)}\right)} {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right) + 6 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) - 2 \, {\left(4 \, {\left(f x + e\right)}^{3} b d^{3} - 9 \, {\left(b d^{3} e - b c d^{2} f\right)} {\left(f x + e\right)}^{2} + 9 \, {\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(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 6 \, {\left(4 \, {\left(f x + e\right)} b d^{3} - 3 \, b d^{3} e + 3 \, b c d^{2} f\right)} {\rm Li}_{3}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b})}{{\left(a^{2} + b^{2}\right)} f^{3}}}{12 \, f}"," ",0,"-1/12*(18*c^2*d*e*(2*(f*x + e)*a/((a^2 + b^2)*f) - 2*b*log(a*tan(f*x + e) + b)/((a^2 + b^2)*f) + b*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*f)) - 6*(2*(f*x + e)*a/(a^2 + b^2) - 2*b*log(a*tan(f*x + e) + b)/(a^2 + b^2) + b*log(tan(f*x + e)^2 + 1)/(a^2 + b^2))*c^3 - (3*(f*x + e)^4*(a + I*b)*d^3 - 12*I*b*d^3*polylog(4, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - 12*((a + I*b)*d^3*e - (a + I*b)*c*d^2*f)*(f*x + e)^3 + 18*((a + I*b)*d^3*e^2 - 2*(a + I*b)*c*d^2*e*f + (a + I*b)*c^2*d*f^2)*(f*x + e)^2 - 12*((a + I*b)*d^3*e^3 - 3*(a + I*b)*c*d^2*e^2*f)*(f*x + e) - (-12*I*b*d^3*e^3 + 36*I*b*c*d^2*e^2*f)*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - (16*I*(f*x + e)^3*b*d^3 + (-36*I*b*d^3*e + 36*I*b*c*d^2*f)*(f*x + e)^2 + (36*I*b*d^3*e^2 - 72*I*b*c*d^2*e*f + 36*I*b*c^2*d*f^2)*(f*x + e))*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - (-24*I*(f*x + e)^2*b*d^3 - 18*I*b*d^3*e^2 + 36*I*b*c*d^2*e*f - 18*I*b*c^2*d*f^2 + (36*I*b*d^3*e - 36*I*b*c*d^2*f)*(f*x + e))*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) + 6*(b*d^3*e^3 - 3*b*c*d^2*e^2*f)*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) - 2*(4*(f*x + e)^3*b*d^3 - 9*(b*d^3*e - b*c*d^2*f)*(f*x + e)^2 + 9*(b*d^3*e^2 - 2*b*c*d^2*e*f + b*c^2*d*f^2)*(f*x + e))*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - 6*(4*(f*x + e)*b*d^3 - 3*b*d^3*e + 3*b*c*d^2*f)*polylog(3, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)))/((a^2 + b^2)*f^3))/f","B",0
53,1,719,0,0.823007," ","integrate((d*x+c)^2/(a+b*cot(f*x+e)),x, algorithm=""maxima"")","-\frac{6 \, c d e {\left(\frac{2 \, {\left(f x + e\right)} a}{{\left(a^{2} + b^{2}\right)} f} - \frac{2 \, b \log\left(a \tan\left(f x + e\right) + b\right)}{{\left(a^{2} + b^{2}\right)} f} + \frac{b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} f}\right)} - 3 \, {\left(\frac{2 \, {\left(f x + e\right)} a}{a^{2} + b^{2}} - \frac{2 \, b \log\left(a \tan\left(f x + e\right) + b\right)}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{2} - \frac{2 \, {\left(f x + e\right)}^{3} {\left(a + i \, b\right)} d^{2} + 6 \, {\left(f x + e\right)} {\left(a + i \, b\right)} d^{2} e^{2} - 6 i \, b d^{2} e^{2} \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - 3 \, b d^{2} e^{2} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) - 3 \, b d^{2} {\rm Li}_{3}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}) - 6 \, {\left({\left(a + i \, b\right)} d^{2} e - {\left(a + i \, b\right)} c d f\right)} {\left(f x + e\right)}^{2} - {\left(6 i \, {\left(f x + e\right)}^{2} b d^{2} + {\left(-12 i \, b d^{2} e + 12 i \, b c d f\right)} {\left(f x + e\right)}\right)} \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left(-6 i \, {\left(f x + e\right)} b d^{2} + 6 i \, b d^{2} e - 6 i \, b c d f\right)} {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right) - 3 \, {\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(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right)}{{\left(a^{2} + b^{2}\right)} f^{2}}}{6 \, f}"," ",0,"-1/6*(6*c*d*e*(2*(f*x + e)*a/((a^2 + b^2)*f) - 2*b*log(a*tan(f*x + e) + b)/((a^2 + b^2)*f) + b*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*f)) - 3*(2*(f*x + e)*a/(a^2 + b^2) - 2*b*log(a*tan(f*x + e) + b)/(a^2 + b^2) + b*log(tan(f*x + e)^2 + 1)/(a^2 + b^2))*c^2 - (2*(f*x + e)^3*(a + I*b)*d^2 + 6*(f*x + e)*(a + I*b)*d^2*e^2 - 6*I*b*d^2*e^2*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - 3*b*d^2*e^2*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) - 3*b*d^2*polylog(3, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - 6*((a + I*b)*d^2*e - (a + I*b)*c*d*f)*(f*x + e)^2 - (6*I*(f*x + e)^2*b*d^2 + (-12*I*b*d^2*e + 12*I*b*c*d*f)*(f*x + e))*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - (-6*I*(f*x + e)*b*d^2 + 6*I*b*d^2*e - 6*I*b*c*d*f)*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - 3*((f*x + e)^2*b*d^2 - 2*(b*d^2*e - b*c*d*f)*(f*x + e))*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)))/((a^2 + b^2)*f^2))/f","B",0
54,1,406,0,0.665432," ","integrate((d*x+c)/(a+b*cot(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(a + i \, b\right)} d f^{2} x^{2} + 2 \, {\left(a + i \, b\right)} c f^{2} x - 2 i \, b d f x \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - b d f x \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - 2 i \, b c f \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - b c f \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) + i \, b d {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right)}{2 \, {\left(a^{2} + b^{2}\right)} f^{2}}"," ",0,"1/2*((a + I*b)*d*f^2*x^2 + 2*(a + I*b)*c*f^2*x - 2*I*b*d*f*x*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - b*d*f*x*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - 2*I*b*c*f*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - b*c*f*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) + I*b*d*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)))/((a^2 + b^2)*f^2)","B",0
55,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*cot(f*x+e)),x, algorithm=""maxima"")","\frac{-2 \, {\left(a^{2} b + b^{3}\right)} d \int \frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c - 2 \, {\left({\left(a^{4} - b^{4}\right)} d x + {\left(a^{4} - b^{4}\right)} c\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d x + {\left(a^{3} b + a b^{3}\right)} c\right)} \sin\left(2 \, f x + 2 \, e\right)}\,{d x} + a \log\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} d}"," ",0,"(2*(a^2*b + b^3)*d*integrate(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/((a^4 + 2*a^2*b^2 + b^4)*d*x + ((a^4 + 2*a^2*b^2 + b^4)*d*x + (a^4 + 2*a^2*b^2 + b^4)*c)*cos(2*f*x + 2*e)^2 + ((a^4 + 2*a^2*b^2 + b^4)*d*x + (a^4 + 2*a^2*b^2 + b^4)*c)*sin(2*f*x + 2*e)^2 + (a^4 + 2*a^2*b^2 + b^4)*c - 2*((a^4 - b^4)*d*x + (a^4 - b^4)*c)*cos(2*f*x + 2*e) + 4*((a^3*b + a*b^3)*d*x + (a^3*b + a*b^3)*c)*sin(2*f*x + 2*e)), x) + a*log(d*x + c))/((a^2 + b^2)*d)","F",0
56,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*cot(f*x+e)),x, algorithm=""maxima"")","\frac{-2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} x + {\left(a^{2} b + b^{3}\right)} c d\right)} \int \frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d x + {\left(a^{4} - b^{4}\right)} c^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c d x + {\left(a^{3} b + a b^{3}\right)} c^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}\,{d x} - a}{{\left(a^{2} + b^{2}\right)} d^{2} x + {\left(a^{2} + b^{2}\right)} c d}"," ",0,"(2*((a^2*b + b^3)*d^2*x + (a^2*b + b^3)*c*d)*integrate(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/((a^4 + 2*a^2*b^2 + b^4)*d^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*x + (a^4 + 2*a^2*b^2 + b^4)*c^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*x + (a^4 + 2*a^2*b^2 + b^4)*c^2)*cos(2*f*x + 2*e)^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*x + (a^4 + 2*a^2*b^2 + b^4)*c^2)*sin(2*f*x + 2*e)^2 - 2*((a^4 - b^4)*d^2*x^2 + 2*(a^4 - b^4)*c*d*x + (a^4 - b^4)*c^2)*cos(2*f*x + 2*e) + 4*((a^3*b + a*b^3)*d^2*x^2 + 2*(a^3*b + a*b^3)*c*d*x + (a^3*b + a*b^3)*c^2)*sin(2*f*x + 2*e)), x) - a)/((a^2 + b^2)*d^2*x + (a^2 + b^2)*c*d)","F",0
57,1,4699,0,4.717185," ","integrate((d*x+c)^3/(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{b^{2}}{{\left(a^{4} + a^{2} b^{2}\right)} f \tan\left(f x + e\right) + {\left(a^{3} b + a b^{3}\right)} f} + \frac{2 \, a b \log\left(a \tan\left(f x + e\right) + b\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f} - \frac{a b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f} - \frac{{\left(a^{2} - b^{2}\right)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f}\right)} c^{2} d e - {\left(\frac{2 \, a b \log\left(a \tan\left(f x + e\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{b^{2}}{a^{3} b + a b^{3} + {\left(a^{4} + a^{2} b^{2}\right)} \tan\left(f x + e\right)}\right)} c^{3} - \frac{{\left(3 \, a^{3} + 3 i \, a^{2} b + 3 \, a b^{2} + 3 i \, b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} + 24 \, {\left(-i \, a b^{2} - b^{3}\right)} d^{3} e^{3} + 72 \, {\left(i \, a b^{2} + b^{3}\right)} c d^{2} e^{2} f - {\left({\left(12 \, a^{3} + 12 i \, a^{2} b + 12 \, a b^{2} + 12 i \, b^{3}\right)} d^{3} e - {\left(12 \, a^{3} + 12 i \, a^{2} b + 12 \, a b^{2} + 12 i \, b^{3}\right)} c d^{2} f\right)} {\left(f x + e\right)}^{3} + {\left({\left(18 \, a^{3} + 18 i \, a^{2} b + 18 \, a b^{2} + 18 i \, b^{3}\right)} d^{3} e^{2} - {\left(36 \, a^{3} + 36 i \, a^{2} b + 36 \, a b^{2} + 36 i \, b^{3}\right)} c d^{2} e f + {\left(18 \, a^{3} + 18 i \, a^{2} b + 18 \, a b^{2} + 18 i \, b^{3}\right)} c^{2} d f^{2}\right)} {\left(f x + e\right)}^{2} - {\left({\left(12 \, a^{3} + 12 i \, a^{2} b + 12 \, a b^{2} + 12 i \, b^{3}\right)} d^{3} e^{3} - {\left(36 \, a^{3} + 36 i \, a^{2} b + 36 \, a b^{2} + 36 i \, b^{3}\right)} c d^{2} e^{2} f\right)} {\left(f x + e\right)} - {\left({\left(-24 i \, a^{2} b - 24 \, a b^{2}\right)} d^{3} e^{3} - 36 \, {\left(i \, a b^{2} + b^{3}\right)} d^{3} e^{2} - 36 \, {\left(i \, a b^{2} + b^{3}\right)} c^{2} d f^{2} + {\left({\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} e^{2} - 72 \, {\left(-i \, a b^{2} - b^{3}\right)} c d^{2} e\right)} f + {\left({\left(24 i \, a^{2} b - 24 \, a b^{2}\right)} d^{3} e^{3} - 36 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3} e^{2} - 36 \, {\left(-i \, a b^{2} + b^{3}\right)} c^{2} d f^{2} + {\left({\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} e^{2} - 72 \, {\left(i \, a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(24 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e^{3} + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} d^{3} e^{2} + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} c^{2} d f^{2} - {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} e^{2} + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - {\left({\left(32 i \, a^{2} b + 32 \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} + {\left({\left(-72 i \, a^{2} b - 72 \, a b^{2}\right)} d^{3} e + {\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} f - 36 \, {\left(i \, a b^{2} + b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left({\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} d^{3} e^{2} + {\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c^{2} d f^{2} - 72 \, {\left(-i \, a b^{2} - b^{3}\right)} d^{3} e + {\left({\left(-144 i \, a^{2} b - 144 \, a b^{2}\right)} c d^{2} e - 72 \, {\left(i \, a b^{2} + b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)} + {\left({\left(-32 i \, a^{2} b + 32 \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} + {\left({\left(72 i \, a^{2} b - 72 \, a b^{2}\right)} d^{3} e + {\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} f - 36 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left({\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} d^{3} e^{2} + {\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} c^{2} d f^{2} - 72 \, {\left(i \, a b^{2} - b^{3}\right)} d^{3} e + {\left({\left(144 i \, a^{2} b - 144 \, a b^{2}\right)} c d^{2} e - 72 \, {\left(-i \, a b^{2} + b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(32 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} - {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e - 72 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} f + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e^{2} + 72 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{2} d f^{2} + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} d^{3} e - {\left(144 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} e + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left({\left(3 \, a^{3} + 9 i \, a^{2} b - 9 \, a b^{2} - 3 i \, b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} - {\left({\left(12 \, a^{3} + 36 i \, a^{2} b - 36 \, a b^{2} - 12 i \, b^{3}\right)} d^{3} e - {\left(12 \, a^{3} + 36 i \, a^{2} b - 36 \, a b^{2} - 12 i \, b^{3}\right)} c d^{2} f + 24 \, {\left(i \, a b^{2} - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{3} + {\left({\left(18 \, a^{3} + 54 i \, a^{2} b - 54 \, a b^{2} - 18 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 \, a^{3} + 54 i \, a^{2} b - 54 \, a b^{2} - 18 i \, b^{3}\right)} c^{2} d f^{2} - 72 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3} e - {\left({\left(36 \, a^{3} + 108 i \, a^{2} b - 108 \, a b^{2} - 36 i \, b^{3}\right)} c d^{2} e + 72 \, {\left(i \, a b^{2} - b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}^{2} - {\left({\left(12 \, a^{3} + 36 i \, a^{2} b - 36 \, a b^{2} - 12 i \, b^{3}\right)} d^{3} e^{3} + 72 \, {\left(i \, a b^{2} - b^{3}\right)} d^{3} e^{2} + 72 \, {\left(i \, a b^{2} - b^{3}\right)} c^{2} d f^{2} - {\left({\left(36 \, a^{3} + 108 i \, a^{2} b - 108 \, a b^{2} - 36 i \, b^{3}\right)} c d^{2} e^{2} - 144 \, {\left(-i \, a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(-48 i \, a^{2} b - 48 \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{3} + {\left(-36 i \, a^{2} b - 36 \, a b^{2}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b - 36 \, a b^{2}\right)} c^{2} d f^{2} - 36 \, {\left(i \, a b^{2} + b^{3}\right)} d^{3} e + {\left({\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} d^{3} e + {\left(-72 i \, a^{2} b - 72 \, a b^{2}\right)} c d^{2} f - 36 \, {\left(-i \, a b^{2} - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)} + {\left({\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} e - 36 \, {\left(-i \, a b^{2} - b^{3}\right)} c d^{2}\right)} f + {\left({\left(48 i \, a^{2} b - 48 \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{3} + {\left(36 i \, a^{2} b - 36 \, a b^{2}\right)} d^{3} e^{2} + {\left(36 i \, a^{2} b - 36 \, a b^{2}\right)} c^{2} d f^{2} - 36 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3} e + {\left({\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} d^{3} e + {\left(72 i \, a^{2} b - 72 \, a b^{2}\right)} c d^{2} f - 36 \, {\left(i \, a b^{2} - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)} + {\left({\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} c d^{2} e - 36 \, {\left(i \, a b^{2} - b^{3}\right)} c d^{2}\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(48 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{3} + 36 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e^{2} + 36 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{2} d f^{2} + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} d^{3} e - {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e - 72 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} f + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)} - {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} e + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} c d^{2}\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right) + {\left(12 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{3} e^{3} + {\left(18 \, a b^{2} - 18 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 \, a b^{2} - 18 i \, b^{3}\right)} c^{2} d f^{2} - {\left(36 \, {\left(a^{2} b - i \, a b^{2}\right)} c d^{2} e^{2} + {\left(36 \, a b^{2} - 36 i \, b^{3}\right)} c d^{2} e\right)} f - {\left(12 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e^{3} + {\left(18 \, a b^{2} + 18 i \, b^{3}\right)} d^{3} e^{2} + {\left(18 \, a b^{2} + 18 i \, b^{3}\right)} c^{2} d f^{2} - {\left(36 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} e^{2} + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} c d^{2} e\right)} f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(12 i \, a^{2} b - 12 \, a b^{2}\right)} d^{3} e^{3} - 18 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3} e^{2} - 18 \, {\left(-i \, a b^{2} + b^{3}\right)} c^{2} d f^{2} + {\left({\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} c d^{2} e^{2} - 36 \, {\left(i \, a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) - {\left(16 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} - {\left(36 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{3} e - 36 \, {\left(a^{2} b - i \, a b^{2}\right)} c d^{2} f + {\left(18 \, a b^{2} - 18 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(36 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{3} e^{2} + 36 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{2} d f^{2} + {\left(36 \, a b^{2} - 36 i \, b^{3}\right)} d^{3} e - {\left(72 \, {\left(a^{2} b - i \, a b^{2}\right)} c d^{2} e + {\left(36 \, a b^{2} - 36 i \, b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)} - {\left(16 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} - {\left(36 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e - 36 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} f + {\left(18 \, a b^{2} + 18 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(36 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e^{2} + 36 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{2} d f^{2} + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} d^{3} e - {\left(72 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} e + {\left(36 \, a b^{2} + 36 i \, b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(-16 i \, a^{2} b + 16 \, a b^{2}\right)} {\left(f x + e\right)}^{3} d^{3} + {\left({\left(36 i \, a^{2} b - 36 \, a b^{2}\right)} d^{3} e + {\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} c d^{2} f - 18 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{2} + {\left({\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} d^{3} e^{2} + {\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} c^{2} d f^{2} - 36 \, {\left(i \, a b^{2} - b^{3}\right)} d^{3} e + {\left({\left(72 i \, a^{2} b - 72 \, a b^{2}\right)} c d^{2} e - 36 \, {\left(-i \, a b^{2} + b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left({\left(-24 i \, a^{2} b + 24 \, a b^{2}\right)} d^{3} \cos\left(2 \, f x + 2 \, e\right) + 24 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(24 i \, a^{2} b + 24 \, a b^{2}\right)} d^{3}\right)} {\rm Li}_{4}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}) - {\left(48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(f x + e\right)} d^{3} - 36 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{3} e + 36 \, {\left(a^{2} b - i \, a b^{2}\right)} c d^{2} f - {\left(18 \, a b^{2} - 18 i \, b^{3}\right)} d^{3} - {\left(48 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)} d^{3} - 36 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{3} e + 36 \, {\left(a^{2} b + i \, a b^{2}\right)} c d^{2} f - {\left(18 \, a b^{2} + 18 i \, b^{3}\right)} d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(-48 i \, a^{2} b + 48 \, a b^{2}\right)} {\left(f x + e\right)} d^{3} + {\left(36 i \, a^{2} b - 36 \, a b^{2}\right)} d^{3} e + {\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} c d^{2} f - 18 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}) - {\left({\left(3 i \, a^{3} - 9 \, a^{2} b - 9 i \, a b^{2} + 3 \, b^{3}\right)} {\left(f x + e\right)}^{4} d^{3} + {\left({\left(-12 i \, a^{3} + 36 \, a^{2} b + 36 i \, a b^{2} - 12 \, b^{3}\right)} d^{3} e + {\left(12 i \, a^{3} - 36 \, a^{2} b - 36 i \, a b^{2} + 12 \, b^{3}\right)} c d^{2} f + {\left(24 \, a b^{2} + 24 i \, b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}^{3} + {\left({\left(18 i \, a^{3} - 54 \, a^{2} b - 54 i \, a b^{2} + 18 \, b^{3}\right)} d^{3} e^{2} + {\left(18 i \, a^{3} - 54 \, a^{2} b - 54 i \, a b^{2} + 18 \, b^{3}\right)} c^{2} d f^{2} - {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} d^{3} e + {\left({\left(-36 i \, a^{3} + 108 \, a^{2} b + 108 i \, a b^{2} - 36 \, b^{3}\right)} c d^{2} e + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} c d^{2}\right)} f\right)} {\left(f x + e\right)}^{2} + {\left({\left(-12 i \, a^{3} + 36 \, a^{2} b + 36 i \, a b^{2} - 12 \, b^{3}\right)} d^{3} e^{3} + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} d^{3} e^{2} + {\left(72 \, a b^{2} + 72 i \, b^{3}\right)} c^{2} d f^{2} + {\left({\left(36 i \, a^{3} - 108 \, a^{2} b - 108 i \, a b^{2} + 36 \, b^{3}\right)} c d^{2} e^{2} - {\left(144 \, a b^{2} + 144 i \, b^{3}\right)} c d^{2} e\right)} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(12 \, a^{5} + 12 i \, a^{4} b + 24 \, a^{3} b^{2} + 24 i \, a^{2} b^{3} + 12 \, a b^{4} + 12 i \, b^{5}\right)} f^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-12 i \, a^{5} + 12 \, a^{4} b - 24 i \, a^{3} b^{2} + 24 \, a^{2} b^{3} - 12 i \, a b^{4} + 12 \, b^{5}\right)} f^{3} \sin\left(2 \, f x + 2 \, e\right) - {\left(12 \, a^{5} - 12 i \, a^{4} b + 24 \, a^{3} b^{2} - 24 i \, a^{2} b^{3} + 12 \, a b^{4} - 12 i \, b^{5}\right)} f^{3}}}{f}"," ",0,"(3*(b^2/((a^4 + a^2*b^2)*f*tan(f*x + e) + (a^3*b + a*b^3)*f) + 2*a*b*log(a*tan(f*x + e) + b)/((a^4 + 2*a^2*b^2 + b^4)*f) - a*b*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*f) - (a^2 - b^2)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*f))*c^2*d*e - (2*a*b*log(a*tan(f*x + e) + b)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + b^2/(a^3*b + a*b^3 + (a^4 + a^2*b^2)*tan(f*x + e)))*c^3 - ((3*a^3 + 3*I*a^2*b + 3*a*b^2 + 3*I*b^3)*(f*x + e)^4*d^3 + 24*(-I*a*b^2 - b^3)*d^3*e^3 + 72*(I*a*b^2 + b^3)*c*d^2*e^2*f - ((12*a^3 + 12*I*a^2*b + 12*a*b^2 + 12*I*b^3)*d^3*e - (12*a^3 + 12*I*a^2*b + 12*a*b^2 + 12*I*b^3)*c*d^2*f)*(f*x + e)^3 + ((18*a^3 + 18*I*a^2*b + 18*a*b^2 + 18*I*b^3)*d^3*e^2 - (36*a^3 + 36*I*a^2*b + 36*a*b^2 + 36*I*b^3)*c*d^2*e*f + (18*a^3 + 18*I*a^2*b + 18*a*b^2 + 18*I*b^3)*c^2*d*f^2)*(f*x + e)^2 - ((12*a^3 + 12*I*a^2*b + 12*a*b^2 + 12*I*b^3)*d^3*e^3 - (36*a^3 + 36*I*a^2*b + 36*a*b^2 + 36*I*b^3)*c*d^2*e^2*f)*(f*x + e) - ((-24*I*a^2*b - 24*a*b^2)*d^3*e^3 - 36*(I*a*b^2 + b^3)*d^3*e^2 - 36*(I*a*b^2 + b^3)*c^2*d*f^2 + ((72*I*a^2*b + 72*a*b^2)*c*d^2*e^2 - 72*(-I*a*b^2 - b^3)*c*d^2*e)*f + ((24*I*a^2*b - 24*a*b^2)*d^3*e^3 - 36*(-I*a*b^2 + b^3)*d^3*e^2 - 36*(-I*a*b^2 + b^3)*c^2*d*f^2 + ((-72*I*a^2*b + 72*a*b^2)*c*d^2*e^2 - 72*(I*a*b^2 - b^3)*c*d^2*e)*f)*cos(2*f*x + 2*e) - (24*(a^2*b + I*a*b^2)*d^3*e^3 + (36*a*b^2 + 36*I*b^3)*d^3*e^2 + (36*a*b^2 + 36*I*b^3)*c^2*d*f^2 - (72*(a^2*b + I*a*b^2)*c*d^2*e^2 + (72*a*b^2 + 72*I*b^3)*c*d^2*e)*f)*sin(2*f*x + 2*e))*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - ((32*I*a^2*b + 32*a*b^2)*(f*x + e)^3*d^3 + ((-72*I*a^2*b - 72*a*b^2)*d^3*e + (72*I*a^2*b + 72*a*b^2)*c*d^2*f - 36*(I*a*b^2 + b^3)*d^3)*(f*x + e)^2 + ((72*I*a^2*b + 72*a*b^2)*d^3*e^2 + (72*I*a^2*b + 72*a*b^2)*c^2*d*f^2 - 72*(-I*a*b^2 - b^3)*d^3*e + ((-144*I*a^2*b - 144*a*b^2)*c*d^2*e - 72*(I*a*b^2 + b^3)*c*d^2)*f)*(f*x + e) + ((-32*I*a^2*b + 32*a*b^2)*(f*x + e)^3*d^3 + ((72*I*a^2*b - 72*a*b^2)*d^3*e + (-72*I*a^2*b + 72*a*b^2)*c*d^2*f - 36*(-I*a*b^2 + b^3)*d^3)*(f*x + e)^2 + ((-72*I*a^2*b + 72*a*b^2)*d^3*e^2 + (-72*I*a^2*b + 72*a*b^2)*c^2*d*f^2 - 72*(I*a*b^2 - b^3)*d^3*e + ((144*I*a^2*b - 144*a*b^2)*c*d^2*e - 72*(-I*a*b^2 + b^3)*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) + (32*(a^2*b + I*a*b^2)*(f*x + e)^3*d^3 - (72*(a^2*b + I*a*b^2)*d^3*e - 72*(a^2*b + I*a*b^2)*c*d^2*f + (36*a*b^2 + 36*I*b^3)*d^3)*(f*x + e)^2 + (72*(a^2*b + I*a*b^2)*d^3*e^2 + 72*(a^2*b + I*a*b^2)*c^2*d*f^2 + (72*a*b^2 + 72*I*b^3)*d^3*e - (144*(a^2*b + I*a*b^2)*c*d^2*e + (72*a*b^2 + 72*I*b^3)*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - ((3*a^3 + 9*I*a^2*b - 9*a*b^2 - 3*I*b^3)*(f*x + e)^4*d^3 - ((12*a^3 + 36*I*a^2*b - 36*a*b^2 - 12*I*b^3)*d^3*e - (12*a^3 + 36*I*a^2*b - 36*a*b^2 - 12*I*b^3)*c*d^2*f + 24*(I*a*b^2 - b^3)*d^3)*(f*x + e)^3 + ((18*a^3 + 54*I*a^2*b - 54*a*b^2 - 18*I*b^3)*d^3*e^2 + (18*a^3 + 54*I*a^2*b - 54*a*b^2 - 18*I*b^3)*c^2*d*f^2 - 72*(-I*a*b^2 + b^3)*d^3*e - ((36*a^3 + 108*I*a^2*b - 108*a*b^2 - 36*I*b^3)*c*d^2*e + 72*(I*a*b^2 - b^3)*c*d^2)*f)*(f*x + e)^2 - ((12*a^3 + 36*I*a^2*b - 36*a*b^2 - 12*I*b^3)*d^3*e^3 + 72*(I*a*b^2 - b^3)*d^3*e^2 + 72*(I*a*b^2 - b^3)*c^2*d*f^2 - ((36*a^3 + 108*I*a^2*b - 108*a*b^2 - 36*I*b^3)*c*d^2*e^2 - 144*(-I*a*b^2 + b^3)*c*d^2*e)*f)*(f*x + e))*cos(2*f*x + 2*e) - ((-48*I*a^2*b - 48*a*b^2)*(f*x + e)^2*d^3 + (-36*I*a^2*b - 36*a*b^2)*d^3*e^2 + (-36*I*a^2*b - 36*a*b^2)*c^2*d*f^2 - 36*(I*a*b^2 + b^3)*d^3*e + ((72*I*a^2*b + 72*a*b^2)*d^3*e + (-72*I*a^2*b - 72*a*b^2)*c*d^2*f - 36*(-I*a*b^2 - b^3)*d^3)*(f*x + e) + ((72*I*a^2*b + 72*a*b^2)*c*d^2*e - 36*(-I*a*b^2 - b^3)*c*d^2)*f + ((48*I*a^2*b - 48*a*b^2)*(f*x + e)^2*d^3 + (36*I*a^2*b - 36*a*b^2)*d^3*e^2 + (36*I*a^2*b - 36*a*b^2)*c^2*d*f^2 - 36*(-I*a*b^2 + b^3)*d^3*e + ((-72*I*a^2*b + 72*a*b^2)*d^3*e + (72*I*a^2*b - 72*a*b^2)*c*d^2*f - 36*(I*a*b^2 - b^3)*d^3)*(f*x + e) + ((-72*I*a^2*b + 72*a*b^2)*c*d^2*e - 36*(I*a*b^2 - b^3)*c*d^2)*f)*cos(2*f*x + 2*e) - (48*(a^2*b + I*a*b^2)*(f*x + e)^2*d^3 + 36*(a^2*b + I*a*b^2)*d^3*e^2 + 36*(a^2*b + I*a*b^2)*c^2*d*f^2 + (36*a*b^2 + 36*I*b^3)*d^3*e - (72*(a^2*b + I*a*b^2)*d^3*e - 72*(a^2*b + I*a*b^2)*c*d^2*f + (36*a*b^2 + 36*I*b^3)*d^3)*(f*x + e) - (72*(a^2*b + I*a*b^2)*c*d^2*e + (36*a*b^2 + 36*I*b^3)*c*d^2)*f)*sin(2*f*x + 2*e))*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) + (12*(a^2*b - I*a*b^2)*d^3*e^3 + (18*a*b^2 - 18*I*b^3)*d^3*e^2 + (18*a*b^2 - 18*I*b^3)*c^2*d*f^2 - (36*(a^2*b - I*a*b^2)*c*d^2*e^2 + (36*a*b^2 - 36*I*b^3)*c*d^2*e)*f - (12*(a^2*b + I*a*b^2)*d^3*e^3 + (18*a*b^2 + 18*I*b^3)*d^3*e^2 + (18*a*b^2 + 18*I*b^3)*c^2*d*f^2 - (36*(a^2*b + I*a*b^2)*c*d^2*e^2 + (36*a*b^2 + 36*I*b^3)*c*d^2*e)*f)*cos(2*f*x + 2*e) - ((12*I*a^2*b - 12*a*b^2)*d^3*e^3 - 18*(-I*a*b^2 + b^3)*d^3*e^2 - 18*(-I*a*b^2 + b^3)*c^2*d*f^2 + ((-36*I*a^2*b + 36*a*b^2)*c*d^2*e^2 - 36*(I*a*b^2 - b^3)*c*d^2*e)*f)*sin(2*f*x + 2*e))*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) - (16*(a^2*b - I*a*b^2)*(f*x + e)^3*d^3 - (36*(a^2*b - I*a*b^2)*d^3*e - 36*(a^2*b - I*a*b^2)*c*d^2*f + (18*a*b^2 - 18*I*b^3)*d^3)*(f*x + e)^2 + (36*(a^2*b - I*a*b^2)*d^3*e^2 + 36*(a^2*b - I*a*b^2)*c^2*d*f^2 + (36*a*b^2 - 36*I*b^3)*d^3*e - (72*(a^2*b - I*a*b^2)*c*d^2*e + (36*a*b^2 - 36*I*b^3)*c*d^2)*f)*(f*x + e) - (16*(a^2*b + I*a*b^2)*(f*x + e)^3*d^3 - (36*(a^2*b + I*a*b^2)*d^3*e - 36*(a^2*b + I*a*b^2)*c*d^2*f + (18*a*b^2 + 18*I*b^3)*d^3)*(f*x + e)^2 + (36*(a^2*b + I*a*b^2)*d^3*e^2 + 36*(a^2*b + I*a*b^2)*c^2*d*f^2 + (36*a*b^2 + 36*I*b^3)*d^3*e - (72*(a^2*b + I*a*b^2)*c*d^2*e + (36*a*b^2 + 36*I*b^3)*c*d^2)*f)*(f*x + e))*cos(2*f*x + 2*e) + ((-16*I*a^2*b + 16*a*b^2)*(f*x + e)^3*d^3 + ((36*I*a^2*b - 36*a*b^2)*d^3*e + (-36*I*a^2*b + 36*a*b^2)*c*d^2*f - 18*(-I*a*b^2 + b^3)*d^3)*(f*x + e)^2 + ((-36*I*a^2*b + 36*a*b^2)*d^3*e^2 + (-36*I*a^2*b + 36*a*b^2)*c^2*d*f^2 - 36*(I*a*b^2 - b^3)*d^3*e + ((72*I*a^2*b - 72*a*b^2)*c*d^2*e - 36*(-I*a*b^2 + b^3)*c*d^2)*f)*(f*x + e))*sin(2*f*x + 2*e))*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - ((-24*I*a^2*b + 24*a*b^2)*d^3*cos(2*f*x + 2*e) + 24*(a^2*b + I*a*b^2)*d^3*sin(2*f*x + 2*e) + (24*I*a^2*b + 24*a*b^2)*d^3)*polylog(4, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - (48*(a^2*b - I*a*b^2)*(f*x + e)*d^3 - 36*(a^2*b - I*a*b^2)*d^3*e + 36*(a^2*b - I*a*b^2)*c*d^2*f - (18*a*b^2 - 18*I*b^3)*d^3 - (48*(a^2*b + I*a*b^2)*(f*x + e)*d^3 - 36*(a^2*b + I*a*b^2)*d^3*e + 36*(a^2*b + I*a*b^2)*c*d^2*f - (18*a*b^2 + 18*I*b^3)*d^3)*cos(2*f*x + 2*e) + ((-48*I*a^2*b + 48*a*b^2)*(f*x + e)*d^3 + (36*I*a^2*b - 36*a*b^2)*d^3*e + (-36*I*a^2*b + 36*a*b^2)*c*d^2*f - 18*(-I*a*b^2 + b^3)*d^3)*sin(2*f*x + 2*e))*polylog(3, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - ((3*I*a^3 - 9*a^2*b - 9*I*a*b^2 + 3*b^3)*(f*x + e)^4*d^3 + ((-12*I*a^3 + 36*a^2*b + 36*I*a*b^2 - 12*b^3)*d^3*e + (12*I*a^3 - 36*a^2*b - 36*I*a*b^2 + 12*b^3)*c*d^2*f + (24*a*b^2 + 24*I*b^3)*d^3)*(f*x + e)^3 + ((18*I*a^3 - 54*a^2*b - 54*I*a*b^2 + 18*b^3)*d^3*e^2 + (18*I*a^3 - 54*a^2*b - 54*I*a*b^2 + 18*b^3)*c^2*d*f^2 - (72*a*b^2 + 72*I*b^3)*d^3*e + ((-36*I*a^3 + 108*a^2*b + 108*I*a*b^2 - 36*b^3)*c*d^2*e + (72*a*b^2 + 72*I*b^3)*c*d^2)*f)*(f*x + e)^2 + ((-12*I*a^3 + 36*a^2*b + 36*I*a*b^2 - 12*b^3)*d^3*e^3 + (72*a*b^2 + 72*I*b^3)*d^3*e^2 + (72*a*b^2 + 72*I*b^3)*c^2*d*f^2 + ((36*I*a^3 - 108*a^2*b - 108*I*a*b^2 + 36*b^3)*c*d^2*e^2 - (144*a*b^2 + 144*I*b^3)*c*d^2*e)*f)*(f*x + e))*sin(2*f*x + 2*e))/((12*a^5 + 12*I*a^4*b + 24*a^3*b^2 + 24*I*a^2*b^3 + 12*a*b^4 + 12*I*b^5)*f^3*cos(2*f*x + 2*e) - (-12*I*a^5 + 12*a^4*b - 24*I*a^3*b^2 + 24*a^2*b^3 - 12*I*a*b^4 + 12*b^5)*f^3*sin(2*f*x + 2*e) - (12*a^5 - 12*I*a^4*b + 24*a^3*b^2 - 24*I*a^2*b^3 + 12*a*b^4 - 12*I*b^5)*f^3))/f","B",0
58,1,2592,0,2.211669," ","integrate((d*x+c)^2/(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{b^{2}}{{\left(a^{4} + a^{2} b^{2}\right)} f \tan\left(f x + e\right) + {\left(a^{3} b + a b^{3}\right)} f} + \frac{2 \, a b \log\left(a \tan\left(f x + e\right) + b\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f} - \frac{a b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f} - \frac{{\left(a^{2} - b^{2}\right)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f}\right)} c d e - {\left(\frac{2 \, a b \log\left(a \tan\left(f x + e\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{b^{2}}{a^{3} b + a b^{3} + {\left(a^{4} + a^{2} b^{2}\right)} \tan\left(f x + e\right)}\right)} c^{2} - \frac{{\left(a^{3} + i \, a^{2} b + a b^{2} + i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} + {\left(3 \, a^{3} + 3 i \, a^{2} b + 3 \, a b^{2} + 3 i \, b^{3}\right)} {\left(f x + e\right)} d^{2} e^{2} + 6 \, {\left(i \, a b^{2} + b^{3}\right)} d^{2} e^{2} - {\left({\left(3 \, a^{3} + 3 i \, a^{2} b + 3 \, a b^{2} + 3 i \, b^{3}\right)} d^{2} e - {\left(3 \, a^{3} + 3 i \, a^{2} b + 3 \, a b^{2} + 3 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)}^{2} - {\left({\left(6 i \, a^{2} b + 6 \, a b^{2}\right)} d^{2} e^{2} - 6 \, {\left(-i \, a b^{2} - b^{3}\right)} d^{2} e - 6 \, {\left(i \, a b^{2} + b^{3}\right)} c d f + {\left({\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} d^{2} e^{2} - 6 \, {\left(i \, a b^{2} - b^{3}\right)} d^{2} e - 6 \, {\left(-i \, a b^{2} + b^{3}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} e^{2} + {\left(6 \, a b^{2} + 6 i \, b^{3}\right)} d^{2} e - {\left(6 \, a b^{2} + 6 i \, b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - {\left({\left(6 i \, a^{2} b + 6 \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} + {\left({\left(-12 i \, a^{2} b - 12 \, a b^{2}\right)} d^{2} e + {\left(12 i \, a^{2} b + 12 \, a b^{2}\right)} c d f - 6 \, {\left(i \, a b^{2} + b^{3}\right)} d^{2}\right)} {\left(f x + e\right)} + {\left({\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} + {\left({\left(12 i \, a^{2} b - 12 \, a b^{2}\right)} d^{2} e + {\left(-12 i \, a^{2} b + 12 \, a b^{2}\right)} c d f - 6 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} - {\left(12 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} e - 12 \, {\left(a^{2} b + i \, a b^{2}\right)} c d f + {\left(6 \, a b^{2} + 6 i \, b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left({\left(a^{3} + 3 i \, a^{2} b - 3 \, a b^{2} - i \, b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} - {\left({\left(3 \, a^{3} + 9 i \, a^{2} b - 9 \, a b^{2} - 3 i \, b^{3}\right)} d^{2} e - {\left(3 \, a^{3} + 9 i \, a^{2} b - 9 \, a b^{2} - 3 i \, b^{3}\right)} c d f + 6 \, {\left(i \, a b^{2} - b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}^{2} + {\left({\left(3 \, a^{3} + 9 i \, a^{2} b - 9 \, a b^{2} - 3 i \, b^{3}\right)} d^{2} e^{2} - 12 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{2} e - 12 \, {\left(i \, a b^{2} - b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(-6 i \, a^{2} b - 6 \, a b^{2}\right)} {\left(f x + e\right)} d^{2} + {\left(6 i \, a^{2} b + 6 \, a b^{2}\right)} d^{2} e + {\left(-6 i \, a^{2} b - 6 \, a b^{2}\right)} c d f - 3 \, {\left(-i \, a b^{2} - b^{3}\right)} d^{2} + {\left({\left(6 i \, a^{2} b - 6 \, a b^{2}\right)} {\left(f x + e\right)} d^{2} + {\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} d^{2} e + {\left(6 i \, a^{2} b - 6 \, a b^{2}\right)} c d f - 3 \, {\left(i \, a b^{2} - b^{3}\right)} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(6 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)} d^{2} - 6 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} e + 6 \, {\left(a^{2} b + i \, a b^{2}\right)} c d f - {\left(3 \, a b^{2} + 3 i \, b^{3}\right)} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right) - {\left(3 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{2} e^{2} + {\left(3 \, a b^{2} - 3 i \, b^{3}\right)} d^{2} e - {\left(3 \, a b^{2} - 3 i \, b^{3}\right)} c d f - {\left(3 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} e^{2} + {\left(3 \, a b^{2} + 3 i \, b^{3}\right)} d^{2} e - {\left(3 \, a b^{2} + 3 i \, b^{3}\right)} c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(-3 i \, a^{2} b + 3 \, a b^{2}\right)} d^{2} e^{2} - 3 \, {\left(i \, a b^{2} - b^{3}\right)} d^{2} e - 3 \, {\left(-i \, a b^{2} + b^{3}\right)} c d f\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) - {\left(3 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} - {\left(6 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{2} e - 6 \, {\left(a^{2} b - i \, a b^{2}\right)} c d f + {\left(3 \, a b^{2} - 3 i \, b^{3}\right)} d^{2}\right)} {\left(f x + e\right)} - {\left(3 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} - {\left(6 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} e - 6 \, {\left(a^{2} b + i \, a b^{2}\right)} c d f + {\left(3 \, a b^{2} + 3 i \, b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(-3 i \, a^{2} b + 3 \, a b^{2}\right)} {\left(f x + e\right)}^{2} d^{2} + {\left({\left(6 i \, a^{2} b - 6 \, a b^{2}\right)} d^{2} e + {\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} c d f - 3 \, {\left(-i \, a b^{2} + b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) + {\left(3 \, {\left(a^{2} b + i \, a b^{2}\right)} d^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-3 i \, a^{2} b + 3 \, a b^{2}\right)} d^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 \, {\left(a^{2} b - i \, a b^{2}\right)} d^{2}\right)} {\rm Li}_{3}(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}) - {\left({\left(i \, a^{3} - 3 \, a^{2} b - 3 i \, a b^{2} + b^{3}\right)} {\left(f x + e\right)}^{3} d^{2} + {\left({\left(-3 i \, a^{3} + 9 \, a^{2} b + 9 i \, a b^{2} - 3 \, b^{3}\right)} d^{2} e + {\left(3 i \, a^{3} - 9 \, a^{2} b - 9 i \, a b^{2} + 3 \, b^{3}\right)} c d f + {\left(6 \, a b^{2} + 6 i \, b^{3}\right)} d^{2}\right)} {\left(f x + e\right)}^{2} + {\left({\left(3 i \, a^{3} - 9 \, a^{2} b - 9 i \, a b^{2} + 3 \, b^{3}\right)} d^{2} e^{2} - {\left(12 \, a b^{2} + 12 i \, b^{3}\right)} d^{2} e + {\left(12 \, a b^{2} + 12 i \, b^{3}\right)} c d f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(3 \, a^{5} + 3 i \, a^{4} b + 6 \, a^{3} b^{2} + 6 i \, a^{2} b^{3} + 3 \, a b^{4} + 3 i \, b^{5}\right)} f^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-3 i \, a^{5} + 3 \, a^{4} b - 6 i \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 3 i \, a b^{4} + 3 \, b^{5}\right)} f^{2} \sin\left(2 \, f x + 2 \, e\right) - {\left(3 \, a^{5} - 3 i \, a^{4} b + 6 \, a^{3} b^{2} - 6 i \, a^{2} b^{3} + 3 \, a b^{4} - 3 i \, b^{5}\right)} f^{2}}}{f}"," ",0,"(2*(b^2/((a^4 + a^2*b^2)*f*tan(f*x + e) + (a^3*b + a*b^3)*f) + 2*a*b*log(a*tan(f*x + e) + b)/((a^4 + 2*a^2*b^2 + b^4)*f) - a*b*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*f) - (a^2 - b^2)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*f))*c*d*e - (2*a*b*log(a*tan(f*x + e) + b)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + b^2/(a^3*b + a*b^3 + (a^4 + a^2*b^2)*tan(f*x + e)))*c^2 - ((a^3 + I*a^2*b + a*b^2 + I*b^3)*(f*x + e)^3*d^2 + (3*a^3 + 3*I*a^2*b + 3*a*b^2 + 3*I*b^3)*(f*x + e)*d^2*e^2 + 6*(I*a*b^2 + b^3)*d^2*e^2 - ((3*a^3 + 3*I*a^2*b + 3*a*b^2 + 3*I*b^3)*d^2*e - (3*a^3 + 3*I*a^2*b + 3*a*b^2 + 3*I*b^3)*c*d*f)*(f*x + e)^2 - ((6*I*a^2*b + 6*a*b^2)*d^2*e^2 - 6*(-I*a*b^2 - b^3)*d^2*e - 6*(I*a*b^2 + b^3)*c*d*f + ((-6*I*a^2*b + 6*a*b^2)*d^2*e^2 - 6*(I*a*b^2 - b^3)*d^2*e - 6*(-I*a*b^2 + b^3)*c*d*f)*cos(2*f*x + 2*e) + (6*(a^2*b + I*a*b^2)*d^2*e^2 + (6*a*b^2 + 6*I*b^3)*d^2*e - (6*a*b^2 + 6*I*b^3)*c*d*f)*sin(2*f*x + 2*e))*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - ((6*I*a^2*b + 6*a*b^2)*(f*x + e)^2*d^2 + ((-12*I*a^2*b - 12*a*b^2)*d^2*e + (12*I*a^2*b + 12*a*b^2)*c*d*f - 6*(I*a*b^2 + b^3)*d^2)*(f*x + e) + ((-6*I*a^2*b + 6*a*b^2)*(f*x + e)^2*d^2 + ((12*I*a^2*b - 12*a*b^2)*d^2*e + (-12*I*a^2*b + 12*a*b^2)*c*d*f - 6*(-I*a*b^2 + b^3)*d^2)*(f*x + e))*cos(2*f*x + 2*e) + (6*(a^2*b + I*a*b^2)*(f*x + e)^2*d^2 - (12*(a^2*b + I*a*b^2)*d^2*e - 12*(a^2*b + I*a*b^2)*c*d*f + (6*a*b^2 + 6*I*b^3)*d^2)*(f*x + e))*sin(2*f*x + 2*e))*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - ((a^3 + 3*I*a^2*b - 3*a*b^2 - I*b^3)*(f*x + e)^3*d^2 - ((3*a^3 + 9*I*a^2*b - 9*a*b^2 - 3*I*b^3)*d^2*e - (3*a^3 + 9*I*a^2*b - 9*a*b^2 - 3*I*b^3)*c*d*f + 6*(I*a*b^2 - b^3)*d^2)*(f*x + e)^2 + ((3*a^3 + 9*I*a^2*b - 9*a*b^2 - 3*I*b^3)*d^2*e^2 - 12*(-I*a*b^2 + b^3)*d^2*e - 12*(I*a*b^2 - b^3)*c*d*f)*(f*x + e))*cos(2*f*x + 2*e) - ((-6*I*a^2*b - 6*a*b^2)*(f*x + e)*d^2 + (6*I*a^2*b + 6*a*b^2)*d^2*e + (-6*I*a^2*b - 6*a*b^2)*c*d*f - 3*(-I*a*b^2 - b^3)*d^2 + ((6*I*a^2*b - 6*a*b^2)*(f*x + e)*d^2 + (-6*I*a^2*b + 6*a*b^2)*d^2*e + (6*I*a^2*b - 6*a*b^2)*c*d*f - 3*(I*a*b^2 - b^3)*d^2)*cos(2*f*x + 2*e) - (6*(a^2*b + I*a*b^2)*(f*x + e)*d^2 - 6*(a^2*b + I*a*b^2)*d^2*e + 6*(a^2*b + I*a*b^2)*c*d*f - (3*a*b^2 + 3*I*b^3)*d^2)*sin(2*f*x + 2*e))*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - (3*(a^2*b - I*a*b^2)*d^2*e^2 + (3*a*b^2 - 3*I*b^3)*d^2*e - (3*a*b^2 - 3*I*b^3)*c*d*f - (3*(a^2*b + I*a*b^2)*d^2*e^2 + (3*a*b^2 + 3*I*b^3)*d^2*e - (3*a*b^2 + 3*I*b^3)*c*d*f)*cos(2*f*x + 2*e) + ((-3*I*a^2*b + 3*a*b^2)*d^2*e^2 - 3*(I*a*b^2 - b^3)*d^2*e - 3*(-I*a*b^2 + b^3)*c*d*f)*sin(2*f*x + 2*e))*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) - (3*(a^2*b - I*a*b^2)*(f*x + e)^2*d^2 - (6*(a^2*b - I*a*b^2)*d^2*e - 6*(a^2*b - I*a*b^2)*c*d*f + (3*a*b^2 - 3*I*b^3)*d^2)*(f*x + e) - (3*(a^2*b + I*a*b^2)*(f*x + e)^2*d^2 - (6*(a^2*b + I*a*b^2)*d^2*e - 6*(a^2*b + I*a*b^2)*c*d*f + (3*a*b^2 + 3*I*b^3)*d^2)*(f*x + e))*cos(2*f*x + 2*e) + ((-3*I*a^2*b + 3*a*b^2)*(f*x + e)^2*d^2 + ((6*I*a^2*b - 6*a*b^2)*d^2*e + (-6*I*a^2*b + 6*a*b^2)*c*d*f - 3*(-I*a*b^2 + b^3)*d^2)*(f*x + e))*sin(2*f*x + 2*e))*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) + (3*(a^2*b + I*a*b^2)*d^2*cos(2*f*x + 2*e) - (-3*I*a^2*b + 3*a*b^2)*d^2*sin(2*f*x + 2*e) - 3*(a^2*b - I*a*b^2)*d^2)*polylog(3, (I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - ((I*a^3 - 3*a^2*b - 3*I*a*b^2 + b^3)*(f*x + e)^3*d^2 + ((-3*I*a^3 + 9*a^2*b + 9*I*a*b^2 - 3*b^3)*d^2*e + (3*I*a^3 - 9*a^2*b - 9*I*a*b^2 + 3*b^3)*c*d*f + (6*a*b^2 + 6*I*b^3)*d^2)*(f*x + e)^2 + ((3*I*a^3 - 9*a^2*b - 9*I*a*b^2 + 3*b^3)*d^2*e^2 - (12*a*b^2 + 12*I*b^3)*d^2*e + (12*a*b^2 + 12*I*b^3)*c*d*f)*(f*x + e))*sin(2*f*x + 2*e))/((3*a^5 + 3*I*a^4*b + 6*a^3*b^2 + 6*I*a^2*b^3 + 3*a*b^4 + 3*I*b^5)*f^2*cos(2*f*x + 2*e) - (-3*I*a^5 + 3*a^4*b - 6*I*a^3*b^2 + 6*a^2*b^3 - 3*I*a*b^4 + 3*b^5)*f^2*sin(2*f*x + 2*e) - (3*a^5 - 3*I*a^4*b + 6*a^3*b^2 - 6*I*a^2*b^3 + 3*a*b^4 - 3*I*b^5)*f^2))/f","B",0
59,1,1181,0,2.026884," ","integrate((d*x+c)/(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} + i \, a^{2} b + a b^{2} + i \, b^{3}\right)} d f^{2} x^{2} + {\left(2 \, a^{3} + 2 i \, a^{2} b + 2 \, a b^{2} + 2 i \, b^{3}\right)} c f^{2} x + 4 \, {\left(i \, a b^{2} + b^{3}\right)} c f - {\left({\left(4 i \, a^{2} b + 4 \, a b^{2}\right)} c f - 2 \, {\left(i \, a b^{2} + b^{3}\right)} d + {\left({\left(-4 i \, a^{2} b + 4 \, a b^{2}\right)} c f - 2 \, {\left(-i \, a b^{2} + b^{3}\right)} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(4 \, {\left(a^{2} b + i \, a b^{2}\right)} c f - {\left(2 \, a b^{2} + 2 i \, b^{3}\right)} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \arctan\left(b \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) + b, a \cos\left(2 \, f x + 2 \, e\right) - b \sin\left(2 \, f x + 2 \, e\right) - a\right) - {\left({\left(-4 i \, a^{2} b + 4 \, a b^{2}\right)} d f x \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(a^{2} b + i \, a b^{2}\right)} d f x \sin\left(2 \, f x + 2 \, e\right) + {\left(4 i \, a^{2} b + 4 \, a b^{2}\right)} d f x\right)} \arctan\left(-\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{2} - b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, f x + 2 \, e\right) + a^{2} + b^{2} - {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left({\left(a^{3} + 3 i \, a^{2} b - 3 \, a b^{2} - i \, b^{3}\right)} d f^{2} x^{2} + {\left({\left(2 \, a^{3} + 6 i \, a^{2} b - 6 \, a b^{2} - 2 i \, b^{3}\right)} c f^{2} - 4 \, {\left(i \, a b^{2} - b^{3}\right)} d f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left({\left(2 i \, a^{2} b - 2 \, a b^{2}\right)} d \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} d \sin\left(2 \, f x + 2 \, e\right) + {\left(-2 i \, a^{2} b - 2 \, a b^{2}\right)} d\right)} {\rm Li}_2\left(\frac{{\left(i \, a - b\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}{i \, a + b}\right) - {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c f - {\left(a b^{2} - i \, b^{3}\right)} d - {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c f - {\left(a b^{2} + i \, b^{3}\right)} d\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left({\left(-2 i \, a^{2} b + 2 \, a b^{2}\right)} c f + {\left(i \, a b^{2} - b^{3}\right)} d\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right) + {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} d f x \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, a^{2} b + 2 \, a b^{2}\right)} d f x \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} d f x\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, a b \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)}{a^{2} + b^{2}}\right) - {\left({\left(i \, a^{3} - 3 \, a^{2} b - 3 i \, a b^{2} + b^{3}\right)} d f^{2} x^{2} + {\left({\left(2 i \, a^{3} - 6 \, a^{2} b - 6 i \, a b^{2} + 2 \, b^{3}\right)} c f^{2} + {\left(4 \, a b^{2} + 4 i \, b^{3}\right)} d f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(2 \, a^{5} + 2 i \, a^{4} b + 4 \, a^{3} b^{2} + 4 i \, a^{2} b^{3} + 2 \, a b^{4} + 2 i \, b^{5}\right)} f^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2 i \, a^{5} + 2 \, a^{4} b - 4 i \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 2 i \, a b^{4} + 2 \, b^{5}\right)} f^{2} \sin\left(2 \, f x + 2 \, e\right) - {\left(2 \, a^{5} - 2 i \, a^{4} b + 4 \, a^{3} b^{2} - 4 i \, a^{2} b^{3} + 2 \, a b^{4} - 2 i \, b^{5}\right)} f^{2}}"," ",0,"-((a^3 + I*a^2*b + a*b^2 + I*b^3)*d*f^2*x^2 + (2*a^3 + 2*I*a^2*b + 2*a*b^2 + 2*I*b^3)*c*f^2*x + 4*(I*a*b^2 + b^3)*c*f - ((4*I*a^2*b + 4*a*b^2)*c*f - 2*(I*a*b^2 + b^3)*d + ((-4*I*a^2*b + 4*a*b^2)*c*f - 2*(-I*a*b^2 + b^3)*d)*cos(2*f*x + 2*e) + (4*(a^2*b + I*a*b^2)*c*f - (2*a*b^2 + 2*I*b^3)*d)*sin(2*f*x + 2*e))*arctan2(b*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) + b, a*cos(2*f*x + 2*e) - b*sin(2*f*x + 2*e) - a) - ((-4*I*a^2*b + 4*a*b^2)*d*f*x*cos(2*f*x + 2*e) + 4*(a^2*b + I*a*b^2)*d*f*x*sin(2*f*x + 2*e) + (4*I*a^2*b + 4*a*b^2)*d*f*x)*arctan2(-(2*a*b*cos(2*f*x + 2*e) + (a^2 - b^2)*sin(2*f*x + 2*e))/(a^2 + b^2), (2*a*b*sin(2*f*x + 2*e) + a^2 + b^2 - (a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - ((a^3 + 3*I*a^2*b - 3*a*b^2 - I*b^3)*d*f^2*x^2 + ((2*a^3 + 6*I*a^2*b - 6*a*b^2 - 2*I*b^3)*c*f^2 - 4*(I*a*b^2 - b^3)*d*f)*x)*cos(2*f*x + 2*e) - ((2*I*a^2*b - 2*a*b^2)*d*cos(2*f*x + 2*e) - 2*(a^2*b + I*a*b^2)*d*sin(2*f*x + 2*e) + (-2*I*a^2*b - 2*a*b^2)*d)*dilog((I*a - b)*e^(2*I*f*x + 2*I*e)/(I*a + b)) - (2*(a^2*b - I*a*b^2)*c*f - (a*b^2 - I*b^3)*d - (2*(a^2*b + I*a*b^2)*c*f - (a*b^2 + I*b^3)*d)*cos(2*f*x + 2*e) + ((-2*I*a^2*b + 2*a*b^2)*c*f + (I*a*b^2 - b^3)*d)*sin(2*f*x + 2*e))*log((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e)) + (2*(a^2*b + I*a*b^2)*d*f*x*cos(2*f*x + 2*e) - (-2*I*a^2*b + 2*a*b^2)*d*f*x*sin(2*f*x + 2*e) - 2*(a^2*b - I*a*b^2)*d*f*x)*log(((a^2 + b^2)*cos(2*f*x + 2*e)^2 + 4*a*b*sin(2*f*x + 2*e) + (a^2 + b^2)*sin(2*f*x + 2*e)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*f*x + 2*e))/(a^2 + b^2)) - ((I*a^3 - 3*a^2*b - 3*I*a*b^2 + b^3)*d*f^2*x^2 + ((2*I*a^3 - 6*a^2*b - 6*I*a*b^2 + 2*b^3)*c*f^2 + (4*a*b^2 + 4*I*b^3)*d*f)*x)*sin(2*f*x + 2*e))/((2*a^5 + 2*I*a^4*b + 4*a^3*b^2 + 4*I*a^2*b^3 + 2*a*b^4 + 2*I*b^5)*f^2*cos(2*f*x + 2*e) - (-2*I*a^5 + 2*a^4*b - 4*I*a^3*b^2 + 4*a^2*b^3 - 2*I*a*b^4 + 2*b^5)*f^2*sin(2*f*x + 2*e) - (2*a^5 - 2*I*a^4*b + 4*a^3*b^2 - 4*I*a^2*b^3 + 2*a*b^4 - 2*I*b^5)*f^2)","B",0
60,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*cot(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
