1,0,0,0,0.000000," ","integrate(x^3*cot(b*x+a),x, algorithm=""giac"")","\int x^{3} \cot\left(b x + a\right)\,{d x}"," ",0,"integrate(x^3*cot(b*x + a), x)","F",0
2,0,0,0,0.000000," ","integrate(x^2*cot(b*x+a),x, algorithm=""giac"")","\int x^{2} \cot\left(b x + a\right)\,{d x}"," ",0,"integrate(x^2*cot(b*x + a), x)","F",0
3,0,0,0,0.000000," ","integrate(x*cot(b*x+a),x, algorithm=""giac"")","\int x \cot\left(b x + a\right)\,{d x}"," ",0,"integrate(x*cot(b*x + a), x)","F",0
4,0,0,0,0.000000," ","integrate(cot(b*x+a)/x,x, algorithm=""giac"")","\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=""giac"")","\int \frac{\cot\left(b x + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(cot(b*x + a)/x^2, x)","F",0
6,0,0,0,0.000000," ","integrate(x^3*cot(b*x+a)^2,x, algorithm=""giac"")","\int x^{3} \cot\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^3*cot(b*x + a)^2, x)","F",0
7,0,0,0,0.000000," ","integrate(x^2*cot(b*x+a)^2,x, algorithm=""giac"")","\int x^{2} \cot\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^2*cot(b*x + a)^2, x)","F",0
8,1,1250,0,4.742815," ","integrate(x*cot(b*x+a)^2,x, algorithm=""giac"")","-\frac{b^{2} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + b^{2} x^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - b x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} x^{2} \tan\left(\frac{1}{2} \, b x\right) - b^{2} x^{2} \tan\left(\frac{1}{2} \, a\right) + b x \tan\left(\frac{1}{2} \, b x\right)^{2} + 4 \, b x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - \log\left(\frac{16 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 6 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + b x \tan\left(\frac{1}{2} \, a\right)^{2} - \log\left(\frac{16 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 6 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - b x + \log\left(\frac{16 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 6 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right) + \log\left(\frac{16 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 6 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, a\right)}{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + b^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, b x\right) - b^{2} \tan\left(\frac{1}{2} \, a\right)\right)}}"," ",0,"-1/2*(b^2*x^2*tan(1/2*b*x)^2*tan(1/2*a) + b^2*x^2*tan(1/2*b*x)*tan(1/2*a)^2 - b*x*tan(1/2*b*x)^2*tan(1/2*a)^2 - b^2*x^2*tan(1/2*b*x) - b^2*x^2*tan(1/2*a) + b*x*tan(1/2*b*x)^2 + 4*b*x*tan(1/2*b*x)*tan(1/2*a) - log(16*(tan(1/2*b*x)^8*tan(1/2*a)^2 + 2*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^6*tan(1/2*a)^4 - 2*tan(1/2*b*x)^7*tan(1/2*a) - 2*tan(1/2*b*x)^6*tan(1/2*a)^2 + 2*tan(1/2*b*x)^5*tan(1/2*a)^3 + 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + tan(1/2*b*x)^6 - 2*tan(1/2*b*x)^5*tan(1/2*a) - 6*tan(1/2*b*x)^4*tan(1/2*a)^2 - 2*tan(1/2*b*x)^3*tan(1/2*a)^3 + tan(1/2*b*x)^2*tan(1/2*a)^4 + 2*tan(1/2*b*x)^4 + 2*tan(1/2*b*x)^3*tan(1/2*a) - 2*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*b*x)^2 + 2*tan(1/2*b*x)*tan(1/2*a) + tan(1/2*a)^2)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x)^2*tan(1/2*a) + b*x*tan(1/2*a)^2 - log(16*(tan(1/2*b*x)^8*tan(1/2*a)^2 + 2*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^6*tan(1/2*a)^4 - 2*tan(1/2*b*x)^7*tan(1/2*a) - 2*tan(1/2*b*x)^6*tan(1/2*a)^2 + 2*tan(1/2*b*x)^5*tan(1/2*a)^3 + 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + tan(1/2*b*x)^6 - 2*tan(1/2*b*x)^5*tan(1/2*a) - 6*tan(1/2*b*x)^4*tan(1/2*a)^2 - 2*tan(1/2*b*x)^3*tan(1/2*a)^3 + tan(1/2*b*x)^2*tan(1/2*a)^4 + 2*tan(1/2*b*x)^4 + 2*tan(1/2*b*x)^3*tan(1/2*a) - 2*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*b*x)^2 + 2*tan(1/2*b*x)*tan(1/2*a) + tan(1/2*a)^2)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x)*tan(1/2*a)^2 - b*x + log(16*(tan(1/2*b*x)^8*tan(1/2*a)^2 + 2*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^6*tan(1/2*a)^4 - 2*tan(1/2*b*x)^7*tan(1/2*a) - 2*tan(1/2*b*x)^6*tan(1/2*a)^2 + 2*tan(1/2*b*x)^5*tan(1/2*a)^3 + 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + tan(1/2*b*x)^6 - 2*tan(1/2*b*x)^5*tan(1/2*a) - 6*tan(1/2*b*x)^4*tan(1/2*a)^2 - 2*tan(1/2*b*x)^3*tan(1/2*a)^3 + tan(1/2*b*x)^2*tan(1/2*a)^4 + 2*tan(1/2*b*x)^4 + 2*tan(1/2*b*x)^3*tan(1/2*a) - 2*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*b*x)^2 + 2*tan(1/2*b*x)*tan(1/2*a) + tan(1/2*a)^2)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x) + log(16*(tan(1/2*b*x)^8*tan(1/2*a)^2 + 2*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^6*tan(1/2*a)^4 - 2*tan(1/2*b*x)^7*tan(1/2*a) - 2*tan(1/2*b*x)^6*tan(1/2*a)^2 + 2*tan(1/2*b*x)^5*tan(1/2*a)^3 + 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + tan(1/2*b*x)^6 - 2*tan(1/2*b*x)^5*tan(1/2*a) - 6*tan(1/2*b*x)^4*tan(1/2*a)^2 - 2*tan(1/2*b*x)^3*tan(1/2*a)^3 + tan(1/2*b*x)^2*tan(1/2*a)^4 + 2*tan(1/2*b*x)^4 + 2*tan(1/2*b*x)^3*tan(1/2*a) - 2*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*b*x)^2 + 2*tan(1/2*b*x)*tan(1/2*a) + tan(1/2*a)^2)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*a))/(b^2*tan(1/2*b*x)^2*tan(1/2*a) + b^2*tan(1/2*b*x)*tan(1/2*a)^2 - b^2*tan(1/2*b*x) - b^2*tan(1/2*a))","B",0
9,0,0,0,0.000000," ","integrate(cot(b*x+a)^2/x,x, algorithm=""giac"")","\int \frac{\cot\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(cot(b*x + a)^2/x, x)","F",0
10,0,0,0,0.000000," ","integrate(cot(b*x+a)^2/x^2,x, algorithm=""giac"")","\int \frac{\cot\left(b x + a\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(cot(b*x + a)^2/x^2, x)","F",0
11,0,0,0,0.000000," ","integrate(x^3*cot(b*x+a)^3,x, algorithm=""giac"")","\int x^{3} \cot\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(x^3*cot(b*x + a)^3, x)","F",0
12,0,0,0,0.000000," ","integrate(x^2*cot(b*x+a)^3,x, algorithm=""giac"")","\int x^{2} \cot\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(x^2*cot(b*x + a)^3, x)","F",0
13,0,0,0,0.000000," ","integrate(x*cot(b*x+a)^3,x, algorithm=""giac"")","\int x \cot\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(x*cot(b*x + a)^3, x)","F",0
14,0,0,0,0.000000," ","integrate(cot(b*x+a)^3/x,x, algorithm=""giac"")","\int \frac{\cot\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(cot(b*x + a)^3/x, x)","F",0
15,0,0,0,0.000000," ","integrate(cot(b*x+a)^3/x^2,x, algorithm=""giac"")","\int \frac{\cot\left(b x + a\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate(cot(b*x + a)^3/x^2, x)","F",0
16,1,243,0,0.420726," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\frac{2 \, d^{3} f^{4} x^{4} + 8 \, c d^{2} f^{4} x^{3} + 4 i \, d^{3} f^{3} x^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, c^{2} d f^{4} x^{2} + 12 i \, c d^{2} f^{3} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 \, c^{3} f^{4} x + 12 i \, c^{2} d f^{3} x e^{\left(2 i \, f x + 2 i \, e\right)} - 6 \, d^{3} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{3} f^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 12 \, c d^{2} f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} - 6 \, c^{2} d f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, d^{3} f x e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, c d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)}}{16 \, a f^{4}}"," ",0,"1/16*(2*d^3*f^4*x^4 + 8*c*d^2*f^4*x^3 + 4*I*d^3*f^3*x^3*e^(2*I*f*x + 2*I*e) + 12*c^2*d*f^4*x^2 + 12*I*c*d^2*f^3*x^2*e^(2*I*f*x + 2*I*e) + 8*c^3*f^4*x + 12*I*c^2*d*f^3*x*e^(2*I*f*x + 2*I*e) - 6*d^3*f^2*x^2*e^(2*I*f*x + 2*I*e) + 4*I*c^3*f^3*e^(2*I*f*x + 2*I*e) - 12*c*d^2*f^2*x*e^(2*I*f*x + 2*I*e) - 6*c^2*d*f^2*e^(2*I*f*x + 2*I*e) - 6*I*d^3*f*x*e^(2*I*f*x + 2*I*e) - 6*I*c*d^2*f*e^(2*I*f*x + 2*I*e) + 3*d^3*e^(2*I*f*x + 2*I*e))/(a*f^4)","A",0
17,1,143,0,0.417669," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\frac{4 \, d^{2} f^{3} x^{3} + 12 \, c d f^{3} x^{2} + 6 i \, d^{2} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, c^{2} f^{3} x + 12 i \, c d f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, c^{2} f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 6 \, d^{2} f x e^{\left(2 i \, f x + 2 i \, e\right)} - 6 \, c d f e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)}}{24 \, a f^{3}}"," ",0,"1/24*(4*d^2*f^3*x^3 + 12*c*d*f^3*x^2 + 6*I*d^2*f^2*x^2*e^(2*I*f*x + 2*I*e) + 12*c^2*f^3*x + 12*I*c*d*f^2*x*e^(2*I*f*x + 2*I*e) + 6*I*c^2*f^2*e^(2*I*f*x + 2*I*e) - 6*d^2*f*x*e^(2*I*f*x + 2*I*e) - 6*c*d*f*e^(2*I*f*x + 2*I*e) - 3*I*d^2*e^(2*I*f*x + 2*I*e))/(a*f^3)","A",0
18,1,67,0,0.651039," ","integrate((d*x+c)/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\frac{2 \, d f^{2} x^{2} + 4 \, c f^{2} x + 2 i \, d f x e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} - d e^{\left(2 i \, f x + 2 i \, e\right)}}{8 \, a f^{2}}"," ",0,"1/8*(2*d*f^2*x^2 + 4*c*f^2*x + 2*I*d*f*x*e^(2*I*f*x + 2*I*e) + 2*I*c*f*e^(2*I*f*x + 2*I*e) - d*e^(2*I*f*x + 2*I*e))/(a*f^2)","A",0
19,1,367,0,0.551674," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","-\frac{\cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 2 i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 2 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) - \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + i \, \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 i \, \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - i \, \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - \log\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - I*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 2*I*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 2*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) - cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + I*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + I*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) + cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) - 2*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 2*I*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - I*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - log(d*x + c))/(a*d)","B",0
20,1,367,0,47.649490," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","-\frac{i \, {\left(-2 i \, {\left(d x + c\right)} {\left(-\frac{i \, c f}{d x + c} + i \, f + \frac{i \, d e}{d x + c}\right)} f^{2} {\rm Ei}\left(\frac{2 \, {\left(d x + c\right)} {\left(-\frac{i \, c f}{d x + c} + i \, f + \frac{i \, d e}{d x + c}\right)} + 2 i \, c f - 2 i \, d e}{d}\right) e^{\left(\frac{-2 i \, c f + 2 i \, d e}{d}\right)} + 2 \, c f^{3} {\rm Ei}\left(\frac{2 \, {\left(d x + c\right)} {\left(-\frac{i \, c f}{d x + c} + i \, f + \frac{i \, d e}{d x + c}\right)} + 2 i \, c f - 2 i \, d e}{d}\right) e^{\left(\frac{-2 i \, c f + 2 i \, d e}{d}\right)} - 2 \, d f^{2} {\rm Ei}\left(\frac{2 \, {\left(d x + c\right)} {\left(-\frac{i \, c f}{d x + c} + i \, f + \frac{i \, d e}{d x + c}\right)} + 2 i \, c f - 2 i \, d e}{d}\right) e^{\left(\frac{-2 i \, c f + 2 i \, d e}{d} + 1\right)} + i \, d f^{2} e^{\left(\frac{{\left(d x + c\right)} {\left(-\frac{2 i \, c f}{d x + c} + 2 i \, f + \frac{2 i \, d e}{d x + c}\right)}}{d}\right)}\right)} d^{2}}{2 \, {\left(-i \, {\left(d x + c\right)} d^{4} {\left(-\frac{i \, c f}{d x + c} + i \, f + \frac{i \, d e}{d x + c}\right)} + c d^{4} f - d^{5} e\right)} a f} - \frac{1}{2 \, {\left(d x + c\right)} a d}"," ",0,"-1/2*I*(-2*I*(d*x + c)*(-I*c*f/(d*x + c) + I*f + I*d*e/(d*x + c))*f^2*Ei((2*(d*x + c)*(-I*c*f/(d*x + c) + I*f + I*d*e/(d*x + c)) + 2*I*c*f - 2*I*d*e)/d)*e^((-2*I*c*f + 2*I*d*e)/d) + 2*c*f^3*Ei((2*(d*x + c)*(-I*c*f/(d*x + c) + I*f + I*d*e/(d*x + c)) + 2*I*c*f - 2*I*d*e)/d)*e^((-2*I*c*f + 2*I*d*e)/d) - 2*d*f^2*Ei((2*(d*x + c)*(-I*c*f/(d*x + c) + I*f + I*d*e/(d*x + c)) + 2*I*c*f - 2*I*d*e)/d)*e^((-2*I*c*f + 2*I*d*e)/d + 1) + I*d*f^2*e^((d*x + c)*(-2*I*c*f/(d*x + c) + 2*I*f + 2*I*d*e/(d*x + c))/d))*d^2/((-I*(d*x + c)*d^4*(-I*c*f/(d*x + c) + I*f + I*d*e/(d*x + c)) + c*d^4*f - d^5*e)*a*f) - 1/2/((d*x + c)*a*d)","B",0
21,1,1630,0,0.619180," ","integrate(1/(d*x+c)^3/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\frac{4 \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, d^{2} f^{2} x^{2} \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 8 i \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 8 \, d^{2} f^{2} x^{2} \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) - 4 \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 4 i \, d^{2} f^{2} x^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 4 i \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, d^{2} f^{2} x^{2} \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 i \, d^{2} f^{2} x^{2} \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, d^{2} f^{2} x^{2} \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, d^{2} f^{2} x^{2} \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 i \, c d f^{2} x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 16 i \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 16 \, c d f^{2} x \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) - 8 \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 8 i \, c d f^{2} x \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 8 i \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, c d f^{2} x \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 16 \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 16 i \, c d f^{2} x \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 i \, c d f^{2} x \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 \, c d f^{2} x \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, c^{2} f^{2} \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 8 i \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 8 \, c^{2} f^{2} \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) - 4 \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 4 i \, c^{2} f^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 4 i \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, c^{2} f^{2} \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 i \, c^{2} f^{2} \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, c^{2} f^{2} \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, c^{2} f^{2} \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 i \, d^{2} f x \cos\left(2 \, f x\right) \cos\left(e\right)^{2} - 2 \, d^{2} f x \cos\left(e\right)^{2} \sin\left(2 \, f x\right) - 4 \, d^{2} f x \cos\left(2 \, f x\right) \cos\left(e\right) \sin\left(e\right) - 4 i \, d^{2} f x \cos\left(e\right) \sin\left(2 \, f x\right) \sin\left(e\right) - 2 i \, d^{2} f x \cos\left(2 \, f x\right) \sin\left(e\right)^{2} + 2 \, d^{2} f x \sin\left(2 \, f x\right) \sin\left(e\right)^{2} + 2 i \, c d f \cos\left(2 \, f x\right) \cos\left(e\right)^{2} - 2 \, c d f \cos\left(e\right)^{2} \sin\left(2 \, f x\right) - 4 \, c d f \cos\left(2 \, f x\right) \cos\left(e\right) \sin\left(e\right) - 4 i \, c d f \cos\left(e\right) \sin\left(2 \, f x\right) \sin\left(e\right) - 2 i \, c d f \cos\left(2 \, f x\right) \sin\left(e\right)^{2} + 2 \, c d f \sin\left(2 \, f x\right) \sin\left(e\right)^{2} + d^{2} \cos\left(2 \, f x\right) \cos\left(e\right)^{2} + i \, d^{2} \cos\left(e\right)^{2} \sin\left(2 \, f x\right) + 2 i \, d^{2} \cos\left(2 \, f x\right) \cos\left(e\right) \sin\left(e\right) - 2 \, d^{2} \cos\left(e\right) \sin\left(2 \, f x\right) \sin\left(e\right) - d^{2} \cos\left(2 \, f x\right) \sin\left(e\right)^{2} - i \, d^{2} \sin\left(2 \, f x\right) \sin\left(e\right)^{2} - d^{2}}{4 \, {\left(a d^{5} x^{2} + 2 \, a c d^{4} x + a c^{2} d^{3}\right)}}"," ",0,"1/4*(4*d^2*f^2*x^2*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 4*I*d^2*f^2*x^2*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 8*I*d^2*f^2*x^2*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 8*d^2*f^2*x^2*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) - 4*d^2*f^2*x^2*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 4*I*d^2*f^2*x^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 4*I*d^2*f^2*x^2*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 4*d^2*f^2*x^2*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) - 8*d^2*f^2*x^2*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 8*I*d^2*f^2*x^2*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 4*I*d^2*f^2*x^2*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 4*d^2*f^2*x^2*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 8*c*d*f^2*x*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 8*I*c*d*f^2*x*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 16*I*c*d*f^2*x*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 16*c*d*f^2*x*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) - 8*c*d*f^2*x*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 8*I*c*d*f^2*x*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 8*I*c*d*f^2*x*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 8*c*d*f^2*x*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) - 16*c*d*f^2*x*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 16*I*c*d*f^2*x*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 8*I*c*d*f^2*x*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 8*c*d*f^2*x*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 4*c^2*f^2*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 4*I*c^2*f^2*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 8*I*c^2*f^2*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 8*c^2*f^2*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) - 4*c^2*f^2*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 4*I*c^2*f^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 4*I*c^2*f^2*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 4*c^2*f^2*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) - 8*c^2*f^2*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 8*I*c^2*f^2*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 4*I*c^2*f^2*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 4*c^2*f^2*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 2*I*d^2*f*x*cos(2*f*x)*cos(e)^2 - 2*d^2*f*x*cos(e)^2*sin(2*f*x) - 4*d^2*f*x*cos(2*f*x)*cos(e)*sin(e) - 4*I*d^2*f*x*cos(e)*sin(2*f*x)*sin(e) - 2*I*d^2*f*x*cos(2*f*x)*sin(e)^2 + 2*d^2*f*x*sin(2*f*x)*sin(e)^2 + 2*I*c*d*f*cos(2*f*x)*cos(e)^2 - 2*c*d*f*cos(e)^2*sin(2*f*x) - 4*c*d*f*cos(2*f*x)*cos(e)*sin(e) - 4*I*c*d*f*cos(e)*sin(2*f*x)*sin(e) - 2*I*c*d*f*cos(2*f*x)*sin(e)^2 + 2*c*d*f*sin(2*f*x)*sin(e)^2 + d^2*cos(2*f*x)*cos(e)^2 + I*d^2*cos(e)^2*sin(2*f*x) + 2*I*d^2*cos(2*f*x)*cos(e)*sin(e) - 2*d^2*cos(e)*sin(2*f*x)*sin(e) - d^2*cos(2*f*x)*sin(e)^2 - I*d^2*sin(2*f*x)*sin(e)^2 - d^2)/(a*d^5*x^2 + 2*a*c*d^4*x + a*c^2*d^3)","B",0
22,1,433,0,0.512986," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\frac{32 \, d^{3} f^{4} x^{4} + 128 \, c d^{2} f^{4} x^{3} - 32 i \, d^{3} f^{3} x^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 128 i \, d^{3} f^{3} x^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 192 \, c^{2} d f^{4} x^{2} - 96 i \, c d^{2} f^{3} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 384 i \, c d^{2} f^{3} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 128 \, c^{3} f^{4} x - 96 i \, c^{2} d f^{3} x e^{\left(4 i \, f x + 4 i \, e\right)} + 24 \, d^{3} f^{2} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 384 i \, c^{2} d f^{3} x e^{\left(2 i \, f x + 2 i \, e\right)} - 192 \, d^{3} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 32 i \, c^{3} f^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 48 \, c d^{2} f^{2} x e^{\left(4 i \, f x + 4 i \, e\right)} + 128 i \, c^{3} f^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 384 \, c d^{2} f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} + 24 \, c^{2} d f^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i \, d^{3} f x e^{\left(4 i \, f x + 4 i \, e\right)} - 192 \, c^{2} d f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 192 i \, d^{3} f x e^{\left(2 i \, f x + 2 i \, e\right)} + 12 i \, c d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - 192 i \, c d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 3 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)}}{512 \, a^{2} f^{4}}"," ",0,"1/512*(32*d^3*f^4*x^4 + 128*c*d^2*f^4*x^3 - 32*I*d^3*f^3*x^3*e^(4*I*f*x + 4*I*e) + 128*I*d^3*f^3*x^3*e^(2*I*f*x + 2*I*e) + 192*c^2*d*f^4*x^2 - 96*I*c*d^2*f^3*x^2*e^(4*I*f*x + 4*I*e) + 384*I*c*d^2*f^3*x^2*e^(2*I*f*x + 2*I*e) + 128*c^3*f^4*x - 96*I*c^2*d*f^3*x*e^(4*I*f*x + 4*I*e) + 24*d^3*f^2*x^2*e^(4*I*f*x + 4*I*e) + 384*I*c^2*d*f^3*x*e^(2*I*f*x + 2*I*e) - 192*d^3*f^2*x^2*e^(2*I*f*x + 2*I*e) - 32*I*c^3*f^3*e^(4*I*f*x + 4*I*e) + 48*c*d^2*f^2*x*e^(4*I*f*x + 4*I*e) + 128*I*c^3*f^3*e^(2*I*f*x + 2*I*e) - 384*c*d^2*f^2*x*e^(2*I*f*x + 2*I*e) + 24*c^2*d*f^2*e^(4*I*f*x + 4*I*e) + 12*I*d^3*f*x*e^(4*I*f*x + 4*I*e) - 192*c^2*d*f^2*e^(2*I*f*x + 2*I*e) - 192*I*d^3*f*x*e^(2*I*f*x + 2*I*e) + 12*I*c*d^2*f*e^(4*I*f*x + 4*I*e) - 192*I*c*d^2*f*e^(2*I*f*x + 2*I*e) - 3*d^3*e^(4*I*f*x + 4*I*e) + 96*d^3*e^(2*I*f*x + 2*I*e))/(a^2*f^4)","B",0
23,1,247,0,0.503977," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\frac{32 \, d^{2} f^{3} x^{3} + 96 \, c d f^{3} x^{2} - 24 i \, d^{2} f^{2} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, d^{2} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 96 \, c^{2} f^{3} x - 48 i \, c d f^{2} x e^{\left(4 i \, f x + 4 i \, e\right)} + 192 i \, c d f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} - 24 i \, c^{2} f^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 12 \, d^{2} f x e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, c^{2} f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 96 \, d^{2} f x e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, c d f e^{\left(4 i \, f x + 4 i \, e\right)} - 96 \, c d f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 48 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)}}{384 \, a^{2} f^{3}}"," ",0,"1/384*(32*d^2*f^3*x^3 + 96*c*d*f^3*x^2 - 24*I*d^2*f^2*x^2*e^(4*I*f*x + 4*I*e) + 96*I*d^2*f^2*x^2*e^(2*I*f*x + 2*I*e) + 96*c^2*f^3*x - 48*I*c*d*f^2*x*e^(4*I*f*x + 4*I*e) + 192*I*c*d*f^2*x*e^(2*I*f*x + 2*I*e) - 24*I*c^2*f^2*e^(4*I*f*x + 4*I*e) + 12*d^2*f*x*e^(4*I*f*x + 4*I*e) + 96*I*c^2*f^2*e^(2*I*f*x + 2*I*e) - 96*d^2*f*x*e^(2*I*f*x + 2*I*e) + 12*c*d*f*e^(4*I*f*x + 4*I*e) - 96*c*d*f*e^(2*I*f*x + 2*I*e) + 3*I*d^2*e^(4*I*f*x + 4*I*e) - 48*I*d^2*e^(2*I*f*x + 2*I*e))/(a^2*f^3)","A",0
24,1,108,0,1.734450," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\frac{8 \, d f^{2} x^{2} + 16 \, c f^{2} x - 4 i \, d f x e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, d f x e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, c f e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} + d e^{\left(4 i \, f x + 4 i \, e\right)} - 8 \, d e^{\left(2 i \, f x + 2 i \, e\right)}}{64 \, a^{2} f^{2}}"," ",0,"1/64*(8*d*f^2*x^2 + 16*c*f^2*x - 4*I*d*f*x*e^(4*I*f*x + 4*I*e) + 16*I*d*f*x*e^(2*I*f*x + 2*I*e) - 4*I*c*f*e^(4*I*f*x + 4*I*e) + 16*I*c*f*e^(2*I*f*x + 2*I*e) + d*e^(4*I*f*x + 4*I*e) - 8*d*e^(2*I*f*x + 2*I*e))/(a^2*f^2)","A",0
25,1,987,0,1.833966," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\frac{\cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - i \, \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) + 4 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 4 \, \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) - 6 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 6 i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} - 4 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} - 4 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} + \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} - i \, \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} + i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + i \, \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) - 4 i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 4 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) + 2 \, \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 2 i \, \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} - 2 i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 i \, \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 \, \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + \log\left(d x + c\right)}{4 \, a^{2} d}"," ",0,"1/4*(cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) - I*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) + 4*I*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) + 4*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) - 6*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 + 6*I*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 - 4*I*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 - 4*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 + cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 - I*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 + I*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) + cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) - 4*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 4*I*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 6*I*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 6*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 4*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 4*I*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + I*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) - 2*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) + 2*I*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) - 4*I*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) - 4*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) + 2*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 - 2*I*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 - 2*I*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 2*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) + 4*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 4*I*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 2*I*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 2*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + log(d*x + c))/(a^2*d)","B",0
26,1,2369,0,64.087110," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\frac{4 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, d f x \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) - 16 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 16 i \, d f x \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) - 24 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 24 \, d f x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} + 16 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} - 16 i \, d f x \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} + 4 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} + 4 \, d f x \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} - 4 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, d f x \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 16 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 16 \, d f x \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 24 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 24 i \, d f x \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 16 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 16 \, d f x \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, d f x \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, c f \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) - 16 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 16 i \, c f \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) - 24 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 24 \, c f \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} + 16 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} - 16 i \, c f \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} + 4 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} + 4 \, c f \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} - 4 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, c f \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 16 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 16 \, c f \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 24 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 24 i \, c f \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 16 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 16 \, c f \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, c f \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, c f \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, d f x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 8 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 8 i \, d f x \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) + 4 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 4 \, d f x \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 4 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, d f x \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, d f x \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, d f x \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - d \cos\left(4 \, f x\right) \cos\left(e\right)^{4} - 4 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - i \, d \cos\left(e\right)^{4} \sin\left(4 \, f x\right) - 4 \, c f \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) - 4 i \, d \cos\left(4 \, f x\right) \cos\left(e\right)^{3} \sin\left(e\right) + 8 \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 4 \, d \cos\left(e\right)^{3} \sin\left(4 \, f x\right) \sin\left(e\right) - 8 i \, c f \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) + 6 \, d \cos\left(4 \, f x\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} + 4 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 6 i \, d \cos\left(e\right)^{2} \sin\left(4 \, f x\right) \sin\left(e\right)^{2} + 4 \, c f \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 4 i \, d \cos\left(4 \, f x\right) \cos\left(e\right) \sin\left(e\right)^{3} - 4 \, d \cos\left(e\right) \sin\left(4 \, f x\right) \sin\left(e\right)^{3} - d \cos\left(4 \, f x\right) \sin\left(e\right)^{4} - i \, d \sin\left(4 \, f x\right) \sin\left(e\right)^{4} + 4 \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 i \, c f \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, c f \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, c f \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 i \, c f \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 2 \, d \cos\left(2 \, f x\right) \cos\left(e\right)^{2} + 2 i \, d \cos\left(e\right)^{2} \sin\left(2 \, f x\right) + 4 i \, d \cos\left(2 \, f x\right) \cos\left(e\right) \sin\left(e\right) - 4 \, d \cos\left(e\right) \sin\left(2 \, f x\right) \sin\left(e\right) - 2 \, d \cos\left(2 \, f x\right) \sin\left(e\right)^{2} - 2 i \, d \sin\left(2 \, f x\right) \sin\left(e\right)^{2} - d}{4 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)}}"," ",0,"1/4*(4*I*d*f*x*cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) + 4*d*f*x*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) - 16*d*f*x*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) + 16*I*d*f*x*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) - 24*I*d*f*x*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 - 24*d*f*x*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 + 16*d*f*x*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 - 16*I*d*f*x*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 + 4*I*d*f*x*cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 + 4*d*f*x*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 - 4*d*f*x*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 4*I*d*f*x*cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) - 16*I*d*f*x*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 16*d*f*x*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 24*d*f*x*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 24*I*d*f*x*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 16*I*d*f*x*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + 16*d*f*x*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 4*d*f*x*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 4*I*d*f*x*sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 4*I*c*f*cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) + 4*c*f*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) - 16*c*f*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) + 16*I*c*f*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) - 24*I*c*f*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 - 24*c*f*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 + 16*c*f*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 - 16*I*c*f*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 + 4*I*c*f*cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 + 4*c*f*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 - 4*c*f*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 4*I*c*f*cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) - 16*I*c*f*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 16*c*f*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 24*c*f*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 24*I*c*f*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 16*I*c*f*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + 16*c*f*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 4*c*f*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 4*I*c*f*sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) - 4*I*d*f*x*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 4*d*f*x*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 8*d*f*x*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) - 8*I*d*f*x*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) + 4*I*d*f*x*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 4*d*f*x*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 4*d*f*x*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 4*I*d*f*x*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) + 8*I*d*f*x*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 8*d*f*x*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 4*d*f*x*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 4*I*d*f*x*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - d*cos(4*f*x)*cos(e)^4 - 4*I*c*f*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - I*d*cos(e)^4*sin(4*f*x) - 4*c*f*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) - 4*I*d*cos(4*f*x)*cos(e)^3*sin(e) + 8*c*f*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 4*d*cos(e)^3*sin(4*f*x)*sin(e) - 8*I*c*f*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) + 6*d*cos(4*f*x)*cos(e)^2*sin(e)^2 + 4*I*c*f*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 6*I*d*cos(e)^2*sin(4*f*x)*sin(e)^2 + 4*c*f*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 4*I*d*cos(4*f*x)*cos(e)*sin(e)^3 - 4*d*cos(e)*sin(4*f*x)*sin(e)^3 - d*cos(4*f*x)*sin(e)^4 - I*d*sin(4*f*x)*sin(e)^4 + 4*c*f*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 4*I*c*f*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) + 8*I*c*f*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 8*c*f*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 4*c*f*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 4*I*c*f*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 2*d*cos(2*f*x)*cos(e)^2 + 2*I*d*cos(e)^2*sin(2*f*x) + 4*I*d*cos(2*f*x)*cos(e)*sin(e) - 4*d*cos(e)*sin(2*f*x)*sin(e) - 2*d*cos(2*f*x)*sin(e)^2 - 2*I*d*sin(2*f*x)*sin(e)^2 - d)/(a^2*d^3*x + a^2*c*d^2)","B",0
27,1,623,0,0.610741," ","integrate((d*x+c)^3/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","\frac{864 \, d^{3} f^{4} x^{4} + 3456 \, c d^{2} f^{4} x^{3} + 576 i \, d^{3} f^{3} x^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 2592 i \, d^{3} f^{3} x^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 5184 i \, d^{3} f^{3} x^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 5184 \, c^{2} d f^{4} x^{2} + 1728 i \, c d^{2} f^{3} x^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 7776 i \, c d^{2} f^{3} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 15552 i \, c d^{2} f^{3} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 3456 \, c^{3} f^{4} x + 1728 i \, c^{2} d f^{3} x e^{\left(6 i \, f x + 6 i \, e\right)} - 288 \, d^{3} f^{2} x^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 7776 i \, c^{2} d f^{3} x e^{\left(4 i \, f x + 4 i \, e\right)} + 1944 \, d^{3} f^{2} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 15552 i \, c^{2} d f^{3} x e^{\left(2 i \, f x + 2 i \, e\right)} - 7776 \, d^{3} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 576 i \, c^{3} f^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 576 \, c d^{2} f^{2} x e^{\left(6 i \, f x + 6 i \, e\right)} - 2592 i \, c^{3} f^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 3888 \, c d^{2} f^{2} x e^{\left(4 i \, f x + 4 i \, e\right)} + 5184 i \, c^{3} f^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 15552 \, c d^{2} f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} - 288 \, c^{2} d f^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 96 i \, d^{3} f x e^{\left(6 i \, f x + 6 i \, e\right)} + 1944 \, c^{2} d f^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 972 i \, d^{3} f x e^{\left(4 i \, f x + 4 i \, e\right)} - 7776 \, c^{2} d f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 7776 i \, d^{3} f x e^{\left(2 i \, f x + 2 i \, e\right)} - 96 i \, c d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 972 i \, c d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - 7776 i \, c d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 \, d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 243 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 3888 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)}}{27648 \, a^{3} f^{4}}"," ",0,"1/27648*(864*d^3*f^4*x^4 + 3456*c*d^2*f^4*x^3 + 576*I*d^3*f^3*x^3*e^(6*I*f*x + 6*I*e) - 2592*I*d^3*f^3*x^3*e^(4*I*f*x + 4*I*e) + 5184*I*d^3*f^3*x^3*e^(2*I*f*x + 2*I*e) + 5184*c^2*d*f^4*x^2 + 1728*I*c*d^2*f^3*x^2*e^(6*I*f*x + 6*I*e) - 7776*I*c*d^2*f^3*x^2*e^(4*I*f*x + 4*I*e) + 15552*I*c*d^2*f^3*x^2*e^(2*I*f*x + 2*I*e) + 3456*c^3*f^4*x + 1728*I*c^2*d*f^3*x*e^(6*I*f*x + 6*I*e) - 288*d^3*f^2*x^2*e^(6*I*f*x + 6*I*e) - 7776*I*c^2*d*f^3*x*e^(4*I*f*x + 4*I*e) + 1944*d^3*f^2*x^2*e^(4*I*f*x + 4*I*e) + 15552*I*c^2*d*f^3*x*e^(2*I*f*x + 2*I*e) - 7776*d^3*f^2*x^2*e^(2*I*f*x + 2*I*e) + 576*I*c^3*f^3*e^(6*I*f*x + 6*I*e) - 576*c*d^2*f^2*x*e^(6*I*f*x + 6*I*e) - 2592*I*c^3*f^3*e^(4*I*f*x + 4*I*e) + 3888*c*d^2*f^2*x*e^(4*I*f*x + 4*I*e) + 5184*I*c^3*f^3*e^(2*I*f*x + 2*I*e) - 15552*c*d^2*f^2*x*e^(2*I*f*x + 2*I*e) - 288*c^2*d*f^2*e^(6*I*f*x + 6*I*e) - 96*I*d^3*f*x*e^(6*I*f*x + 6*I*e) + 1944*c^2*d*f^2*e^(4*I*f*x + 4*I*e) + 972*I*d^3*f*x*e^(4*I*f*x + 4*I*e) - 7776*c^2*d*f^2*e^(2*I*f*x + 2*I*e) - 7776*I*d^3*f*x*e^(2*I*f*x + 2*I*e) - 96*I*c*d^2*f*e^(6*I*f*x + 6*I*e) + 972*I*c*d^2*f*e^(4*I*f*x + 4*I*e) - 7776*I*c*d^2*f*e^(2*I*f*x + 2*I*e) + 16*d^3*e^(6*I*f*x + 6*I*e) - 243*d^3*e^(4*I*f*x + 4*I*e) + 3888*d^3*e^(2*I*f*x + 2*I*e))/(a^3*f^4)","B",0
28,1,351,0,0.551906," ","integrate((d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","\frac{288 \, d^{2} f^{3} x^{3} + 864 \, c d f^{3} x^{2} + 144 i \, d^{2} f^{2} x^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 648 i \, d^{2} f^{2} x^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 1296 i \, d^{2} f^{2} x^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 864 \, c^{2} f^{3} x + 288 i \, c d f^{2} x e^{\left(6 i \, f x + 6 i \, e\right)} - 1296 i \, c d f^{2} x e^{\left(4 i \, f x + 4 i \, e\right)} + 2592 i \, c d f^{2} x e^{\left(2 i \, f x + 2 i \, e\right)} + 144 i \, c^{2} f^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 48 \, d^{2} f x e^{\left(6 i \, f x + 6 i \, e\right)} - 648 i \, c^{2} f^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 324 \, d^{2} f x e^{\left(4 i \, f x + 4 i \, e\right)} + 1296 i \, c^{2} f^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 1296 \, d^{2} f x e^{\left(2 i \, f x + 2 i \, e\right)} - 48 \, c d f e^{\left(6 i \, f x + 6 i \, e\right)} + 324 \, c d f e^{\left(4 i \, f x + 4 i \, e\right)} - 1296 \, c d f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 81 i \, d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 648 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)}}{6912 \, a^{3} f^{3}}"," ",0,"1/6912*(288*d^2*f^3*x^3 + 864*c*d*f^3*x^2 + 144*I*d^2*f^2*x^2*e^(6*I*f*x + 6*I*e) - 648*I*d^2*f^2*x^2*e^(4*I*f*x + 4*I*e) + 1296*I*d^2*f^2*x^2*e^(2*I*f*x + 2*I*e) + 864*c^2*f^3*x + 288*I*c*d*f^2*x*e^(6*I*f*x + 6*I*e) - 1296*I*c*d*f^2*x*e^(4*I*f*x + 4*I*e) + 2592*I*c*d*f^2*x*e^(2*I*f*x + 2*I*e) + 144*I*c^2*f^2*e^(6*I*f*x + 6*I*e) - 48*d^2*f*x*e^(6*I*f*x + 6*I*e) - 648*I*c^2*f^2*e^(4*I*f*x + 4*I*e) + 324*d^2*f*x*e^(4*I*f*x + 4*I*e) + 1296*I*c^2*f^2*e^(2*I*f*x + 2*I*e) - 1296*d^2*f*x*e^(2*I*f*x + 2*I*e) - 48*c*d*f*e^(6*I*f*x + 6*I*e) + 324*c*d*f*e^(4*I*f*x + 4*I*e) - 1296*c*d*f*e^(2*I*f*x + 2*I*e) - 8*I*d^2*e^(6*I*f*x + 6*I*e) + 81*I*d^2*e^(4*I*f*x + 4*I*e) - 648*I*d^2*e^(2*I*f*x + 2*I*e))/(a^3*f^3)","A",0
29,1,151,0,2.084271," ","integrate((d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","\frac{72 \, d f^{2} x^{2} + 144 \, c f^{2} x + 24 i \, d f x e^{\left(6 i \, f x + 6 i \, e\right)} - 108 i \, d f x e^{\left(4 i \, f x + 4 i \, e\right)} + 216 i \, d f x e^{\left(2 i \, f x + 2 i \, e\right)} + 24 i \, c f e^{\left(6 i \, f x + 6 i \, e\right)} - 108 i \, c f e^{\left(4 i \, f x + 4 i \, e\right)} + 216 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, d e^{\left(6 i \, f x + 6 i \, e\right)} + 27 \, d e^{\left(4 i \, f x + 4 i \, e\right)} - 108 \, d e^{\left(2 i \, f x + 2 i \, e\right)}}{1152 \, a^{3} f^{2}}"," ",0,"1/1152*(72*d*f^2*x^2 + 144*c*f^2*x + 24*I*d*f*x*e^(6*I*f*x + 6*I*e) - 108*I*d*f*x*e^(4*I*f*x + 4*I*e) + 216*I*d*f*x*e^(2*I*f*x + 2*I*e) + 24*I*c*f*e^(6*I*f*x + 6*I*e) - 108*I*c*f*e^(4*I*f*x + 4*I*e) + 216*I*c*f*e^(2*I*f*x + 2*I*e) - 4*d*e^(6*I*f*x + 6*I*e) + 27*d*e^(4*I*f*x + 4*I*e) - 108*d*e^(2*I*f*x + 2*I*e))/(a^3*f^2)","A",0
30,1,1887,0,1.535243," ","integrate(1/(d*x+c)/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","-\frac{\cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - i \, \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) + 6 i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 6 \, \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) - 15 \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 15 i \, \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} - 20 i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} - 20 \, \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} + 15 \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} - 15 i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} + 6 i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{5} + 6 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} - \cos\left(\frac{6 \, c f}{d}\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{6} + i \, \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} + i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + \cos\left(e\right)^{6} \sin\left(\frac{6 \, c f}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, \cos\left(e\right)^{5} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 15 i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 15 \, \cos\left(e\right)^{4} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 20 \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 20 i \, \cos\left(e\right)^{3} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 15 i \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 15 \, \cos\left(e\right)^{2} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, \cos\left(e\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - i \, \cos\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 3 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 3 i \, \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) - 12 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 12 \, \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) + 18 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 18 i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} + 12 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} + 12 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} - 3 \, \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} + 3 i \, \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} - 3 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 3 \, \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 12 i \, \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 18 i \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 18 \, \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 12 \, \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 3 i \, \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 3 \, \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 3 \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 3 i \, \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 6 i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 6 \, \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) - 3 \, \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 3 i \, \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 3 i \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 3 \, \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 3 i \, \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 3 \, \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - \log\left(d x + c\right)}{8 \, a^{3} d}"," ",0,"-1/8*(cos(6*c*f/d)*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d) - I*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d) + 6*I*cos(6*c*f/d)*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(e) + 6*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e) - 15*cos(6*c*f/d)*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^2 + 15*I*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^2 - 20*I*cos(6*c*f/d)*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^3 - 20*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^3 + 15*cos(6*c*f/d)*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^4 - 15*I*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^4 + 6*I*cos(6*c*f/d)*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^5 + 6*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^5 - cos(6*c*f/d)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^6 + I*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^6 + I*cos(6*c*f/d)*cos(e)^6*sin_integral(6*(d*f*x + c*f)/d) + cos(e)^6*sin(6*c*f/d)*sin_integral(6*(d*f*x + c*f)/d) - 6*cos(6*c*f/d)*cos(e)^5*sin(e)*sin_integral(6*(d*f*x + c*f)/d) + 6*I*cos(e)^5*sin(6*c*f/d)*sin(e)*sin_integral(6*(d*f*x + c*f)/d) - 15*I*cos(6*c*f/d)*cos(e)^4*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) - 15*cos(e)^4*sin(6*c*f/d)*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) + 20*cos(6*c*f/d)*cos(e)^3*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) - 20*I*cos(e)^3*sin(6*c*f/d)*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) + 15*I*cos(6*c*f/d)*cos(e)^2*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) + 15*cos(e)^2*sin(6*c*f/d)*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) - 6*cos(6*c*f/d)*cos(e)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) + 6*I*cos(e)*sin(6*c*f/d)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) - I*cos(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) - sin(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) - 3*cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) + 3*I*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) - 12*I*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) - 12*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) + 18*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 - 18*I*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 + 12*I*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 + 12*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 - 3*cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 + 3*I*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 - 3*I*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) - 3*cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) + 12*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 12*I*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 18*I*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 18*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 12*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + 12*I*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 3*I*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) - 3*sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 3*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 3*I*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 6*I*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 6*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) - 3*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 3*I*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 3*I*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 3*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) - 6*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 6*I*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 3*I*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 3*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - log(d*x + c))/(a^3*d)","B",0
31,1,4524,0,87.905953," ","integrate(1/(d*x+c)^2/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","\frac{-6 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, d f x \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) + 36 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 36 i \, d f x \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) + 90 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 90 \, d f x \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} - 120 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} + 120 i \, d f x \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} - 90 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} - 90 \, d f x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} + 36 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{5} - 36 i \, d f x \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} + 6 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{6} + 6 \, d f x \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} + 6 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, d f x \cos\left(e\right)^{6} \sin\left(\frac{6 \, c f}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 \, d f x \cos\left(e\right)^{5} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 90 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 90 i \, d f x \cos\left(e\right)^{4} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 120 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 120 \, d f x \cos\left(e\right)^{3} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 90 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 90 i \, d f x \cos\left(e\right)^{2} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 i \, d f x \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 \, d f x \cos\left(e\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, d f x \cos\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, d f x \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, c f \cos\left(e\right)^{6} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) + 36 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 36 i \, c f \cos\left(e\right)^{5} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) + 90 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 90 \, c f \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} - 120 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} + 120 i \, c f \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} - 90 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} - 90 \, c f \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} + 36 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{5} - 36 i \, c f \cos\left(e\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} + 6 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{6} + 6 \, c f \operatorname{Ci}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} + 6 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, c f \cos\left(e\right)^{6} \sin\left(\frac{6 \, c f}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{5} \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 \, c f \cos\left(e\right)^{5} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 90 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{4} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 90 i \, c f \cos\left(e\right)^{4} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 120 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 120 \, c f \cos\left(e\right)^{3} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 90 \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 90 i \, c f \cos\left(e\right)^{2} \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 i \, c f \cos\left(\frac{6 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 36 \, c f \cos\left(e\right) \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{5} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, c f \cos\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, c f \sin\left(\frac{6 \, c f}{d}\right) \sin\left(e\right)^{6} \operatorname{Si}\left(\frac{6 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 \, d f x \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) - 48 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 48 i \, d f x \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) - 72 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 72 \, d f x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} + 48 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} - 48 i \, d f x \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} + 12 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} + 12 \, d f x \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} - 12 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, d f x \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 48 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 48 \, d f x \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 72 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 72 i \, d f x \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 48 i \, d f x \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 48 \, d f x \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 12 \, d f x \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, d f x \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + d \cos\left(6 \, f x\right) \cos\left(e\right)^{6} + 12 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + i \, d \cos\left(e\right)^{6} \sin\left(6 \, f x\right) + 12 \, c f \cos\left(e\right)^{4} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) + 6 i \, d \cos\left(6 \, f x\right) \cos\left(e\right)^{5} \sin\left(e\right) - 48 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 6 \, d \cos\left(e\right)^{5} \sin\left(6 \, f x\right) \sin\left(e\right) + 48 i \, c f \cos\left(e\right)^{3} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) - 15 \, d \cos\left(6 \, f x\right) \cos\left(e\right)^{4} \sin\left(e\right)^{2} - 72 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} - 15 i \, d \cos\left(e\right)^{4} \sin\left(6 \, f x\right) \sin\left(e\right)^{2} - 72 \, c f \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} - 20 i \, d \cos\left(6 \, f x\right) \cos\left(e\right)^{3} \sin\left(e\right)^{3} + 48 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{3} + 20 \, d \cos\left(e\right)^{3} \sin\left(6 \, f x\right) \sin\left(e\right)^{3} - 48 i \, c f \cos\left(e\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} + 15 \, d \cos\left(6 \, f x\right) \cos\left(e\right)^{2} \sin\left(e\right)^{4} + 12 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{4} + 15 i \, d \cos\left(e\right)^{2} \sin\left(6 \, f x\right) \sin\left(e\right)^{4} + 12 \, c f \operatorname{Ci}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} + 6 i \, d \cos\left(6 \, f x\right) \cos\left(e\right) \sin\left(e\right)^{5} - 6 \, d \cos\left(e\right) \sin\left(6 \, f x\right) \sin\left(e\right)^{5} - d \cos\left(6 \, f x\right) \sin\left(e\right)^{6} - i \, d \sin\left(6 \, f x\right) \sin\left(e\right)^{6} - 12 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, c f \cos\left(e\right)^{4} \sin\left(\frac{4 \, c f}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 48 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{3} \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 48 \, c f \cos\left(e\right)^{3} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 72 \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 72 i \, c f \cos\left(e\right)^{2} \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 48 i \, c f \cos\left(\frac{4 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 48 \, c f \cos\left(e\right) \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{3} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 12 \, c f \cos\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, c f \sin\left(\frac{4 \, c f}{d}\right) \sin\left(e\right)^{4} \operatorname{Si}\left(\frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, d f x \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) + 12 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) - 12 i \, d f x \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) + 6 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 6 \, d f x \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 6 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, d f x \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, d f x \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 12 \, d f x \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, d f x \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, d f x \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 3 \, d \cos\left(4 \, f x\right) \cos\left(e\right)^{4} - 6 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 3 i \, d \cos\left(e\right)^{4} \sin\left(4 \, f x\right) - 6 \, c f \cos\left(e\right)^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) - 12 i \, d \cos\left(4 \, f x\right) \cos\left(e\right)^{3} \sin\left(e\right) + 12 \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right) + 12 \, d \cos\left(e\right)^{3} \sin\left(4 \, f x\right) \sin\left(e\right) - 12 i \, c f \cos\left(e\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) + 18 \, d \cos\left(4 \, f x\right) \cos\left(e\right)^{2} \sin\left(e\right)^{2} + 6 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(e\right)^{2} + 18 i \, d \cos\left(e\right)^{2} \sin\left(4 \, f x\right) \sin\left(e\right)^{2} + 6 \, c f \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} + 12 i \, d \cos\left(4 \, f x\right) \cos\left(e\right) \sin\left(e\right)^{3} - 12 \, d \cos\left(e\right) \sin\left(4 \, f x\right) \sin\left(e\right)^{3} - 3 \, d \cos\left(4 \, f x\right) \sin\left(e\right)^{4} - 3 i \, d \sin\left(4 \, f x\right) \sin\left(e\right)^{4} + 6 \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 i \, c f \cos\left(e\right)^{2} \sin\left(\frac{2 \, c f}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 12 i \, c f \cos\left(\frac{2 \, c f}{d}\right) \cos\left(e\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 12 \, c f \cos\left(e\right) \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 6 \, c f \cos\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 6 i \, c f \sin\left(\frac{2 \, c f}{d}\right) \sin\left(e\right)^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 3 \, d \cos\left(2 \, f x\right) \cos\left(e\right)^{2} + 3 i \, d \cos\left(e\right)^{2} \sin\left(2 \, f x\right) + 6 i \, d \cos\left(2 \, f x\right) \cos\left(e\right) \sin\left(e\right) - 6 \, d \cos\left(e\right) \sin\left(2 \, f x\right) \sin\left(e\right) - 3 \, d \cos\left(2 \, f x\right) \sin\left(e\right)^{2} - 3 i \, d \sin\left(2 \, f x\right) \sin\left(e\right)^{2} - d}{8 \, {\left(a^{3} d^{3} x + a^{3} c d^{2}\right)}}"," ",0,"1/8*(-6*I*d*f*x*cos(6*c*f/d)*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d) - 6*d*f*x*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d) + 36*d*f*x*cos(6*c*f/d)*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(e) - 36*I*d*f*x*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e) + 90*I*d*f*x*cos(6*c*f/d)*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^2 + 90*d*f*x*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^2 - 120*d*f*x*cos(6*c*f/d)*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^3 + 120*I*d*f*x*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^3 - 90*I*d*f*x*cos(6*c*f/d)*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^4 - 90*d*f*x*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^4 + 36*d*f*x*cos(6*c*f/d)*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^5 - 36*I*d*f*x*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^5 + 6*I*d*f*x*cos(6*c*f/d)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^6 + 6*d*f*x*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^6 + 6*d*f*x*cos(6*c*f/d)*cos(e)^6*sin_integral(6*(d*f*x + c*f)/d) - 6*I*d*f*x*cos(e)^6*sin(6*c*f/d)*sin_integral(6*(d*f*x + c*f)/d) + 36*I*d*f*x*cos(6*c*f/d)*cos(e)^5*sin(e)*sin_integral(6*(d*f*x + c*f)/d) + 36*d*f*x*cos(e)^5*sin(6*c*f/d)*sin(e)*sin_integral(6*(d*f*x + c*f)/d) - 90*d*f*x*cos(6*c*f/d)*cos(e)^4*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) + 90*I*d*f*x*cos(e)^4*sin(6*c*f/d)*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) - 120*I*d*f*x*cos(6*c*f/d)*cos(e)^3*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) - 120*d*f*x*cos(e)^3*sin(6*c*f/d)*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) + 90*d*f*x*cos(6*c*f/d)*cos(e)^2*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) - 90*I*d*f*x*cos(e)^2*sin(6*c*f/d)*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) + 36*I*d*f*x*cos(6*c*f/d)*cos(e)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) + 36*d*f*x*cos(e)*sin(6*c*f/d)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) - 6*d*f*x*cos(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) + 6*I*d*f*x*sin(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) - 6*I*c*f*cos(6*c*f/d)*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d) - 6*c*f*cos(e)^6*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d) + 36*c*f*cos(6*c*f/d)*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(e) - 36*I*c*f*cos(e)^5*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e) + 90*I*c*f*cos(6*c*f/d)*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^2 + 90*c*f*cos(e)^4*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^2 - 120*c*f*cos(6*c*f/d)*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^3 + 120*I*c*f*cos(e)^3*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^3 - 90*I*c*f*cos(6*c*f/d)*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^4 - 90*c*f*cos(e)^2*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^4 + 36*c*f*cos(6*c*f/d)*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^5 - 36*I*c*f*cos(e)*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^5 + 6*I*c*f*cos(6*c*f/d)*cos_integral(6*(d*f*x + c*f)/d)*sin(e)^6 + 6*c*f*cos_integral(6*(d*f*x + c*f)/d)*sin(6*c*f/d)*sin(e)^6 + 6*c*f*cos(6*c*f/d)*cos(e)^6*sin_integral(6*(d*f*x + c*f)/d) - 6*I*c*f*cos(e)^6*sin(6*c*f/d)*sin_integral(6*(d*f*x + c*f)/d) + 36*I*c*f*cos(6*c*f/d)*cos(e)^5*sin(e)*sin_integral(6*(d*f*x + c*f)/d) + 36*c*f*cos(e)^5*sin(6*c*f/d)*sin(e)*sin_integral(6*(d*f*x + c*f)/d) - 90*c*f*cos(6*c*f/d)*cos(e)^4*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) + 90*I*c*f*cos(e)^4*sin(6*c*f/d)*sin(e)^2*sin_integral(6*(d*f*x + c*f)/d) - 120*I*c*f*cos(6*c*f/d)*cos(e)^3*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) - 120*c*f*cos(e)^3*sin(6*c*f/d)*sin(e)^3*sin_integral(6*(d*f*x + c*f)/d) + 90*c*f*cos(6*c*f/d)*cos(e)^2*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) - 90*I*c*f*cos(e)^2*sin(6*c*f/d)*sin(e)^4*sin_integral(6*(d*f*x + c*f)/d) + 36*I*c*f*cos(6*c*f/d)*cos(e)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) + 36*c*f*cos(e)*sin(6*c*f/d)*sin(e)^5*sin_integral(6*(d*f*x + c*f)/d) - 6*c*f*cos(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) + 6*I*c*f*sin(6*c*f/d)*sin(e)^6*sin_integral(6*(d*f*x + c*f)/d) + 12*I*d*f*x*cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) + 12*d*f*x*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) - 48*d*f*x*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) + 48*I*d*f*x*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) - 72*I*d*f*x*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 - 72*d*f*x*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 + 48*d*f*x*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 - 48*I*d*f*x*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 + 12*I*d*f*x*cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 + 12*d*f*x*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 - 12*d*f*x*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 12*I*d*f*x*cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) - 48*I*d*f*x*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 48*d*f*x*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 72*d*f*x*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 72*I*d*f*x*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 48*I*d*f*x*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + 48*d*f*x*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 12*d*f*x*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 12*I*d*f*x*sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + d*cos(6*f*x)*cos(e)^6 + 12*I*c*f*cos(4*c*f/d)*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d) + I*d*cos(e)^6*sin(6*f*x) + 12*c*f*cos(e)^4*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d) + 6*I*d*cos(6*f*x)*cos(e)^5*sin(e) - 48*c*f*cos(4*c*f/d)*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(e) - 6*d*cos(e)^5*sin(6*f*x)*sin(e) + 48*I*c*f*cos(e)^3*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e) - 15*d*cos(6*f*x)*cos(e)^4*sin(e)^2 - 72*I*c*f*cos(4*c*f/d)*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^2 - 15*I*d*cos(e)^4*sin(6*f*x)*sin(e)^2 - 72*c*f*cos(e)^2*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^2 - 20*I*d*cos(6*f*x)*cos(e)^3*sin(e)^3 + 48*c*f*cos(4*c*f/d)*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^3 + 20*d*cos(e)^3*sin(6*f*x)*sin(e)^3 - 48*I*c*f*cos(e)*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^3 + 15*d*cos(6*f*x)*cos(e)^2*sin(e)^4 + 12*I*c*f*cos(4*c*f/d)*cos_integral(4*(d*f*x + c*f)/d)*sin(e)^4 + 15*I*d*cos(e)^2*sin(6*f*x)*sin(e)^4 + 12*c*f*cos_integral(4*(d*f*x + c*f)/d)*sin(4*c*f/d)*sin(e)^4 + 6*I*d*cos(6*f*x)*cos(e)*sin(e)^5 - 6*d*cos(e)*sin(6*f*x)*sin(e)^5 - d*cos(6*f*x)*sin(e)^6 - I*d*sin(6*f*x)*sin(e)^6 - 12*c*f*cos(4*c*f/d)*cos(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 12*I*c*f*cos(e)^4*sin(4*c*f/d)*sin_integral(4*(d*f*x + c*f)/d) - 48*I*c*f*cos(4*c*f/d)*cos(e)^3*sin(e)*sin_integral(4*(d*f*x + c*f)/d) - 48*c*f*cos(e)^3*sin(4*c*f/d)*sin(e)*sin_integral(4*(d*f*x + c*f)/d) + 72*c*f*cos(4*c*f/d)*cos(e)^2*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) - 72*I*c*f*cos(e)^2*sin(4*c*f/d)*sin(e)^2*sin_integral(4*(d*f*x + c*f)/d) + 48*I*c*f*cos(4*c*f/d)*cos(e)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) + 48*c*f*cos(e)*sin(4*c*f/d)*sin(e)^3*sin_integral(4*(d*f*x + c*f)/d) - 12*c*f*cos(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) + 12*I*c*f*sin(4*c*f/d)*sin(e)^4*sin_integral(4*(d*f*x + c*f)/d) - 6*I*d*f*x*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 6*d*f*x*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) + 12*d*f*x*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) - 12*I*d*f*x*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) + 6*I*d*f*x*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 6*d*f*x*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 6*d*f*x*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 6*I*d*f*x*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) + 12*I*d*f*x*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 12*d*f*x*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 6*d*f*x*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 6*I*d*f*x*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 3*d*cos(4*f*x)*cos(e)^4 - 6*I*c*f*cos(2*c*f/d)*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d) - 3*I*d*cos(e)^4*sin(4*f*x) - 6*c*f*cos(e)^2*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d) - 12*I*d*cos(4*f*x)*cos(e)^3*sin(e) + 12*c*f*cos(2*c*f/d)*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(e) + 12*d*cos(e)^3*sin(4*f*x)*sin(e) - 12*I*c*f*cos(e)*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e) + 18*d*cos(4*f*x)*cos(e)^2*sin(e)^2 + 6*I*c*f*cos(2*c*f/d)*cos_integral(2*(d*f*x + c*f)/d)*sin(e)^2 + 18*I*d*cos(e)^2*sin(4*f*x)*sin(e)^2 + 6*c*f*cos_integral(2*(d*f*x + c*f)/d)*sin(2*c*f/d)*sin(e)^2 + 12*I*d*cos(4*f*x)*cos(e)*sin(e)^3 - 12*d*cos(e)*sin(4*f*x)*sin(e)^3 - 3*d*cos(4*f*x)*sin(e)^4 - 3*I*d*sin(4*f*x)*sin(e)^4 + 6*c*f*cos(2*c*f/d)*cos(e)^2*sin_integral(2*(d*f*x + c*f)/d) - 6*I*c*f*cos(e)^2*sin(2*c*f/d)*sin_integral(2*(d*f*x + c*f)/d) + 12*I*c*f*cos(2*c*f/d)*cos(e)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) + 12*c*f*cos(e)*sin(2*c*f/d)*sin(e)*sin_integral(2*(d*f*x + c*f)/d) - 6*c*f*cos(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 6*I*c*f*sin(2*c*f/d)*sin(e)^2*sin_integral(2*(d*f*x + c*f)/d) + 3*d*cos(2*f*x)*cos(e)^2 + 3*I*d*cos(e)^2*sin(2*f*x) + 6*I*d*cos(2*f*x)*cos(e)*sin(e) - 6*d*cos(e)*sin(2*f*x)*sin(e) - 3*d*cos(2*f*x)*sin(e)^2 - 3*I*d*sin(2*f*x)*sin(e)^2 - d)/(a^3*d^3*x + a^3*c*d^2)","B",0
32,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\int {\left(i \, a \cot\left(f x + e\right) + a\right)}^{2} {\left(d x + c\right)}^{m}\,{d x}"," ",0,"integrate((I*a*cot(f*x + e) + a)^2*(d*x + c)^m, x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\int {\left(i \, a \cot\left(f x + e\right) + a\right)} {\left(d x + c\right)}^{m}\,{d x}"," ",0,"integrate((I*a*cot(f*x + e) + a)*(d*x + c)^m, x)","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{m}}{i \, a \cot\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(I*a*cot(f*x + e) + a), x)","F",0
35,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(i \, a \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^m/(I*a*cot(f*x + e) + a)^2, x)","F",0
36,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+I*a*cot(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(i \, a \cot\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x + c)^m/(I*a*cot(f*x + e) + a)^3, x)","F",0
37,0,0,0,0.000000," ","integrate((d*x+c)^3*(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} {\left(b \cot\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*x + c)^3*(b*cot(f*x + e) + a), x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)^2*(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} {\left(b \cot\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*x + c)^2*(b*cot(f*x + e) + a), x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)*(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int {\left(d x + c\right)} {\left(b \cot\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*x + c)*(b*cot(f*x + e) + a), x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))/(d*x+c),x, algorithm=""giac"")","\int \frac{b \cot\left(f x + e\right) + a}{d x + c}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)/(d*x + c), x)","F",0
41,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))/(d*x+c)^2,x, algorithm=""giac"")","\int \frac{b \cot\left(f x + e\right) + a}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)/(d*x + c)^2, x)","F",0
42,0,0,0,0.000000," ","integrate((d*x+c)^3*(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} {\left(b \cot\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*x + c)^3*(b*cot(f*x + e) + a)^2, x)","F",0
43,0,0,0,0.000000," ","integrate((d*x+c)^2*(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} {\left(b \cot\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*x + c)^2*(b*cot(f*x + e) + a)^2, x)","F",0
44,0,0,0,0.000000," ","integrate((d*x+c)*(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d x + c\right)} {\left(b \cot\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*x + c)*(b*cot(f*x + e) + a)^2, x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^2/(d*x+c),x, algorithm=""giac"")","\int \frac{{\left(b \cot\left(f x + e\right) + a\right)}^{2}}{d x + c}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)^2/(d*x + c), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^2/(d*x+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b \cot\left(f x + e\right) + a\right)}^{2}}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)^2/(d*x + c)^2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*x+c)^3*(a+b*cot(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} {\left(b \cot\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((d*x + c)^3*(b*cot(f*x + e) + a)^3, x)","F",0
48,0,0,0,0.000000," ","integrate((d*x+c)^2*(a+b*cot(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} {\left(b \cot\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((d*x + c)^2*(b*cot(f*x + e) + a)^3, x)","F",0
49,0,0,0,0.000000," ","integrate((d*x+c)*(a+b*cot(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d x + c\right)} {\left(b \cot\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((d*x + c)*(b*cot(f*x + e) + a)^3, x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^3/(d*x+c),x, algorithm=""giac"")","\int \frac{{\left(b \cot\left(f x + e\right) + a\right)}^{3}}{d x + c}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)^3/(d*x + c), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^3/(d*x+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b \cot\left(f x + e\right) + a\right)}^{3}}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)^3/(d*x + c)^2, x)","F",0
52,0,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{b \cot\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^3/(b*cot(f*x + e) + a), x)","F",0
53,0,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{b \cot\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^2/(b*cot(f*x + e) + a), x)","F",0
54,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{d x + c}{b \cot\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)/(b*cot(f*x + e) + a), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)} {\left(b \cot\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)*(b*cot(f*x + e) + a)), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*cot(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)}^{2} {\left(b \cot\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*(b*cot(f*x + e) + a)), x)","F",0
57,0,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{{\left(b \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^3/(b*cot(f*x + e) + a)^2, x)","F",0
58,0,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{{\left(b \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^2/(b*cot(f*x + e) + a)^2, x)","F",0
59,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{d x + c}{{\left(b \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)/(b*cot(f*x + e) + a)^2, x)","F",0
60,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)} {\left(b \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*x + c)*(b*cot(f*x + e) + a)^2), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*cot(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)}^{2} {\left(b \cot\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*(b*cot(f*x + e) + a)^2), x)","F",0
