1,1,47,0,0.650378," ","integrate(x^5*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{{\left(2 \, d x^{2} \sin\left(d x^{2} + c\right) - {\left(d^{2} x^{4} - 2\right)} \cos\left(d x^{2} + c\right)\right)} b}{2 \, d^{3}}"," ",0,"1/6*a*x^6 + 1/2*(2*d*x^2*sin(d*x^2 + c) - (d^2*x^4 - 2)*cos(d*x^2 + c))*b/d^3","A",0
2,1,37,0,0.891839," ","integrate(x^3*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} - \frac{{\left(d x^{2} \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right)} b}{2 \, d^{2}}"," ",0,"1/4*a*x^4 - 1/2*(d*x^2*cos(d*x^2 + c) - sin(d*x^2 + c))*b/d^2","A",0
3,1,21,0,0.484787," ","integrate(x*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} - \frac{b \cos\left(d x^{2} + c\right)}{2 \, d}"," ",0,"1/2*a*x^2 - 1/2*b*cos(d*x^2 + c)/d","A",0
4,1,50,0,1.230019," ","integrate((a+b*sin(d*x^2+c))/x,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(i \, {\rm Ei}\left(i \, d x^{2}\right) - i \, {\rm Ei}\left(-i \, d x^{2}\right)\right)} \cos\left(c\right) - {\left({\rm Ei}\left(i \, d x^{2}\right) + {\rm Ei}\left(-i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} b + a \log\left(x\right)"," ",0,"-1/4*((I*Ei(I*d*x^2) - I*Ei(-I*d*x^2))*cos(c) - (Ei(I*d*x^2) + Ei(-I*d*x^2))*sin(c))*b + a*log(x)","C",0
5,1,57,0,2.446305," ","integrate((a+b*sin(d*x^2+c))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(\Gamma\left(-1, i \, d x^{2}\right) + \Gamma\left(-1, -i \, d x^{2}\right)\right)} \cos\left(c\right) - {\left(i \, \Gamma\left(-1, i \, d x^{2}\right) - i \, \Gamma\left(-1, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} b d - \frac{a}{2 \, x^{2}}"," ",0,"1/4*((gamma(-1, I*d*x^2) + gamma(-1, -I*d*x^2))*cos(c) - (I*gamma(-1, I*d*x^2) - I*gamma(-1, -I*d*x^2))*sin(c))*b*d - 1/2*a/x^2","C",0
6,1,58,0,1.002733," ","integrate((a+b*sin(d*x^2+c))/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(i \, \Gamma\left(-2, i \, d x^{2}\right) - i \, \Gamma\left(-2, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\Gamma\left(-2, i \, d x^{2}\right) + \Gamma\left(-2, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} b d^{2} - \frac{a}{4 \, x^{4}}"," ",0,"1/4*((I*gamma(-2, I*d*x^2) - I*gamma(-2, -I*d*x^2))*cos(c) + (gamma(-2, I*d*x^2) + gamma(-2, -I*d*x^2))*sin(c))*b*d^2 - 1/4*a/x^4","C",0
7,1,92,0,0.635140," ","integrate(x^4*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} - \frac{{\left(16 \, d^{3} x^{3} \cos\left(d x^{2} + c\right) - 24 \, d^{2} x \sin\left(d x^{2} + c\right) - \sqrt{2} \sqrt{\pi} {\left({\left(-\left(3 i + 3\right) \, \cos\left(c\right) + \left(3 i - 3\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(\left(3 i - 3\right) \, \cos\left(c\right) - \left(3 i + 3\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} b}{32 \, d^{4}}"," ",0,"1/5*a*x^5 - 1/32*(16*d^3*x^3*cos(d*x^2 + c) - 24*d^2*x*sin(d*x^2 + c) - sqrt(2)*sqrt(pi)*((-(3*I + 3)*cos(c) + (3*I - 3)*sin(c))*erf(sqrt(I*d)*x) + ((3*I - 3)*cos(c) - (3*I + 3)*sin(c))*erf(sqrt(-I*d)*x))*d^(3/2))*b/d^4","C",0
8,1,75,0,0.552424," ","integrate(x^2*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} - \frac{{\left(8 \, d^{2} x \cos\left(d x^{2} + c\right) + \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(c\right) + \left(i + 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(-\left(i + 1\right) \, \cos\left(c\right) - \left(i - 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} b}{16 \, d^{3}}"," ",0,"1/3*a*x^3 - 1/16*(8*d^2*x*cos(d*x^2 + c) + sqrt(2)*sqrt(pi)*(((I - 1)*cos(c) + (I + 1)*sin(c))*erf(sqrt(I*d)*x) + (-(I + 1)*cos(c) - (I - 1)*sin(c))*erf(sqrt(-I*d)*x))*d^(3/2))*b/d^3","C",0
9,1,53,0,0.506213," ","integrate(a+b*sin(d*x^2+c),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(c\right) + \left(i - 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(\left(i - 1\right) \, \cos\left(c\right) - \left(i + 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} b}{8 \, \sqrt{d}} + a x"," ",0,"-1/8*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(c) + (I - 1)*sin(c))*erf(sqrt(I*d)*x) + ((I - 1)*cos(c) - (I + 1)*sin(c))*erf(sqrt(-I*d)*x))*b/sqrt(d) + a*x","C",0
10,1,81,0,1.555114," ","integrate((a+b*sin(d*x^2+c))/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{d x^{2}} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, d x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, d x^{2}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} b}{8 \, x} - \frac{a}{x}"," ",0,"-1/8*sqrt(d*x^2)*(((I - 1)*sqrt(2)*gamma(-1/2, I*d*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -I*d*x^2))*cos(c) + ((I + 1)*sqrt(2)*gamma(-1/2, I*d*x^2) - (I - 1)*sqrt(2)*gamma(-1/2, -I*d*x^2))*sin(c))*b/x - a/x","C",0
11,1,82,0,1.038699," ","integrate((a+b*sin(d*x^2+c))/x^4,x, algorithm=""maxima"")","-\frac{\sqrt{d x^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, i \, d x^{2}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, i \, d x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} b d}{8 \, x} - \frac{a}{3 \, x^{3}}"," ",0,"-1/8*sqrt(d*x^2)*((-(I + 1)*sqrt(2)*gamma(-3/2, I*d*x^2) + (I - 1)*sqrt(2)*gamma(-3/2, -I*d*x^2))*cos(c) + ((I - 1)*sqrt(2)*gamma(-3/2, I*d*x^2) - (I + 1)*sqrt(2)*gamma(-3/2, -I*d*x^2))*sin(c))*b*d/x - 1/3*a/x^3","C",0
12,1,106,0,0.867327," ","integrate(x^5*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} + \frac{{\left(2 \, d x^{2} \sin\left(d x^{2} + c\right) - {\left(d^{2} x^{4} - 2\right)} \cos\left(d x^{2} + c\right)\right)} a b}{d^{3}} + \frac{{\left(4 \, d^{3} x^{6} - 6 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) - 3 \, {\left(2 \, d^{2} x^{4} - 1\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} b^{2}}{48 \, d^{3}}"," ",0,"1/6*a^2*x^6 + (2*d*x^2*sin(d*x^2 + c) - (d^2*x^4 - 2)*cos(d*x^2 + c))*a*b/d^3 + 1/48*(4*d^3*x^6 - 6*d*x^2*cos(2*d*x^2 + 2*c) - 3*(2*d^2*x^4 - 1)*sin(2*d*x^2 + 2*c))*b^2/d^3","A",0
13,1,87,0,0.497301," ","integrate(x^3*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} x^{4} - \frac{{\left(d x^{2} \cos\left(d x^{2} + c\right) - \sin\left(d x^{2} + c\right)\right)} a b}{d^{2}} + \frac{{\left(2 \, d^{2} x^{4} - 2 \, d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - \cos\left(2 \, d x^{2} + 2 \, c\right)\right)} b^{2}}{16 \, d^{2}}"," ",0,"1/4*a^2*x^4 - (d*x^2*cos(d*x^2 + c) - sin(d*x^2 + c))*a*b/d^2 + 1/16*(2*d^2*x^4 - 2*d*x^2*sin(2*d*x^2 + 2*c) - cos(2*d*x^2 + 2*c))*b^2/d^2","A",0
14,1,52,0,1.175365," ","integrate(x*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{{\left(2 \, d x^{2} - \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} b^{2}}{8 \, d} - \frac{a b \cos\left(d x^{2} + c\right)}{d}"," ",0,"1/2*a^2*x^2 + 1/8*(2*d*x^2 - sin(2*d*x^2 + 2*c))*b^2/d - a*b*cos(d*x^2 + c)/d","A",0
15,1,108,0,0.496867," ","integrate((a+b*sin(d*x^2+c))^2/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(i \, {\rm Ei}\left(i \, d x^{2}\right) - i \, {\rm Ei}\left(-i \, d x^{2}\right)\right)} \cos\left(c\right) - {\left({\rm Ei}\left(i \, d x^{2}\right) + {\rm Ei}\left(-i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} a b - \frac{1}{8} \, {\left({\left({\rm Ei}\left(2 i \, d x^{2}\right) + {\rm Ei}\left(-2 i \, d x^{2}\right)\right)} \cos\left(2 \, c\right) - {\left(-i \, {\rm Ei}\left(2 i \, d x^{2}\right) + i \, {\rm Ei}\left(-2 i \, d x^{2}\right)\right)} \sin\left(2 \, c\right) - 4 \, \log\left(x\right)\right)} b^{2} + a^{2} \log\left(x\right)"," ",0,"-1/2*((I*Ei(I*d*x^2) - I*Ei(-I*d*x^2))*cos(c) - (Ei(I*d*x^2) + Ei(-I*d*x^2))*sin(c))*a*b - 1/8*((Ei(2*I*d*x^2) + Ei(-2*I*d*x^2))*cos(2*c) - (-I*Ei(2*I*d*x^2) + I*Ei(-2*I*d*x^2))*sin(2*c) - 4*log(x))*b^2 + a^2*log(x)","C",0
16,1,124,0,0.491411," ","integrate((a+b*sin(d*x^2+c))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(\Gamma\left(-1, i \, d x^{2}\right) + \Gamma\left(-1, -i \, d x^{2}\right)\right)} \cos\left(c\right) - {\left(i \, \Gamma\left(-1, i \, d x^{2}\right) - i \, \Gamma\left(-1, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} a b d + \frac{{\left({\left({\left(i \, \Gamma\left(-1, 2 i \, d x^{2}\right) - i \, \Gamma\left(-1, -2 i \, d x^{2}\right)\right)} \cos\left(2 \, c\right) + {\left(\Gamma\left(-1, 2 i \, d x^{2}\right) + \Gamma\left(-1, -2 i \, d x^{2}\right)\right)} \sin\left(2 \, c\right)\right)} d x^{2} - 1\right)} b^{2}}{4 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/2*((gamma(-1, I*d*x^2) + gamma(-1, -I*d*x^2))*cos(c) - (I*gamma(-1, I*d*x^2) - I*gamma(-1, -I*d*x^2))*sin(c))*a*b*d + 1/4*(((I*gamma(-1, 2*I*d*x^2) - I*gamma(-1, -2*I*d*x^2))*cos(2*c) + (gamma(-1, 2*I*d*x^2) + gamma(-1, -2*I*d*x^2))*sin(2*c))*d*x^2 - 1)*b^2/x^2 - 1/2*a^2/x^2","C",0
17,1,129,0,0.539532," ","integrate((a+b*sin(d*x^2+c))^2/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(i \, \Gamma\left(-2, i \, d x^{2}\right) - i \, \Gamma\left(-2, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\Gamma\left(-2, i \, d x^{2}\right) + \Gamma\left(-2, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} a b d^{2} - \frac{{\left({\left(4 \, {\left(\Gamma\left(-2, 2 i \, d x^{2}\right) + \Gamma\left(-2, -2 i \, d x^{2}\right)\right)} \cos\left(2 \, c\right) - {\left(4 i \, \Gamma\left(-2, 2 i \, d x^{2}\right) - 4 i \, \Gamma\left(-2, -2 i \, d x^{2}\right)\right)} \sin\left(2 \, c\right)\right)} d^{2} x^{4} + 1\right)} b^{2}}{8 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/2*((I*gamma(-2, I*d*x^2) - I*gamma(-2, -I*d*x^2))*cos(c) + (gamma(-2, I*d*x^2) + gamma(-2, -I*d*x^2))*sin(c))*a*b*d^2 - 1/8*((4*(gamma(-2, 2*I*d*x^2) + gamma(-2, -2*I*d*x^2))*cos(2*c) - (4*I*gamma(-2, 2*I*d*x^2) - 4*I*gamma(-2, -2*I*d*x^2))*sin(2*c))*d^2*x^4 + 1)*b^2/x^4 - 1/4*a^2/x^4","C",0
18,1,207,0,0.493960," ","integrate(x^4*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} - \frac{{\left(16 \, d^{3} x^{3} \cos\left(d x^{2} + c\right) - 24 \, d^{2} x \sin\left(d x^{2} + c\right) - \sqrt{2} \sqrt{\pi} {\left({\left(-\left(3 i + 3\right) \, \cos\left(c\right) + \left(3 i - 3\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(\left(3 i - 3\right) \, \cos\left(c\right) - \left(3 i + 3\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} a b}{16 \, d^{4}} + \frac{{\left(256 \, d^{4} x^{5} - 320 \, d^{3} x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right) - 240 \, d^{2} x \cos\left(2 \, d x^{2} + 2 \, c\right) - 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(\left(15 i - 15\right) \, \cos\left(2 \, c\right) + \left(15 i + 15\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{2 i \, d} x\right) + {\left(-\left(15 i + 15\right) \, \cos\left(2 \, c\right) - \left(15 i - 15\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{-2 i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} b^{2}}{2560 \, d^{4}}"," ",0,"1/5*a^2*x^5 - 1/16*(16*d^3*x^3*cos(d*x^2 + c) - 24*d^2*x*sin(d*x^2 + c) - sqrt(2)*sqrt(pi)*((-(3*I + 3)*cos(c) + (3*I - 3)*sin(c))*erf(sqrt(I*d)*x) + ((3*I - 3)*cos(c) - (3*I + 3)*sin(c))*erf(sqrt(-I*d)*x))*d^(3/2))*a*b/d^4 + 1/2560*(256*d^4*x^5 - 320*d^3*x^3*sin(2*d*x^2 + 2*c) - 240*d^2*x*cos(2*d*x^2 + 2*c) - 4^(1/4)*sqrt(2)*sqrt(pi)*(((15*I - 15)*cos(2*c) + (15*I + 15)*sin(2*c))*erf(sqrt(2*I*d)*x) + (-(15*I + 15)*cos(2*c) - (15*I - 15)*sin(2*c))*erf(sqrt(-2*I*d)*x))*d^(3/2))*b^2/d^4","C",0
19,1,171,0,0.494628," ","integrate(x^2*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} - \frac{{\left(8 \, d^{2} x \cos\left(d x^{2} + c\right) + \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(c\right) + \left(i + 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(-\left(i + 1\right) \, \cos\left(c\right) - \left(i - 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} a b}{8 \, d^{3}} + \frac{{\left(64 \, d^{3} x^{3} - 48 \, d^{2} x \sin\left(2 \, d x^{2} + 2 \, c\right) - 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(-\left(3 i + 3\right) \, \cos\left(2 \, c\right) + \left(3 i - 3\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{2 i \, d} x\right) + {\left(\left(3 i - 3\right) \, \cos\left(2 \, c\right) - \left(3 i + 3\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{-2 i \, d} x\right)\right)} d^{\frac{3}{2}}\right)} b^{2}}{384 \, d^{3}}"," ",0,"1/3*a^2*x^3 - 1/8*(8*d^2*x*cos(d*x^2 + c) + sqrt(2)*sqrt(pi)*(((I - 1)*cos(c) + (I + 1)*sin(c))*erf(sqrt(I*d)*x) + (-(I + 1)*cos(c) - (I - 1)*sin(c))*erf(sqrt(-I*d)*x))*d^(3/2))*a*b/d^3 + 1/384*(64*d^3*x^3 - 48*d^2*x*sin(2*d*x^2 + 2*c) - 4^(1/4)*sqrt(2)*sqrt(pi)*((-(3*I + 3)*cos(2*c) + (3*I - 3)*sin(2*c))*erf(sqrt(2*I*d)*x) + ((3*I - 3)*cos(2*c) - (3*I + 3)*sin(2*c))*erf(sqrt(-2*I*d)*x))*d^(3/2))*b^2/d^3","C",0
20,1,129,0,0.603079," ","integrate((a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(c\right) + \left(i - 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{i \, d} x\right) + {\left(\left(i - 1\right) \, \cos\left(c\right) - \left(i + 1\right) \, \sin\left(c\right)\right)} \operatorname{erf}\left(\sqrt{-i \, d} x\right)\right)} a b}{4 \, \sqrt{d}} + a^{2} x + \frac{{\left(4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(2 \, c\right) + \left(i + 1\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{2 i \, d} x\right) + {\left(-\left(i + 1\right) \, \cos\left(2 \, c\right) - \left(i - 1\right) \, \sin\left(2 \, c\right)\right)} \operatorname{erf}\left(\sqrt{-2 i \, d} x\right)\right)} d^{\frac{3}{2}} + 16 \, d^{2} x\right)} b^{2}}{32 \, d^{2}}"," ",0,"-1/4*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(c) + (I - 1)*sin(c))*erf(sqrt(I*d)*x) + ((I - 1)*cos(c) - (I + 1)*sin(c))*erf(sqrt(-I*d)*x))*a*b/sqrt(d) + a^2*x + 1/32*(4^(1/4)*sqrt(2)*sqrt(pi)*(((I - 1)*cos(2*c) + (I + 1)*sin(2*c))*erf(sqrt(2*I*d)*x) + (-(I + 1)*cos(2*c) - (I - 1)*sin(2*c))*erf(sqrt(-2*I*d)*x))*d^(3/2) + 16*d^2*x)*b^2/d^2","C",0
21,1,170,0,0.609029," ","integrate((a+b*sin(d*x^2+c))^2/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{d x^{2}} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, d x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, d x^{2}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} a b}{4 \, x} - \frac{{\left(\sqrt{2} \sqrt{d x^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 2 i \, d x^{2}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -2 i \, d x^{2}\right)\right)} \cos\left(2 \, c\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 2 i \, d x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -2 i \, d x^{2}\right)\right)} \sin\left(2 \, c\right)\right)} + 8\right)} b^{2}}{16 \, x} - \frac{a^{2}}{x}"," ",0,"-1/4*sqrt(d*x^2)*(((I - 1)*sqrt(2)*gamma(-1/2, I*d*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -I*d*x^2))*cos(c) + ((I + 1)*sqrt(2)*gamma(-1/2, I*d*x^2) - (I - 1)*sqrt(2)*gamma(-1/2, -I*d*x^2))*sin(c))*a*b/x - 1/16*(sqrt(2)*sqrt(d*x^2)*((-(I + 1)*sqrt(2)*gamma(-1/2, 2*I*d*x^2) + (I - 1)*sqrt(2)*gamma(-1/2, -2*I*d*x^2))*cos(2*c) + ((I - 1)*sqrt(2)*gamma(-1/2, 2*I*d*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -2*I*d*x^2))*sin(2*c)) + 8)*b^2/x - a^2/x","C",0
22,1,175,0,0.631051," ","integrate((a+b*sin(d*x^2+c))^2/x^4,x, algorithm=""maxima"")","-\frac{\sqrt{d x^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, i \, d x^{2}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -i \, d x^{2}\right)\right)} \cos\left(c\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, i \, d x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -i \, d x^{2}\right)\right)} \sin\left(c\right)\right)} a b d}{4 \, x} + \frac{{\left(\sqrt{2} \sqrt{d x^{2}} {\left({\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, 2 i \, d x^{2}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -2 i \, d x^{2}\right)\right)} \cos\left(2 \, c\right) + {\left(\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, 2 i \, d x^{2}\right) - \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -2 i \, d x^{2}\right)\right)} \sin\left(2 \, c\right)\right)} d x^{2} - 4\right)} b^{2}}{24 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/4*sqrt(d*x^2)*((-(I + 1)*sqrt(2)*gamma(-3/2, I*d*x^2) + (I - 1)*sqrt(2)*gamma(-3/2, -I*d*x^2))*cos(c) + ((I - 1)*sqrt(2)*gamma(-3/2, I*d*x^2) - (I + 1)*sqrt(2)*gamma(-3/2, -I*d*x^2))*sin(c))*a*b*d/x + 1/24*(sqrt(2)*sqrt(d*x^2)*(((3*I - 3)*sqrt(2)*gamma(-3/2, 2*I*d*x^2) - (3*I + 3)*sqrt(2)*gamma(-3/2, -2*I*d*x^2))*cos(2*c) + ((3*I + 3)*sqrt(2)*gamma(-3/2, 2*I*d*x^2) - (3*I - 3)*sqrt(2)*gamma(-3/2, -2*I*d*x^2))*sin(2*c))*d*x^2 - 4)*b^2/x^3 - 1/3*a^2/x^3","C",0
23,1,79,0,0.348317," ","integrate(x^5*sin(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{6 \, b x^{2} \sin\left(3 \, b x^{2} + 3 \, a\right) - 162 \, b x^{2} \sin\left(b x^{2} + a\right) - {\left(9 \, b^{2} x^{4} - 2\right)} \cos\left(3 \, b x^{2} + 3 \, a\right) + 81 \, {\left(b^{2} x^{4} - 2\right)} \cos\left(b x^{2} + a\right)}{216 \, b^{3}}"," ",0,"-1/216*(6*b*x^2*sin(3*b*x^2 + 3*a) - 162*b*x^2*sin(b*x^2 + a) - (9*b^2*x^4 - 2)*cos(3*b*x^2 + 3*a) + 81*(b^2*x^4 - 2)*cos(b*x^2 + a))/b^3","A",0
24,1,60,0,0.338723," ","integrate(x^3*sin(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, b x^{2} \cos\left(3 \, b x^{2} + 3 \, a\right) - 27 \, b x^{2} \cos\left(b x^{2} + a\right) - \sin\left(3 \, b x^{2} + 3 \, a\right) + 27 \, \sin\left(b x^{2} + a\right)}{72 \, b^{2}}"," ",0,"1/72*(3*b*x^2*cos(3*b*x^2 + 3*a) - 27*b*x^2*cos(b*x^2 + a) - sin(3*b*x^2 + 3*a) + 27*sin(b*x^2 + a))/b^2","A",0
25,1,27,0,0.315446," ","integrate(x*sin(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{\cos\left(3 \, b x^{2} + 3 \, a\right) - 9 \, \cos\left(b x^{2} + a\right)}{24 \, b}"," ",0,"1/24*(cos(3*b*x^2 + 3*a) - 9*cos(b*x^2 + a))/b","A",0
26,1,89,0,0.470436," ","integrate(sin(b*x^2+a)^3/x,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(i \, {\rm Ei}\left(3 i \, b x^{2}\right) - i \, {\rm Ei}\left(-3 i \, b x^{2}\right)\right)} \cos\left(3 \, a\right) + \frac{1}{16} \, {\left(-3 i \, {\rm Ei}\left(i \, b x^{2}\right) + 3 i \, {\rm Ei}\left(-i \, b x^{2}\right)\right)} \cos\left(a\right) - \frac{1}{16} \, {\left({\rm Ei}\left(3 i \, b x^{2}\right) + {\rm Ei}\left(-3 i \, b x^{2}\right)\right)} \sin\left(3 \, a\right) + \frac{3}{16} \, {\left({\rm Ei}\left(i \, b x^{2}\right) + {\rm Ei}\left(-i \, b x^{2}\right)\right)} \sin\left(a\right)"," ",0,"1/16*(I*Ei(3*I*b*x^2) - I*Ei(-3*I*b*x^2))*cos(3*a) + 1/16*(-3*I*Ei(I*b*x^2) + 3*I*Ei(-I*b*x^2))*cos(a) - 1/16*(Ei(3*I*b*x^2) + Ei(-3*I*b*x^2))*sin(3*a) + 3/16*(Ei(I*b*x^2) + Ei(-I*b*x^2))*sin(a)","C",0
27,1,100,0,0.602750," ","integrate(sin(b*x^2+a)^3/x^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(3 \, {\left(\Gamma\left(-1, 3 i \, b x^{2}\right) + \Gamma\left(-1, -3 i \, b x^{2}\right)\right)} \cos\left(3 \, a\right) - 3 \, {\left(\Gamma\left(-1, i \, b x^{2}\right) + \Gamma\left(-1, -i \, b x^{2}\right)\right)} \cos\left(a\right) - {\left(3 i \, \Gamma\left(-1, 3 i \, b x^{2}\right) - 3 i \, \Gamma\left(-1, -3 i \, b x^{2}\right)\right)} \sin\left(3 \, a\right) - {\left(-3 i \, \Gamma\left(-1, i \, b x^{2}\right) + 3 i \, \Gamma\left(-1, -i \, b x^{2}\right)\right)} \sin\left(a\right)\right)} b"," ",0,"-1/16*(3*(gamma(-1, 3*I*b*x^2) + gamma(-1, -3*I*b*x^2))*cos(3*a) - 3*(gamma(-1, I*b*x^2) + gamma(-1, -I*b*x^2))*cos(a) - (3*I*gamma(-1, 3*I*b*x^2) - 3*I*gamma(-1, -3*I*b*x^2))*sin(3*a) - (-3*I*gamma(-1, I*b*x^2) + 3*I*gamma(-1, -I*b*x^2))*sin(a))*b","C",0
28,1,143,0,0.445206," ","integrate(x^2*sin(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{72 \, b^{2} x \cos\left(3 \, b x^{2} + 3 \, a\right) - 648 \, b^{2} x \cos\left(b x^{2} + a\right) + 3 \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(3 \, a\right) + \left(i + 1\right) \, \sin\left(3 \, a\right)\right)} \operatorname{erf}\left(\sqrt{3 i \, b} x\right) + {\left(-\left(i + 1\right) \, \cos\left(3 \, a\right) - \left(i - 1\right) \, \sin\left(3 \, a\right)\right)} \operatorname{erf}\left(\sqrt{-3 i \, b} x\right)\right)} b^{\frac{3}{2}} + \sqrt{2} \sqrt{\pi} {\left({\left(-\left(81 i - 81\right) \, \cos\left(a\right) - \left(81 i + 81\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{i \, b} x\right) + {\left(\left(81 i + 81\right) \, \cos\left(a\right) + \left(81 i - 81\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{-i \, b} x\right)\right)} b^{\frac{3}{2}}}{1728 \, b^{3}}"," ",0,"1/1728*(72*b^2*x*cos(3*b*x^2 + 3*a) - 648*b^2*x*cos(b*x^2 + a) + 3*9^(1/4)*sqrt(2)*sqrt(pi)*(((I - 1)*cos(3*a) + (I + 1)*sin(3*a))*erf(sqrt(3*I*b)*x) + (-(I + 1)*cos(3*a) - (I - 1)*sin(3*a))*erf(sqrt(-3*I*b)*x))*b^(3/2) + sqrt(2)*sqrt(pi)*((-(81*I - 81)*cos(a) - (81*I + 81)*sin(a))*erf(sqrt(I*b)*x) + ((81*I + 81)*cos(a) + (81*I - 81)*sin(a))*erf(sqrt(-I*b)*x))*b^(3/2))/b^3","C",0
29,1,112,0,1.188668," ","integrate(sin(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(3 \, a\right) + \left(i - 1\right) \, \sin\left(3 \, a\right)\right)} \operatorname{erf}\left(\sqrt{3 i \, b} x\right) + {\left(\left(i - 1\right) \, \cos\left(3 \, a\right) - \left(i + 1\right) \, \sin\left(3 \, a\right)\right)} \operatorname{erf}\left(\sqrt{-3 i \, b} x\right)\right)} b^{\frac{3}{2}} + \sqrt{2} \sqrt{\pi} {\left({\left(\left(27 i + 27\right) \, \cos\left(a\right) - \left(27 i - 27\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{i \, b} x\right) + {\left(-\left(27 i - 27\right) \, \cos\left(a\right) + \left(27 i + 27\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{-i \, b} x\right)\right)} b^{\frac{3}{2}}}{288 \, b^{2}}"," ",0,"1/288*(3*9^(1/4)*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(3*a) + (I - 1)*sin(3*a))*erf(sqrt(3*I*b)*x) + ((I - 1)*cos(3*a) - (I + 1)*sin(3*a))*erf(sqrt(-3*I*b)*x))*b^(3/2) + sqrt(2)*sqrt(pi)*(((27*I + 27)*cos(a) - (27*I - 27)*sin(a))*erf(sqrt(I*b)*x) + (-(27*I - 27)*cos(a) + (27*I + 27)*sin(a))*erf(sqrt(-I*b)*x))*b^(3/2))/b^2","C",0
30,1,151,0,0.585935," ","integrate(sin(b*x^2+a)^3/x^2,x, algorithm=""maxima"")","\frac{\sqrt{3} \sqrt{b x^{2}} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 3 i \, b x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -3 i \, b x^{2}\right)\right)} \cos\left(3 \, a\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 3 i \, b x^{2}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -3 i \, b x^{2}\right)\right)} \sin\left(3 \, a\right)\right)} + \sqrt{b x^{2}} {\left({\left(-\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, b x^{2}\right) + \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, b x^{2}\right)\right)} \cos\left(a\right) + {\left(-\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, b x^{2}\right) + \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, b x^{2}\right)\right)} \sin\left(a\right)\right)}}{32 \, x}"," ",0,"1/32*(sqrt(3)*sqrt(b*x^2)*(((I - 1)*sqrt(2)*gamma(-1/2, 3*I*b*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -3*I*b*x^2))*cos(3*a) + ((I + 1)*sqrt(2)*gamma(-1/2, 3*I*b*x^2) - (I - 1)*sqrt(2)*gamma(-1/2, -3*I*b*x^2))*sin(3*a)) + sqrt(b*x^2)*((-(3*I - 3)*sqrt(2)*gamma(-1/2, I*b*x^2) + (3*I + 3)*sqrt(2)*gamma(-1/2, -I*b*x^2))*cos(a) + (-(3*I + 3)*sqrt(2)*gamma(-1/2, I*b*x^2) + (3*I - 3)*sqrt(2)*gamma(-1/2, -I*b*x^2))*sin(a)))/x","C",0
31,1,97,0,1.661386," ","integrate(x^2*sin(x^2)^3,x, algorithm=""maxima"")","\frac{1}{24} \, x \cos\left(3 \, x^{2}\right) - \frac{3}{8} \, x \cos\left(x^{2}\right) + \frac{1}{1152} \, \sqrt{\pi} {\left(\left(2 i - 2\right) \, \sqrt{3} \sqrt{2} \operatorname{erf}\left(\sqrt{3 i} x\right) - \left(2 i + 2\right) \, \sqrt{3} \sqrt{2} \operatorname{erf}\left(\sqrt{-3 i} x\right) - \left(27 i - 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} x\right) - \left(27 i + 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} x\right) + \left(27 i + 27\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} x\right) - \left(27 i - 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} x\right)\right)}"," ",0,"1/24*x*cos(3*x^2) - 3/8*x*cos(x^2) + 1/1152*sqrt(pi)*((2*I - 2)*sqrt(3)*sqrt(2)*erf(sqrt(3*I)*x) - (2*I + 2)*sqrt(3)*sqrt(2)*erf(sqrt(-3*I)*x) - (27*I - 27)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) - (27*I + 27)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) + (27*I + 27)*sqrt(2)*erf(sqrt(-I)*x) - (27*I - 27)*sqrt(2)*erf((-1)^(1/4)*x))","C",0
32,1,117,0,0.811715," ","integrate(x^4*cos(x^2)*sin(x^2)^2,x, algorithm=""maxima"")","-\frac{1}{24} \, x^{3} \sin\left(3 \, x^{2}\right) + \frac{1}{8} \, x^{3} \sin\left(x^{2}\right) - \frac{1}{48} \, x \cos\left(3 \, x^{2}\right) + \frac{3}{16} \, x \cos\left(x^{2}\right) - \frac{1}{2304} \, \sqrt{\pi} {\left(\left(2 i - 2\right) \, \sqrt{3} \sqrt{2} \operatorname{erf}\left(\sqrt{3 i} x\right) - \left(2 i + 2\right) \, \sqrt{3} \sqrt{2} \operatorname{erf}\left(\sqrt{-3 i} x\right) - \left(27 i - 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} x\right) - \left(27 i + 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} x\right) + \left(27 i + 27\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} x\right) - \left(27 i - 27\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} x\right)\right)}"," ",0,"-1/24*x^3*sin(3*x^2) + 1/8*x^3*sin(x^2) - 1/48*x*cos(3*x^2) + 3/16*x*cos(x^2) - 1/2304*sqrt(pi)*((2*I - 2)*sqrt(3)*sqrt(2)*erf(sqrt(3*I)*x) - (2*I + 2)*sqrt(3)*sqrt(2)*erf(sqrt(-3*I)*x) - (27*I - 27)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) - (27*I + 27)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) + (27*I + 27)*sqrt(2)*erf(sqrt(-I)*x) - (27*I - 27)*sqrt(2)*erf((-1)^(1/4)*x))","C",0
33,1,55,0,0.322817," ","integrate(x*sin(b*x^2+a)^7,x, algorithm=""maxima"")","\frac{5 \, \cos\left(7 \, b x^{2} + 7 \, a\right) - 49 \, \cos\left(5 \, b x^{2} + 5 \, a\right) + 245 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 1225 \, \cos\left(b x^{2} + a\right)}{4480 \, b}"," ",0,"1/4480*(5*cos(7*b*x^2 + 7*a) - 49*cos(5*b*x^2 + 5*a) + 245*cos(3*b*x^2 + 3*a) - 1225*cos(b*x^2 + a))/b","A",0
34,1,54,0,0.400590," ","integrate((1+sin(x^2))^2/x^3,x, algorithm=""maxima"")","\frac{x^{2} {\left(i \, \Gamma\left(-1, 2 i \, x^{2}\right) - i \, \Gamma\left(-1, -2 i \, x^{2}\right)\right)} - 1}{4 \, x^{2}} - \frac{1}{2 \, x^{2}} + \frac{1}{2} \, \Gamma\left(-1, i \, x^{2}\right) + \frac{1}{2} \, \Gamma\left(-1, -i \, x^{2}\right)"," ",0,"1/4*(x^2*(I*gamma(-1, 2*I*x^2) - I*gamma(-1, -2*I*x^2)) - 1)/x^2 - 1/2/x^2 + 1/2*gamma(-1, I*x^2) + 1/2*gamma(-1, -I*x^2)","C",0
35,0,0,0,0.000000," ","integrate(x^5/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{x^{5}}{b \sin\left(d x^{2} + c\right) + a}\,{d x}"," ",0,"integrate(x^5/(b*sin(d*x^2 + c) + a), x)","F",0
36,0,0,0,0.000000," ","integrate(x^3/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{x^{3}}{b \sin\left(d x^{2} + c\right) + a}\,{d x}"," ",0,"integrate(x^3/(b*sin(d*x^2 + c) + a), x)","F",0
37,1,8078,0,36.952381," ","integrate(x/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\frac{\arctan\left(-\frac{2 \, {\left(4 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - 4 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left(3 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3} + {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} - {\left(a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} - {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) - 4 \, {\left({\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(c\right)^{5} + {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} - {\left(a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 3 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} - {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) - 4 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) + b^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + 4 \, a b^{4} \cos\left(c\right) \sin\left(c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} + 2 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3} + 2 \, {\left(a b^{4} \cos\left(c\right)^{2} - a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left({\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + 2 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + 2 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} - {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + {\left({\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5} + 4 \, {\left(a b^{4} \cos\left(c\right)^{2} - a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{4} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}\right)}}{b^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{6} + 3 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(b^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} - 2 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} - 6 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(b^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} - 4 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 6 \, {\left({\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) - 2 \, {\left(3 \, b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} - 3 \, b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(c\right)^{6} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) - 12 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 6 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) - 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4} - 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 3 \, {\left({\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}, \frac{b^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{6} + {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(3 \, b^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} - 6 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} - 2 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + {\left({\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left(3 \, b^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} - 12 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 12 \, {\left(3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 2 \, {\left({\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) - 4 \, {\left(b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} - b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{6} + {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(3 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, a^{2} b^{3} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, a^{2} b^{3} \cos\left(c\right)^{3} - 4 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(a^{3} b^{2} \cos\left(c\right)^{4} + 6 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, a^{3} b^{2} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{2} \cos\left(c\right)^{4} - b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 6 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + a^{3} b^{2} \sin\left(c\right)^{4} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 3 \, {\left(3 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right) + a^{2} b^{3} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 6 \, {\left(a^{2} b^{3} \cos\left(c\right)^{3} + 3 \, a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{2} \cos\left(c\right)^{3} \sin\left(c\right) + a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}{b^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{6} + 3 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(b^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} - 2 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} - 6 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(b^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} - 4 \, a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 6 \, {\left({\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) - 2 \, {\left(3 \, b^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} - 3 \, b^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(c\right)^{6} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, b^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) - 12 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 6 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) - 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4} - 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 3 \, {\left({\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(b^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}\right)}{2 \, \sqrt{a^{2} - b^{2}} d}"," ",0,"1/2*arctan2(-2*(4*(a^2*b^4 - b^6)*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) - 4*(a^2*b^4 - b^6)*cos(c)*sin(d*x^2 + 2*c)^4*sin(c) - 4*((a^3*b^3 - a*b^5)*cos(c)^3 + 3*(a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 4*(3*(a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + (a^3*b^3 - a*b^5)*sin(c)^3 + ((a^2*b^4 - b^6)*cos(c)^2 - (a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 + 4*((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 4*((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)*sin(c)^3 + 3*((a^3*b^3 - a*b^5)*cos(c)^3 - (a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 4*((2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^5 + 2*(2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^3*sin(c)^2 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) - 4*((2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^4*sin(c) + 2*(2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^2*sin(c)^3 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*sin(c)^5 + ((a^2*b^4 - b^6)*cos(c)^2 - (a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 3*((a^3*b^3 - a*b^5)*cos(c)^2*sin(c) - (a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + ((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^4 - (4*a^4*b^2 - 5*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + (b^5*cos(d*x^2 + 2*c)^5*cos(c) - 4*a*b^4*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) + b^5*sin(d*x^2 + 2*c)^5*sin(c) + (b^5*cos(d*x^2 + 2*c)*cos(c) + 4*a*b^4*cos(c)*sin(c))*sin(d*x^2 + 2*c)^4 + 2*((2*a^2*b^3 - b^5)*cos(c)^3 + 3*(2*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(b^5*cos(d*x^2 + 2*c)^2*sin(c) + 3*(2*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (2*a^2*b^3 - b^5)*sin(c)^3 + 2*(a*b^4*cos(c)^2 - a*b^4*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 - 4*((4*a^3*b^2 - 3*a*b^4)*cos(c)^3*sin(c) + (4*a^3*b^2 - 3*a*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 2*(b^5*cos(d*x^2 + 2*c)^3*cos(c) + 2*(4*a^3*b^2 - 3*a*b^4)*cos(c)^3*sin(c) + 2*(4*a^3*b^2 - 3*a*b^4)*cos(c)*sin(c)^3 + 3*((2*a^2*b^3 - b^5)*cos(c)^3 - (2*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + ((8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^5 + 2*(8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + (b^5*cos(d*x^2 + 2*c)^4*sin(c) + (8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (8*a^4*b - 8*a^2*b^3 + b^5)*sin(c)^5 + 4*(a*b^4*cos(c)^2 - a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 6*((2*a^2*b^3 - b^5)*cos(c)^2*sin(c) - (2*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((4*a^3*b^2 - 3*a*b^4)*cos(c)^4 - (4*a^3*b^2 - 3*a*b^4)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(a^2 - b^2))/(b^6*cos(d*x^2 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^2 + 2*c)^5 + b^6*sin(d*x^2 + 2*c)^6 - 6*a*b^5*cos(d*x^2 + 2*c)^5*sin(c) + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^6 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^4*sin(c)^2 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^2*sin(c)^4 + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*sin(c)^6 + 3*((2*a^2*b^4 - b^6)*cos(c)^2 + 5*(2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(b^6*cos(d*x^2 + 2*c)^2 - 2*a*b^5*cos(d*x^2 + 2*c)*sin(c) + 5*(2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + 5*(4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^2 + 2*c)^2*cos(c) + 5*(4*a^3*b^3 - 3*a*b^5)*cos(c)^3 - 6*(2*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + 3*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(b^6*cos(d*x^2 + 2*c)^4 - 4*a*b^5*cos(d*x^2 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4 + 6*((2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + (4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 6*((16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^4*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^2*sin(c)^3 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 6*(a*b^5*cos(d*x^2 + 2*c)^4*cos(c) + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^5 - 4*(2*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^3*sin(c)^2 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)*sin(c)^4 + 2*((4*a^3*b^3 - 3*a*b^5)*cos(c)^3 + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) - 2*(3*b^5*cos(c)*sin(d*x^2 + 2*c)^5 - 3*b^5*cos(d*x^2 + 2*c)^5*sin(c) + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^6 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^4*sin(c)^2 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^2*sin(c)^4 + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*sin(c)^6 + 3*(a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(5*a*b^4*cos(c)^2 - b^5*cos(d*x^2 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + 5*(4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 2*(3*b^5*cos(d*x^2 + 2*c)^2*cos(c) - 12*a*b^4*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 5*(4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + 6*((2*a^3*b^2 - a*b^4)*cos(c)^4 + 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 + 5*(2*a^3*b^2 - a*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 - 6*(b^5*cos(d*x^2 + 2*c)^3*sin(c) - 5*(2*a^3*b^2 - a*b^4)*cos(c)^4 - 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 - (2*a^3*b^2 - a*b^4)*sin(c)^4 - 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^2 + (3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 3*((16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (16*a^4*b - 12*a^2*b^3 + b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 3*(b^5*cos(d*x^2 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^5 + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)*sin(c)^4 + 2*((4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 16*((2*a^3*b^2 - a*b^4)*cos(c)^3*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(a^2 - b^2)), (b^6*cos(d*x^2 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^2 + 2*c)^5 + b^6*sin(d*x^2 + 2*c)^6 - 6*a*b^5*cos(d*x^2 + 2*c)^5*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^6 + 3*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4*sin(c)^2 + 3*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^4 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^6 + ((4*a^2*b^4 - b^6)*cos(c)^2 + 5*(4*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (3*b^6*cos(d*x^2 + 2*c)^2 - 6*a*b^5*cos(d*x^2 + 2*c)*sin(c) + 5*(4*a^2*b^4 - b^6)*cos(c)^2 + (4*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(3*(2*a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + 5*(2*a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^2 + 2*c)^2*cos(c) + 5*(2*a^3*b^3 - a*b^5)*cos(c)^3 - 2*(4*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*(2*a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + ((8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + (3*b^6*cos(d*x^2 + 2*c)^4 - 12*a*b^5*cos(d*x^2 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 4*a^2*b^4 - b^6)*sin(c)^4 + 6*((4*a^2*b^4 - b^6)*cos(c)^2 + (4*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 12*(3*(2*a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + (2*a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 2*((8*a^5*b - 5*a*b^5)*cos(c)^4*sin(c) + 2*(8*a^5*b - 5*a*b^5)*cos(c)^2*sin(c)^3 + (8*a^5*b - 5*a*b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 2*(3*a*b^5*cos(d*x^2 + 2*c)^4*cos(c) + (8*a^5*b - 5*a*b^5)*cos(c)^5 - 4*(4*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + 2*(8*a^5*b - 5*a*b^5)*cos(c)^3*sin(c)^2 + (8*a^5*b - 5*a*b^5)*cos(c)*sin(c)^4 + 6*((2*a^3*b^3 - a*b^5)*cos(c)^3 + 3*(2*a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) - 4*(b^5*cos(c)*sin(d*x^2 + 2*c)^5 - b^5*cos(d*x^2 + 2*c)^5*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)^6 + 3*(2*a^3*b^2 - a*b^4)*cos(c)^4*sin(c)^2 + 3*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^4 + (2*a^3*b^2 - a*b^4)*sin(c)^6 + (a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (5*a*b^4*cos(c)^2 - b^5*cos(d*x^2 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(3*a^2*b^3*cos(c)^2*sin(c) + 5*a^2*b^3*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 2*(b^5*cos(d*x^2 + 2*c)^2*cos(c) + 5*a^2*b^3*cos(c)^3 - 4*a*b^4*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*a^2*b^3*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + 2*(a^3*b^2*cos(c)^4 + 6*a^3*b^2*cos(c)^2*sin(c)^2 + 5*a^3*b^2*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 2*(5*a^3*b^2*cos(c)^4 - b^5*cos(d*x^2 + 2*c)^3*sin(c) + 6*a^3*b^2*cos(c)^2*sin(c)^2 + a^3*b^2*sin(c)^4 + 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 3*(3*a^2*b^3*cos(c)^2*sin(c) + a^2*b^3*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - ((4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^4*sin(c) + 2*(4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^2*sin(c)^3 + (4*a^4*b + 2*a^2*b^3 - b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + (b^5*cos(d*x^2 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^5 + 2*(4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^3*sin(c)^2 + (4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)*sin(c)^4 + 6*(a^2*b^3*cos(c)^3 + 3*a^2*b^3*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 16*(a^3*b^2*cos(c)^3*sin(c) + a^3*b^2*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(a^2 - b^2))/(b^6*cos(d*x^2 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^2 + 2*c)^5 + b^6*sin(d*x^2 + 2*c)^6 - 6*a*b^5*cos(d*x^2 + 2*c)^5*sin(c) + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^6 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^4*sin(c)^2 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^2*sin(c)^4 + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*sin(c)^6 + 3*((2*a^2*b^4 - b^6)*cos(c)^2 + 5*(2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(b^6*cos(d*x^2 + 2*c)^2 - 2*a*b^5*cos(d*x^2 + 2*c)*sin(c) + 5*(2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + 5*(4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^2 + 2*c)^2*cos(c) + 5*(4*a^3*b^3 - 3*a*b^5)*cos(c)^3 - 6*(2*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + 3*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(b^6*cos(d*x^2 + 2*c)^4 - 4*a*b^5*cos(d*x^2 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4 + 6*((2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + (4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 6*((16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^4*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^2*sin(c)^3 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 6*(a*b^5*cos(d*x^2 + 2*c)^4*cos(c) + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^5 - 4*(2*a^2*b^4 - b^6)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^3*sin(c)^2 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)*sin(c)^4 + 2*((4*a^3*b^3 - 3*a*b^5)*cos(c)^3 + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) - 2*(3*b^5*cos(c)*sin(d*x^2 + 2*c)^5 - 3*b^5*cos(d*x^2 + 2*c)^5*sin(c) + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^6 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^4*sin(c)^2 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^2*sin(c)^4 + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*sin(c)^6 + 3*(a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(5*a*b^4*cos(c)^2 - b^5*cos(d*x^2 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + 5*(4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 2*(3*b^5*cos(d*x^2 + 2*c)^2*cos(c) - 12*a*b^4*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 5*(4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*sin(d*x^2 + 2*c)^3 + 6*((2*a^3*b^2 - a*b^4)*cos(c)^4 + 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 + 5*(2*a^3*b^2 - a*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 - 6*(b^5*cos(d*x^2 + 2*c)^3*sin(c) - 5*(2*a^3*b^2 - a*b^4)*cos(c)^4 - 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 - (2*a^3*b^2 - a*b^4)*sin(c)^4 - 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^2 + 2*c)^2 + (3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 3*((16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (16*a^4*b - 12*a^2*b^3 + b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 3*(b^5*cos(d*x^2 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^5 + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)*sin(c)^4 + 2*((4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 16*((2*a^3*b^2 - a*b^4)*cos(c)^3*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*d)","B",0
38,0,0,0,0.000000," ","integrate(1/x/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{2} + c\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^2 + c) + a)*x), x)","F",0
39,0,0,0,0.000000," ","integrate(1/x^3/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{2} + c\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^2 + c) + a)*x^3), x)","F",0
40,0,0,0,0.000000," ","integrate(x^2/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{x^{2}}{b \sin\left(d x^{2} + c\right) + a}\,{d x}"," ",0,"integrate(x^2/(b*sin(d*x^2 + c) + a), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(d x^{2} + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*sin(d*x^2 + c) + a), x)","F",0
42,0,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{2} + c\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^2 + c) + a)*x^2), x)","F",0
43,-2,0,0,0.000000," ","integrate(x^5/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
44,-2,0,0,0.000000," ","integrate(x^3/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
45,-1,0,0,0.000000," ","integrate(x/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate(1/x/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate(1/x^3/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(x^2/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \sin\left(d x^{2} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sin(d*x^2 + c) + a)^p, x)","F",0
52,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^3,x, algorithm=""maxima"")","\frac{\left(e x\right)^{m + 1} a^{3}}{e {\left(m + 1\right)}} + \frac{\frac{3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m \cos\left(c\right) + {\left(4 \, a^{2} b + b^{3}\right)} e^{m} \cos\left(c\right)\right)} d x^{3} x^{m} \Gamma\left(\frac{1}{4} \, m + \frac{3}{4}\right) \,_1F_2\left(\begin{matrix} \frac{1}{4} \, m + \frac{3}{4} \\ \frac{3}{2},\frac{1}{4} \, m + \frac{7}{4} \end{matrix} ; -\frac{1}{4} \, d^{2} x^{4} \right)}{4 \, \Gamma\left(\frac{1}{4} \, m + \frac{7}{4}\right)} + 12 \, a b^{2} e^{m} x x^{m} + \frac{3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m \sin\left(c\right) + {\left(4 \, a^{2} b + b^{3}\right)} e^{m} \sin\left(c\right)\right)} x x^{m} \Gamma\left(\frac{1}{4} \, m + \frac{1}{4}\right) \,_1F_2\left(\begin{matrix} \frac{1}{4} \, m + \frac{1}{4} \\ \frac{1}{2},\frac{1}{4} \, m + \frac{5}{4} \end{matrix} ; -\frac{1}{4} \, d^{2} x^{4} \right)}{4 \, \Gamma\left(\frac{1}{4} \, m + \frac{5}{4}\right)} - 12 \, {\left(a b^{2} e^{m} m + a b^{2} e^{m}\right)} \int x^{m} \cos\left(2 \, d x^{2} + 2 \, c\right)\,{d x} - 2 \, {\left(b^{3} e^{m} m + b^{3} e^{m}\right)} \int x^{m} \sin\left(3 \, d x^{2} + 3 \, c\right)\,{d x} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m + {\left(4 \, a^{2} b + b^{3}\right)} e^{m}\right)} \int x^{m} \sin\left(d x^{2} + c\right)\,{d x}}{8 \, {\left(m + 1\right)}}"," ",0,"(e*x)^(m + 1)*a^3/(e*(m + 1)) + 1/8*(12*a*b^2*e^m*x*x^m - 12*(a*b^2*e^m*m + a*b^2*e^m)*integrate(x^m*cos(2*d*x^2 + 2*c), x) + 3*((4*a^2*b + b^3)*e^m*m*sin(c) + (4*a^2*b + b^3)*e^m*sin(c))*integrate(x^m*cos(d*x^2), x) - 2*(b^3*e^m*m + b^3*e^m)*integrate(x^m*sin(3*d*x^2 + 3*c), x) + 3*((4*a^2*b + b^3)*e^m*m + (4*a^2*b + b^3)*e^m)*integrate(x^m*sin(d*x^2 + c), x) + 3*((4*a^2*b + b^3)*e^m*m*cos(c) + (4*a^2*b + b^3)*e^m*cos(c))*integrate(x^m*sin(d*x^2), x))/(m + 1)","F",0
53,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{m + 1} a^{2}}{e {\left(m + 1\right)}} + \frac{b^{2} e^{m} x x^{m} - {\left(b^{2} e^{m} m + b^{2} e^{m}\right)} \int x^{m} \cos\left(2 \, d x^{2} + 2 \, c\right)\,{d x} + 4 \, {\left(a b e^{m} m + a b e^{m}\right)} \int x^{m} \sin\left(d x^{2} + c\right)\,{d x}}{2 \, {\left(m + 1\right)}}"," ",0,"(e*x)^(m + 1)*a^2/(e*(m + 1)) + 1/2*(b^2*e^m*x*x^m - (b^2*e^m*m + b^2*e^m)*integrate(x^m*cos(2*d*x^2 + 2*c), x) + 4*(a*b*e^m*m + a*b*e^m)*integrate(x^m*sin(d*x^2 + c), x))/(m + 1)","F",0
54,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","b e^{m} \int x^{m} \sin\left(d x^{2} + c\right)\,{d x} + \frac{\left(e x\right)^{m + 1} a}{e {\left(m + 1\right)}}"," ",0,"b*e^m*integrate(x^m*sin(d*x^2 + c), x) + (e*x)^(m + 1)*a/(e*(m + 1))","F",0
55,0,0,0,0.000000," ","integrate((e*x)^m/(a+b*sin(d*x^2+c)),x, algorithm=""maxima"")","\int \frac{\left(e x\right)^{m}}{b \sin\left(d x^{2} + c\right) + a}\,{d x}"," ",0,"integrate((e*x)^m/(b*sin(d*x^2 + c) + a), x)","F",0
56,-1,0,0,0.000000," ","integrate((e*x)^m/(a+b*sin(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,1,37,0,0.328371," ","integrate(x^5*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} - \frac{{\left(d x^{3} \cos\left(d x^{3} + c\right) - \sin\left(d x^{3} + c\right)\right)} b}{3 \, d^{2}}"," ",0,"1/6*a*x^6 - 1/3*(d*x^3*cos(d*x^3 + c) - sin(d*x^3 + c))*b/d^2","A",0
58,1,21,0,0.320352," ","integrate(x^2*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} - \frac{b \cos\left(d x^{3} + c\right)}{3 \, d}"," ",0,"1/3*a*x^3 - 1/3*b*cos(d*x^3 + c)/d","A",0
59,1,50,0,0.429803," ","integrate((a+b*sin(d*x^3+c))/x,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(i \, {\rm Ei}\left(i \, d x^{3}\right) - i \, {\rm Ei}\left(-i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\rm Ei}\left(i \, d x^{3}\right) + {\rm Ei}\left(-i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b + a \log\left(x\right)"," ",0,"-1/6*((I*Ei(I*d*x^3) - I*Ei(-I*d*x^3))*cos(c) - (Ei(I*d*x^3) + Ei(-I*d*x^3))*sin(c))*b + a*log(x)","C",0
60,1,57,0,0.428595," ","integrate((a+b*sin(d*x^3+c))/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(\Gamma\left(-1, i \, d x^{3}\right) + \Gamma\left(-1, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left(i \, \Gamma\left(-1, i \, d x^{3}\right) - i \, \Gamma\left(-1, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b d - \frac{a}{3 \, x^{3}}"," ",0,"1/6*((gamma(-1, I*d*x^3) + gamma(-1, -I*d*x^3))*cos(c) - (I*gamma(-1, I*d*x^3) - I*gamma(-1, -I*d*x^3))*sin(c))*b*d - 1/3*a/x^3","C",0
61,1,109,0,0.578769," ","integrate(x^4*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} - \frac{{\left(6 \, d x^{3} \cos\left(d x^{3} + c\right) - \left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)}\right)} b}{18 \, d^{2} x}"," ",0,"1/5*a*x^5 - 1/18*(6*d*x^3*cos(d*x^3 + c) - (d*x^3)^(1/3)*(((I*sqrt(3) - 1)*gamma(2/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(2/3, -I*d*x^3))*cos(c) + ((sqrt(3) + I)*gamma(2/3, I*d*x^3) + (sqrt(3) - I)*gamma(2/3, -I*d*x^3))*sin(c)))*b/(d^2*x)","A",0
62,1,93,0,0.538406," ","integrate(x*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} - \frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b}{12 \, d x}"," ",0,"1/2*a*x^2 - 1/12*(d*x^3)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*d*x^3) + (sqrt(3) - I)*gamma(2/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) - 1)*gamma(2/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(2/3, -I*d*x^3))*sin(c))*b/(d*x)","A",0
63,1,89,0,0.540514," ","integrate((a+b*sin(d*x^3+c))/x^2,x, algorithm=""maxima"")","-\frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b}{12 \, x} - \frac{a}{x}"," ",0,"-1/12*(d*x^3)^(1/3)*(((I*sqrt(3) - 1)*gamma(-1/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(-1/3, -I*d*x^3))*cos(c) + ((sqrt(3) + I)*gamma(-1/3, I*d*x^3) + (sqrt(3) - I)*gamma(-1/3, -I*d*x^3))*sin(c))*b/x - a/x","A",0
64,1,91,0,0.565758," ","integrate((a+b*sin(d*x^3+c))/x^5,x, algorithm=""maxima"")","\frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{4}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{4}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b d}{12 \, x} - \frac{a}{4 \, x^{4}}"," ",0,"1/12*(d*x^3)^(1/3)*(((sqrt(3) + I)*gamma(-4/3, I*d*x^3) + (sqrt(3) - I)*gamma(-4/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) - 1)*gamma(-4/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(-4/3, -I*d*x^3))*sin(c))*b*d/x - 1/4*a/x^4","A",0
65,1,110,0,0.552050," ","integrate(x^3*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} - \frac{{\left(12 \, \left(d x^{3}\right)^{\frac{1}{3}} x \cos\left(d x^{3} + c\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} x\right)} b}{36 \, \left(d x^{3}\right)^{\frac{1}{3}} d}"," ",0,"1/4*a*x^4 - 1/36*(12*(d*x^3)^(1/3)*x*cos(d*x^3 + c) + (((sqrt(3) - I)*gamma(1/3, I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -I*d*x^3))*cos(c) + ((-I*sqrt(3) - 1)*gamma(1/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(1/3, -I*d*x^3))*sin(c))*x)*b/((d*x^3)^(1/3)*d)","A",0
66,1,85,0,0.535074," ","integrate(a+b*sin(d*x^3+c),x, algorithm=""maxima"")","\frac{{\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b x}{12 \, \left(d x^{3}\right)^{\frac{1}{3}}} + a x"," ",0,"1/12*(((-I*sqrt(3) - 1)*gamma(1/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(1/3, -I*d*x^3))*cos(c) - ((sqrt(3) - I)*gamma(1/3, I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -I*d*x^3))*sin(c))*b*x/(d*x^3)^(1/3) + a*x","A",0
67,1,90,0,0.523624," ","integrate((a+b*sin(d*x^3+c))/x^3,x, algorithm=""maxima"")","\frac{\left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b}{12 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/12*(d*x^3)^(2/3)*(((sqrt(3) - I)*gamma(-2/3, I*d*x^3) + (sqrt(3) + I)*gamma(-2/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) + 1)*gamma(-2/3, I*d*x^3) + (-I*sqrt(3) + 1)*gamma(-2/3, -I*d*x^3))*sin(c))*b/x^2 - 1/2*a/x^2","A",0
68,1,91,0,0.544390," ","integrate((a+b*sin(d*x^3+c))/x^6,x, algorithm=""maxima"")","-\frac{\left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{5}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{5}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} b d}{12 \, x^{2}} - \frac{a}{5 \, x^{5}}"," ",0,"-1/12*(d*x^3)^(2/3)*(((-I*sqrt(3) - 1)*gamma(-5/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(-5/3, -I*d*x^3))*cos(c) - ((sqrt(3) - I)*gamma(-5/3, I*d*x^3) + (sqrt(3) + I)*gamma(-5/3, -I*d*x^3))*sin(c))*b*d/x^2 - 1/5*a/x^5","A",0
69,1,87,0,0.340340," ","integrate(x^5*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} - \frac{2 \, {\left(d x^{3} \cos\left(d x^{3} + c\right) - \sin\left(d x^{3} + c\right)\right)} a b}{3 \, d^{2}} + \frac{{\left(2 \, d^{2} x^{6} - 2 \, d x^{3} \sin\left(2 \, d x^{3} + 2 \, c\right) - \cos\left(2 \, d x^{3} + 2 \, c\right)\right)} b^{2}}{24 \, d^{2}}"," ",0,"1/6*a^2*x^6 - 2/3*(d*x^3*cos(d*x^3 + c) - sin(d*x^3 + c))*a*b/d^2 + 1/24*(2*d^2*x^6 - 2*d*x^3*sin(2*d*x^3 + 2*c) - cos(2*d*x^3 + 2*c))*b^2/d^2","A",0
70,1,52,0,0.322711," ","integrate(x^2*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{{\left(2 \, d x^{3} - \sin\left(2 \, d x^{3} + 2 \, c\right)\right)} b^{2}}{12 \, d} - \frac{2 \, a b \cos\left(d x^{3} + c\right)}{3 \, d}"," ",0,"1/3*a^2*x^3 + 1/12*(2*d*x^3 - sin(2*d*x^3 + 2*c))*b^2/d - 2/3*a*b*cos(d*x^3 + c)/d","A",0
71,1,108,0,0.483657," ","integrate((a+b*sin(d*x^3+c))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left({\left(i \, {\rm Ei}\left(i \, d x^{3}\right) - i \, {\rm Ei}\left(-i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\rm Ei}\left(i \, d x^{3}\right) + {\rm Ei}\left(-i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b - \frac{1}{12} \, {\left({\left({\rm Ei}\left(2 i \, d x^{3}\right) + {\rm Ei}\left(-2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) - {\left(-i \, {\rm Ei}\left(2 i \, d x^{3}\right) + i \, {\rm Ei}\left(-2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right) - 6 \, \log\left(x\right)\right)} b^{2} + a^{2} \log\left(x\right)"," ",0,"-1/3*((I*Ei(I*d*x^3) - I*Ei(-I*d*x^3))*cos(c) - (Ei(I*d*x^3) + Ei(-I*d*x^3))*sin(c))*a*b - 1/12*((Ei(2*I*d*x^3) + Ei(-2*I*d*x^3))*cos(2*c) - (-I*Ei(2*I*d*x^3) + I*Ei(-2*I*d*x^3))*sin(2*c) - 6*log(x))*b^2 + a^2*log(x)","C",0
72,1,124,0,0.483979," ","integrate((a+b*sin(d*x^3+c))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left({\left(\Gamma\left(-1, i \, d x^{3}\right) + \Gamma\left(-1, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left(i \, \Gamma\left(-1, i \, d x^{3}\right) - i \, \Gamma\left(-1, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b d + \frac{{\left({\left({\left(i \, \Gamma\left(-1, 2 i \, d x^{3}\right) - i \, \Gamma\left(-1, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + {\left(\Gamma\left(-1, 2 i \, d x^{3}\right) + \Gamma\left(-1, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} d x^{3} - 1\right)} b^{2}}{6 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"1/3*((gamma(-1, I*d*x^3) + gamma(-1, -I*d*x^3))*cos(c) - (I*gamma(-1, I*d*x^3) - I*gamma(-1, -I*d*x^3))*sin(c))*a*b*d + 1/6*(((I*gamma(-1, 2*I*d*x^3) - I*gamma(-1, -2*I*d*x^3))*cos(2*c) + (gamma(-1, 2*I*d*x^3) + gamma(-1, -2*I*d*x^3))*sin(2*c))*d*x^3 - 1)*b^2/x^3 - 1/3*a^2/x^3","C",0
73,1,239,0,0.578303," ","integrate(x^4*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} - \frac{{\left(6 \, d x^{3} \cos\left(d x^{3} + c\right) - \left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)}\right)} a b}{9 \, d^{2} x} + \frac{{\left(72 \, d^{2} x^{6} - 60 \, d x^{3} \sin\left(2 \, d x^{3} + 2 \, c\right) - 2^{\frac{1}{3}} \left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(5 \, \sqrt{3} + 5 i\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(5 \, \sqrt{3} - 5 i\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + 5 \, {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)}\right)} b^{2}}{720 \, d^{2} x}"," ",0,"1/5*a^2*x^5 - 1/9*(6*d*x^3*cos(d*x^3 + c) - (d*x^3)^(1/3)*(((I*sqrt(3) - 1)*gamma(2/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(2/3, -I*d*x^3))*cos(c) + ((sqrt(3) + I)*gamma(2/3, I*d*x^3) + (sqrt(3) - I)*gamma(2/3, -I*d*x^3))*sin(c)))*a*b/(d^2*x) + 1/720*(72*d^2*x^6 - 60*d*x^3*sin(2*d*x^3 + 2*c) - 2^(1/3)*(d*x^3)^(1/3)*(((5*sqrt(3) + 5*I)*gamma(2/3, 2*I*d*x^3) + (5*sqrt(3) - 5*I)*gamma(2/3, -2*I*d*x^3))*cos(2*c) + 5*((-I*sqrt(3) + 1)*gamma(2/3, 2*I*d*x^3) + (I*sqrt(3) + 1)*gamma(2/3, -2*I*d*x^3))*sin(2*c)))*b^2/(d^2*x)","A",0
74,1,199,0,0.569608," ","integrate(x*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} - \frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b}{6 \, d x} + \frac{{\left(12 \, d x^{3} - 2^{\frac{1}{3}} \left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)}\right)} b^{2}}{48 \, d x}"," ",0,"1/2*a^2*x^2 - 1/6*(d*x^3)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*d*x^3) + (sqrt(3) - I)*gamma(2/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) - 1)*gamma(2/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(2/3, -I*d*x^3))*sin(c))*a*b/(d*x) + 1/48*(12*d*x^3 - 2^(1/3)*(d*x^3)^(1/3)*(((I*sqrt(3) - 1)*gamma(2/3, 2*I*d*x^3) + (-I*sqrt(3) - 1)*gamma(2/3, -2*I*d*x^3))*cos(2*c) + ((sqrt(3) + I)*gamma(2/3, 2*I*d*x^3) + (sqrt(3) - I)*gamma(2/3, -2*I*d*x^3))*sin(2*c)))*b^2/(d*x)","A",0
75,1,187,0,0.580866," ","integrate((a+b*sin(d*x^3+c))^2/x^2,x, algorithm=""maxima"")","-\frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b}{6 \, x} + \frac{{\left(2^{\frac{1}{3}} \left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} - 12\right)} b^{2}}{24 \, x} - \frac{a^{2}}{x}"," ",0,"-1/6*(d*x^3)^(1/3)*(((I*sqrt(3) - 1)*gamma(-1/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(-1/3, -I*d*x^3))*cos(c) + ((sqrt(3) + I)*gamma(-1/3, I*d*x^3) + (sqrt(3) - I)*gamma(-1/3, -I*d*x^3))*sin(c))*a*b/x + 1/24*(2^(1/3)*(d*x^3)^(1/3)*(((sqrt(3) + I)*gamma(-1/3, 2*I*d*x^3) + (sqrt(3) - I)*gamma(-1/3, -2*I*d*x^3))*cos(2*c) - ((I*sqrt(3) - 1)*gamma(-1/3, 2*I*d*x^3) + (-I*sqrt(3) - 1)*gamma(-1/3, -2*I*d*x^3))*sin(2*c)) - 12)*b^2/x - a^2/x","A",0
76,1,198,0,0.597852," ","integrate((a+b*sin(d*x^3+c))^2/x^5,x, algorithm=""maxima"")","\frac{\left(d x^{3}\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{4}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{4}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b d}{6 \, x} - \frac{{\left(2^{\frac{1}{3}} \left(d x^{3}\right)^{\frac{1}{3}} {\left(2 \, {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{4}{3}, 2 i \, d x^{3}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{4}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) - {\left({\left(2 \, \sqrt{3} + 2 i\right)} \Gamma\left(-\frac{4}{3}, 2 i \, d x^{3}\right) + {\left(2 \, \sqrt{3} - 2 i\right)} \Gamma\left(-\frac{4}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} d x^{3} + 3\right)} b^{2}}{24 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/6*(d*x^3)^(1/3)*(((sqrt(3) + I)*gamma(-4/3, I*d*x^3) + (sqrt(3) - I)*gamma(-4/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) - 1)*gamma(-4/3, I*d*x^3) + (-I*sqrt(3) - 1)*gamma(-4/3, -I*d*x^3))*sin(c))*a*b*d/x - 1/24*(2^(1/3)*(d*x^3)^(1/3)*(2*((-I*sqrt(3) + 1)*gamma(-4/3, 2*I*d*x^3) + (I*sqrt(3) + 1)*gamma(-4/3, -2*I*d*x^3))*cos(2*c) - ((2*sqrt(3) + 2*I)*gamma(-4/3, 2*I*d*x^3) + (2*sqrt(3) - 2*I)*gamma(-4/3, -2*I*d*x^3))*sin(2*c))*d*x^3 + 3)*b^2/x^4 - 1/4*a^2/x^4","A",0
77,1,240,0,0.582112," ","integrate(x^3*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} x^{4} - \frac{2^{\frac{2}{3}} {\left({\left({\left({\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + {\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} x - 6 \cdot 2^{\frac{1}{3}} {\left(3 \, d x^{4} - 2 \, x \sin\left(2 \, d x^{3} + 2 \, c\right)\right)} \left(d x^{3}\right)^{\frac{1}{3}}\right)} b^{2}}{288 \, \left(d x^{3}\right)^{\frac{1}{3}} d} - \frac{{\left(12 \, \left(d x^{3}\right)^{\frac{1}{3}} x \cos\left(d x^{3} + c\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} x\right)} a b}{18 \, \left(d x^{3}\right)^{\frac{1}{3}} d}"," ",0,"1/4*a^2*x^4 - 1/288*2^(2/3)*((((I*sqrt(3) + 1)*gamma(1/3, 2*I*d*x^3) + (-I*sqrt(3) + 1)*gamma(1/3, -2*I*d*x^3))*cos(2*c) + ((sqrt(3) - I)*gamma(1/3, 2*I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -2*I*d*x^3))*sin(2*c))*x - 6*2^(1/3)*(3*d*x^4 - 2*x*sin(2*d*x^3 + 2*c))*(d*x^3)^(1/3))*b^2/((d*x^3)^(1/3)*d) - 1/18*(12*(d*x^3)^(1/3)*x*cos(d*x^3 + c) + (((sqrt(3) - I)*gamma(1/3, I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -I*d*x^3))*cos(c) + ((-I*sqrt(3) - 1)*gamma(1/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(1/3, -I*d*x^3))*sin(c))*x)*a*b/((d*x^3)^(1/3)*d)","A",0
78,1,192,0,0.565699," ","integrate((a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{{\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b x}{6 \, \left(d x^{3}\right)^{\frac{1}{3}}} + \frac{2^{\frac{2}{3}} {\left({\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} x + 12 \cdot 2^{\frac{1}{3}} \left(d x^{3}\right)^{\frac{1}{3}} x\right)} b^{2}}{48 \, \left(d x^{3}\right)^{\frac{1}{3}}} + a^{2} x"," ",0,"1/6*(((-I*sqrt(3) - 1)*gamma(1/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(1/3, -I*d*x^3))*cos(c) - ((sqrt(3) - I)*gamma(1/3, I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -I*d*x^3))*sin(c))*a*b*x/(d*x^3)^(1/3) + 1/48*2^(2/3)*((((sqrt(3) - I)*gamma(1/3, 2*I*d*x^3) + (sqrt(3) + I)*gamma(1/3, -2*I*d*x^3))*cos(2*c) + ((-I*sqrt(3) - 1)*gamma(1/3, 2*I*d*x^3) + (I*sqrt(3) - 1)*gamma(1/3, -2*I*d*x^3))*sin(2*c))*x + 12*2^(1/3)*(d*x^3)^(1/3)*x)*b^2/(d*x^3)^(1/3) + a^2*x","A",0
79,1,188,0,0.593760," ","integrate((a+b*sin(d*x^3+c))^2/x^3,x, algorithm=""maxima"")","\frac{\left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{2}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{2}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{2}{3}, i \, d x^{3}\right) + {\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(-\frac{2}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b}{6 \, x^{2}} - \frac{{\left(2^{\frac{2}{3}} \left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{2}{3}, 2 i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{2}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} + 6\right)} b^{2}}{24 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/6*(d*x^3)^(2/3)*(((sqrt(3) - I)*gamma(-2/3, I*d*x^3) + (sqrt(3) + I)*gamma(-2/3, -I*d*x^3))*cos(c) - ((I*sqrt(3) + 1)*gamma(-2/3, I*d*x^3) + (-I*sqrt(3) + 1)*gamma(-2/3, -I*d*x^3))*sin(c))*a*b/x^2 - 1/24*(2^(2/3)*(d*x^3)^(2/3)*(((-I*sqrt(3) - 1)*gamma(-2/3, 2*I*d*x^3) + (I*sqrt(3) - 1)*gamma(-2/3, -2*I*d*x^3))*cos(2*c) - ((sqrt(3) - I)*gamma(-2/3, 2*I*d*x^3) + (sqrt(3) + I)*gamma(-2/3, -2*I*d*x^3))*sin(2*c)) + 6)*b^2/x^2 - 1/2*a^2/x^2","A",0
80,1,197,0,0.590360," ","integrate((a+b*sin(d*x^3+c))^2/x^6,x, algorithm=""maxima"")","-\frac{\left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, -i \, d x^{3}\right)\right)} \cos\left(c\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{5}{3}, i \, d x^{3}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{5}{3}, -i \, d x^{3}\right)\right)} \sin\left(c\right)\right)} a b d}{6 \, x^{2}} - \frac{{\left(2^{\frac{2}{3}} \left(d x^{3}\right)^{\frac{2}{3}} {\left({\left({\left(5 \, \sqrt{3} - 5 i\right)} \Gamma\left(-\frac{5}{3}, 2 i \, d x^{3}\right) + {\left(5 \, \sqrt{3} + 5 i\right)} \Gamma\left(-\frac{5}{3}, -2 i \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + 5 \, {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, 2 i \, d x^{3}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{5}{3}, -2 i \, d x^{3}\right)\right)} \sin\left(2 \, c\right)\right)} d x^{3} + 6\right)} b^{2}}{60 \, x^{5}} - \frac{a^{2}}{5 \, x^{5}}"," ",0,"-1/6*(d*x^3)^(2/3)*(((-I*sqrt(3) - 1)*gamma(-5/3, I*d*x^3) + (I*sqrt(3) - 1)*gamma(-5/3, -I*d*x^3))*cos(c) - ((sqrt(3) - I)*gamma(-5/3, I*d*x^3) + (sqrt(3) + I)*gamma(-5/3, -I*d*x^3))*sin(c))*a*b*d/x^2 - 1/60*(2^(2/3)*(d*x^3)^(2/3)*(((5*sqrt(3) - 5*I)*gamma(-5/3, 2*I*d*x^3) + (5*sqrt(3) + 5*I)*gamma(-5/3, -2*I*d*x^3))*cos(2*c) + 5*((-I*sqrt(3) - 1)*gamma(-5/3, 2*I*d*x^3) + (I*sqrt(3) - 1)*gamma(-5/3, -2*I*d*x^3))*sin(2*c))*d*x^3 + 6)*b^2/x^5 - 1/5*a^2/x^5","A",0
81,0,0,0,0.000000," ","integrate(x^5/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{x^{5}}{b \sin\left(d x^{3} + c\right) + a}\,{d x}"," ",0,"integrate(x^5/(b*sin(d*x^3 + c) + a), x)","F",0
82,1,8078,0,30.564538," ","integrate(x^2/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\frac{\arctan\left(-\frac{2 \, {\left(4 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - 4 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} - 4 \, {\left(3 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3} + {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} - {\left(a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 4 \, {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} - {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left({\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right) - 4 \, {\left({\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(c\right)^{5} + {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} - {\left(a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} - 3 \, {\left({\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} - {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \cos\left(c\right) - 4 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) + b^{5} \sin\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) + 4 \, a b^{4} \cos\left(c\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} + 2 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 2 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \sin\left(c\right) + 3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3} + 2 \, {\left(a b^{4} \cos\left(c\right)^{2} - a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} - 4 \, {\left({\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + 2 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) + 2 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + 2 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} - {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} + {\left({\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \sin\left(c\right) + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5} + 4 \, {\left(a b^{4} \cos\left(c\right)^{2} - a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} - 6 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + 4 \, {\left({\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(c\right)^{4} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}\right)}}{b^{6} \cos\left(d x^{3} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{3} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{6} + 3 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + 3 \, {\left(b^{6} \cos\left(d x^{3} + 2 \, c\right)^{2} - 2 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} - 6 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 3 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + 3 \, {\left(b^{6} \cos\left(d x^{3} + 2 \, c\right)^{4} - 4 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 6 \, {\left({\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + 6 \, {\left(a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right) - 2 \, {\left(3 \, b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} - 3 \, b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(c\right)^{6} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + 3 \, {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 2 \, {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 2 \, {\left(3 \, b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) - 12 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 6 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) - 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4} - 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 3 \, {\left({\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + 3 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 16 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}, \frac{b^{6} \cos\left(d x^{3} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{3} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{6} + {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + {\left(3 \, b^{6} \cos\left(d x^{3} + 2 \, c\right)^{2} - 6 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} - 2 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + {\left({\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + {\left(3 \, b^{6} \cos\left(d x^{3} + 2 \, c\right)^{4} - 12 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(4 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 12 \, {\left(3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 2 \, {\left({\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + 2 \, {\left(3 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(8 \, a^{5} b - 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right) - 4 \, {\left(b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} - b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{6} + {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 2 \, {\left(3 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, a^{2} b^{3} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 2 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, a^{2} b^{3} \cos\left(c\right)^{3} - 4 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 2 \, {\left(a^{3} b^{2} \cos\left(c\right)^{4} + 6 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, a^{3} b^{2} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{2} \cos\left(c\right)^{4} - b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) + 6 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + a^{3} b^{2} \sin\left(c\right)^{4} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 3 \, {\left(3 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right) + a^{2} b^{3} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - {\left({\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(4 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 6 \, {\left(a^{2} b^{3} \cos\left(c\right)^{3} + 3 \, a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{2} \cos\left(c\right)^{3} \sin\left(c\right) + a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}{b^{6} \cos\left(d x^{3} + 2 \, c\right)^{6} + 6 \, a b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} + b^{6} \sin\left(d x^{3} + 2 \, c\right)^{6} - 6 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{6} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(32 \, a^{6} - 48 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{6} + 3 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + 3 \, {\left(b^{6} \cos\left(d x^{3} + 2 \, c\right)^{2} - 2 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) + 5 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} - 6 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 3 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + 3 \, {\left(b^{6} \cos\left(d x^{3} + 2 \, c\right)^{4} - 4 \, a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) + 5 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{4} + 6 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \sin\left(c\right)^{4} + 6 \, {\left({\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(c\right)^{2} + {\left(2 \, a^{2} b^{4} - b^{6}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left(3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 6 \, {\left({\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + 6 \, {\left(a b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{5} - 4 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + 2 \, {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{5} b - 20 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 4 \, {\left({\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right) - 2 \, {\left(3 \, b^{5} \cos\left(c\right) \sin\left(d x^{3} + 2 \, c\right)^{5} - 3 \, b^{5} \cos\left(d x^{3} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(16 \, a^{5} - 16 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(c\right)^{6} + 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + 5 \, a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{4} + 3 \, {\left(5 \, a b^{4} \cos\left(c\right)^{2} - b^{5} \cos\left(d x^{3} + 2 \, c\right) \sin\left(c\right) + a b^{4} \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{4} - 2 \, {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)^{3} + 2 \, {\left(3 \, b^{5} \cos\left(d x^{3} + 2 \, c\right)^{2} \cos\left(c\right) - 12 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 5 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \sin\left(d x^{3} + 2 \, c\right)^{3} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 6 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{3} \sin\left(c\right) - 5 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(c\right)^{4} - 3 \, {\left(a b^{4} \cos\left(c\right)^{2} + a b^{4} \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} + {\left(3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(4 \, a^{2} b^{3} - b^{5}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)^{2} - 3 \, {\left({\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{3} + 2 \, c\right) + 3 \, {\left(b^{5} \cos\left(d x^{3} + 2 \, c\right)^{4} \cos\left(c\right) - 8 \, a b^{4} \cos\left(d x^{3} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(16 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 2 \, {\left({\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right)^{3} + 3 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{3} + 2 \, c\right)^{2} - 16 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{3} + 2 \, c\right)\right)} \sin\left(d x^{3} + 2 \, c\right)\right)} \sqrt{a^{2} - b^{2}}}\right)}{3 \, \sqrt{a^{2} - b^{2}} d}"," ",0,"1/3*arctan2(-2*(4*(a^2*b^4 - b^6)*cos(d*x^3 + 2*c)^4*cos(c)*sin(c) - 4*(a^2*b^4 - b^6)*cos(c)*sin(d*x^3 + 2*c)^4*sin(c) - 4*((a^3*b^3 - a*b^5)*cos(c)^3 + 3*(a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^3 - 4*(3*(a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + (a^3*b^3 - a*b^5)*sin(c)^3 + ((a^2*b^4 - b^6)*cos(c)^2 - (a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^3 + 4*((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c)^2 - 4*((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)*sin(c)^3 + 3*((a^3*b^3 - a*b^5)*cos(c)^3 - (a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 4*((2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^5 + 2*(2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^3*sin(c)^2 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)*sin(c)^4)*cos(d*x^3 + 2*c) - 4*((2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^4*sin(c) + 2*(2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(c)^2*sin(c)^3 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*sin(c)^5 + ((a^2*b^4 - b^6)*cos(c)^2 - (a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^3 - 3*((a^3*b^3 - a*b^5)*cos(c)^2*sin(c) - (a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^2 + ((4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(c)^4 - (4*a^4*b^2 - 5*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c) + (b^5*cos(d*x^3 + 2*c)^5*cos(c) - 4*a*b^4*cos(d*x^3 + 2*c)^4*cos(c)*sin(c) + b^5*sin(d*x^3 + 2*c)^5*sin(c) + (b^5*cos(d*x^3 + 2*c)*cos(c) + 4*a*b^4*cos(c)*sin(c))*sin(d*x^3 + 2*c)^4 + 2*((2*a^2*b^3 - b^5)*cos(c)^3 + 3*(2*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^3 + 2*(b^5*cos(d*x^3 + 2*c)^2*sin(c) + 3*(2*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (2*a^2*b^3 - b^5)*sin(c)^3 + 2*(a*b^4*cos(c)^2 - a*b^4*sin(c)^2)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^3 - 4*((4*a^3*b^2 - 3*a*b^4)*cos(c)^3*sin(c) + (4*a^3*b^2 - 3*a*b^4)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c)^2 + 2*(b^5*cos(d*x^3 + 2*c)^3*cos(c) + 2*(4*a^3*b^2 - 3*a*b^4)*cos(c)^3*sin(c) + 2*(4*a^3*b^2 - 3*a*b^4)*cos(c)*sin(c)^3 + 3*((2*a^2*b^3 - b^5)*cos(c)^3 - (2*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 + ((8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^5 + 2*(8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)*sin(c)^4)*cos(d*x^3 + 2*c) + (b^5*cos(d*x^3 + 2*c)^4*sin(c) + (8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(8*a^4*b - 8*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (8*a^4*b - 8*a^2*b^3 + b^5)*sin(c)^5 + 4*(a*b^4*cos(c)^2 - a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^3 - 6*((2*a^2*b^3 - b^5)*cos(c)^2*sin(c) - (2*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^2 + 4*((4*a^3*b^2 - 3*a*b^4)*cos(c)^4 - (4*a^3*b^2 - 3*a*b^4)*sin(c)^4)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c))*sqrt(a^2 - b^2))/(b^6*cos(d*x^3 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^3 + 2*c)^5 + b^6*sin(d*x^3 + 2*c)^6 - 6*a*b^5*cos(d*x^3 + 2*c)^5*sin(c) + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^6 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^4*sin(c)^2 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^2*sin(c)^4 + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*sin(c)^6 + 3*((2*a^2*b^4 - b^6)*cos(c)^2 + 5*(2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^4 + 3*(b^6*cos(d*x^3 + 2*c)^2 - 2*a*b^5*cos(d*x^3 + 2*c)*sin(c) + 5*(2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + 5*(4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^3 + 2*c)^2*cos(c) + 5*(4*a^3*b^3 - 3*a*b^5)*cos(c)^3 - 6*(2*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + 3*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^3 + 2*c)^2 + 3*(b^6*cos(d*x^3 + 2*c)^4 - 4*a*b^5*cos(d*x^3 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4 + 6*((2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + (4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 6*((16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^4*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^2*sin(c)^3 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + 6*(a*b^5*cos(d*x^3 + 2*c)^4*cos(c) + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^5 - 4*(2*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^3*sin(c)^2 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)*sin(c)^4 + 2*((4*a^3*b^3 - 3*a*b^5)*cos(c)^3 + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 4*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c) - 2*(3*b^5*cos(c)*sin(d*x^3 + 2*c)^5 - 3*b^5*cos(d*x^3 + 2*c)^5*sin(c) + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^6 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^4*sin(c)^2 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^2*sin(c)^4 + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*sin(c)^6 + 3*(a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^4 + 3*(5*a*b^4*cos(c)^2 - b^5*cos(d*x^3 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 2*(3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + 5*(4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 2*(3*b^5*cos(d*x^3 + 2*c)^2*cos(c) - 12*a*b^4*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 5*(4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + 6*((2*a^3*b^2 - a*b^4)*cos(c)^4 + 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 + 5*(2*a^3*b^2 - a*b^4)*sin(c)^4)*cos(d*x^3 + 2*c)^2 - 6*(b^5*cos(d*x^3 + 2*c)^3*sin(c) - 5*(2*a^3*b^2 - a*b^4)*cos(c)^4 - 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 - (2*a^3*b^2 - a*b^4)*sin(c)^4 - 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^2 + (3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 3*((16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (16*a^4*b - 12*a^2*b^3 + b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + 3*(b^5*cos(d*x^3 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^5 + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)*sin(c)^4 + 2*((4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 16*((2*a^3*b^2 - a*b^4)*cos(c)^3*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c))*sqrt(a^2 - b^2)), (b^6*cos(d*x^3 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^3 + 2*c)^5 + b^6*sin(d*x^3 + 2*c)^6 - 6*a*b^5*cos(d*x^3 + 2*c)^5*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^6 + 3*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4*sin(c)^2 + 3*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^4 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^6 + ((4*a^2*b^4 - b^6)*cos(c)^2 + 5*(4*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^4 + (3*b^6*cos(d*x^3 + 2*c)^2 - 6*a*b^5*cos(d*x^3 + 2*c)*sin(c) + 5*(4*a^2*b^4 - b^6)*cos(c)^2 + (4*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 4*(3*(2*a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + 5*(2*a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^3 + 2*c)^2*cos(c) + 5*(2*a^3*b^3 - a*b^5)*cos(c)^3 - 2*(4*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 3*(2*a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + ((8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*sin(c)^4)*cos(d*x^3 + 2*c)^2 + (3*b^6*cos(d*x^3 + 2*c)^4 - 12*a*b^5*cos(d*x^3 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 4*a^2*b^4 - b^6)*sin(c)^4 + 6*((4*a^2*b^4 - b^6)*cos(c)^2 + (4*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 12*(3*(2*a^3*b^3 - a*b^5)*cos(c)^2*sin(c) + (2*a^3*b^3 - a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 2*((8*a^5*b - 5*a*b^5)*cos(c)^4*sin(c) + 2*(8*a^5*b - 5*a*b^5)*cos(c)^2*sin(c)^3 + (8*a^5*b - 5*a*b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + 2*(3*a*b^5*cos(d*x^3 + 2*c)^4*cos(c) + (8*a^5*b - 5*a*b^5)*cos(c)^5 - 4*(4*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + 2*(8*a^5*b - 5*a*b^5)*cos(c)^3*sin(c)^2 + (8*a^5*b - 5*a*b^5)*cos(c)*sin(c)^4 + 6*((2*a^3*b^3 - a*b^5)*cos(c)^3 + 3*(2*a^3*b^3 - a*b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 4*((8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 4*a^2*b^4 - b^6)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c) - 4*(b^5*cos(c)*sin(d*x^3 + 2*c)^5 - b^5*cos(d*x^3 + 2*c)^5*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)^6 + 3*(2*a^3*b^2 - a*b^4)*cos(c)^4*sin(c)^2 + 3*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^4 + (2*a^3*b^2 - a*b^4)*sin(c)^6 + (a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^4 + (5*a*b^4*cos(c)^2 - b^5*cos(d*x^3 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 2*(3*a^2*b^3*cos(c)^2*sin(c) + 5*a^2*b^3*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 2*(b^5*cos(d*x^3 + 2*c)^2*cos(c) + 5*a^2*b^3*cos(c)^3 - 4*a*b^4*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 3*a^2*b^3*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + 2*(a^3*b^2*cos(c)^4 + 6*a^3*b^2*cos(c)^2*sin(c)^2 + 5*a^3*b^2*sin(c)^4)*cos(d*x^3 + 2*c)^2 + 2*(5*a^3*b^2*cos(c)^4 - b^5*cos(d*x^3 + 2*c)^3*sin(c) + 6*a^3*b^2*cos(c)^2*sin(c)^2 + a^3*b^2*sin(c)^4 + 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 3*(3*a^2*b^3*cos(c)^2*sin(c) + a^2*b^3*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - ((4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^4*sin(c) + 2*(4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^2*sin(c)^3 + (4*a^4*b + 2*a^2*b^3 - b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + (b^5*cos(d*x^3 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + (4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^5 + 2*(4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)^3*sin(c)^2 + (4*a^4*b + 2*a^2*b^3 - b^5)*cos(c)*sin(c)^4 + 6*(a^2*b^3*cos(c)^3 + 3*a^2*b^3*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 16*(a^3*b^2*cos(c)^3*sin(c) + a^3*b^2*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c))*sqrt(a^2 - b^2))/(b^6*cos(d*x^3 + 2*c)^6 + 6*a*b^5*cos(c)*sin(d*x^3 + 2*c)^5 + b^6*sin(d*x^3 + 2*c)^6 - 6*a*b^5*cos(d*x^3 + 2*c)^5*sin(c) + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^6 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^4*sin(c)^2 + 3*(32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*cos(c)^2*sin(c)^4 + (32*a^6 - 48*a^4*b^2 + 18*a^2*b^4 - b^6)*sin(c)^6 + 3*((2*a^2*b^4 - b^6)*cos(c)^2 + 5*(2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^4 + 3*(b^6*cos(d*x^3 + 2*c)^2 - 2*a*b^5*cos(d*x^3 + 2*c)*sin(c) + 5*(2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + 5*(4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 4*(3*a*b^5*cos(d*x^3 + 2*c)^2*cos(c) + 5*(4*a^3*b^3 - 3*a*b^5)*cos(c)^3 - 6*(2*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + 3*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4)*cos(d*x^3 + 2*c)^2 + 3*(b^6*cos(d*x^3 + 2*c)^4 - 4*a*b^5*cos(d*x^3 + 2*c)^3*sin(c) + 5*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^4 + 6*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^2*sin(c)^2 + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*sin(c)^4 + 6*((2*a^2*b^4 - b^6)*cos(c)^2 + (2*a^2*b^4 - b^6)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 4*(3*(4*a^3*b^3 - 3*a*b^5)*cos(c)^2*sin(c) + (4*a^3*b^3 - 3*a*b^5)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 6*((16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^4*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^2*sin(c)^3 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + 6*(a*b^5*cos(d*x^3 + 2*c)^4*cos(c) + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^5 - 4*(2*a^2*b^4 - b^6)*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + 2*(16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)^3*sin(c)^2 + (16*a^5*b - 20*a^3*b^3 + 5*a*b^5)*cos(c)*sin(c)^4 + 2*((4*a^3*b^3 - 3*a*b^5)*cos(c)^3 + 3*(4*a^3*b^3 - 3*a*b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 4*((8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)^3*sin(c) + (8*a^4*b^2 - 8*a^2*b^4 + b^6)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c) - 2*(3*b^5*cos(c)*sin(d*x^3 + 2*c)^5 - 3*b^5*cos(d*x^3 + 2*c)^5*sin(c) + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^6 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^4*sin(c)^2 + 3*(16*a^5 - 16*a^3*b^2 + 3*a*b^4)*cos(c)^2*sin(c)^4 + (16*a^5 - 16*a^3*b^2 + 3*a*b^4)*sin(c)^6 + 3*(a*b^4*cos(c)^2 + 5*a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^4 + 3*(5*a*b^4*cos(c)^2 - b^5*cos(d*x^3 + 2*c)*sin(c) + a*b^4*sin(c)^2)*sin(d*x^3 + 2*c)^4 - 2*(3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + 5*(4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^3 + 2*c)^3 + 2*(3*b^5*cos(d*x^3 + 2*c)^2*cos(c) - 12*a*b^4*cos(d*x^3 + 2*c)*cos(c)*sin(c) + 5*(4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*sin(d*x^3 + 2*c)^3 + 6*((2*a^3*b^2 - a*b^4)*cos(c)^4 + 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 + 5*(2*a^3*b^2 - a*b^4)*sin(c)^4)*cos(d*x^3 + 2*c)^2 - 6*(b^5*cos(d*x^3 + 2*c)^3*sin(c) - 5*(2*a^3*b^2 - a*b^4)*cos(c)^4 - 6*(2*a^3*b^2 - a*b^4)*cos(c)^2*sin(c)^2 - (2*a^3*b^2 - a*b^4)*sin(c)^4 - 3*(a*b^4*cos(c)^2 + a*b^4*sin(c)^2)*cos(d*x^3 + 2*c)^2 + (3*(4*a^2*b^3 - b^5)*cos(c)^2*sin(c) + (4*a^2*b^3 - b^5)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c)^2 - 3*((16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^4*sin(c) + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^2*sin(c)^3 + (16*a^4*b - 12*a^2*b^3 + b^5)*sin(c)^5)*cos(d*x^3 + 2*c) + 3*(b^5*cos(d*x^3 + 2*c)^4*cos(c) - 8*a*b^4*cos(d*x^3 + 2*c)^3*cos(c)*sin(c) + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^5 + 2*(16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)^3*sin(c)^2 + (16*a^4*b - 12*a^2*b^3 + b^5)*cos(c)*sin(c)^4 + 2*((4*a^2*b^3 - b^5)*cos(c)^3 + 3*(4*a^2*b^3 - b^5)*cos(c)*sin(c)^2)*cos(d*x^3 + 2*c)^2 - 16*((2*a^3*b^2 - a*b^4)*cos(c)^3*sin(c) + (2*a^3*b^2 - a*b^4)*cos(c)*sin(c)^3)*cos(d*x^3 + 2*c))*sin(d*x^3 + 2*c))*sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*d)","B",0
83,0,0,0,0.000000," ","integrate(1/x/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{3} + c\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^3 + c) + a)*x), x)","F",0
84,0,0,0,0.000000," ","integrate(1/x^4/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{3} + c\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^3 + c) + a)*x^4), x)","F",0
85,0,0,0,0.000000," ","integrate(x/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{x}{b \sin\left(d x^{3} + c\right) + a}\,{d x}"," ",0,"integrate(x/(b*sin(d*x^3 + c) + a), x)","F",0
86,0,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{3} + c\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^3 + c) + a)*x^2), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(d x^{3} + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*sin(d*x^3 + c) + a), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x^3/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(d x^{3} + c\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*sin(d*x^3 + c) + a)*x^3), x)","F",0
89,-2,0,0,0.000000," ","integrate(x^5/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
90,-1,0,0,0.000000," ","integrate(x^2/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(1/x/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(1/x^4/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,0,0,0,0.000000," ","integrate(x/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) + 2 \, {\left(a b \cos\left(2 \, d x^{3}\right) \cos\left(2 \, c\right) - 2 \, a^{2} \cos\left(c\right) \sin\left(d x^{3}\right) - a b \sin\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \cos\left(d x^{3}\right) \sin\left(c\right) - a b\right)} \cos\left(d x^{3} + c\right) + 2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)} \int \frac{2 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) - {\left(a b - {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + a b \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) - 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - a^{2} \sin\left(c\right)\right)} \cos\left(d x^{3}\right) - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - a b \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + a^{2} \cos\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \cos\left(d x^{3} + c\right) + {\left(3 \, a b d x^{3} - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - a b \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + a^{2} \cos\left(c\right)\right)} \cos\left(d x^{3}\right) + {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + a b \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - a^{2} \sin\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \sin\left(d x^{3} + c\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)}\,{d x} + 2 \, {\left(2 \, a^{2} \cos\left(d x^{3}\right) \cos\left(c\right) + a b \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + a b \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \sin\left(d x^{3}\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + c\right)}{3 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)}}"," ",0,"1/3*(4*a*b*cos(d*x^3)*cos(c) + 2*b^2*cos(2*c)*sin(2*d*x^3) + 2*b^2*cos(2*d*x^3)*sin(2*c) - 4*a*b*sin(d*x^3)*sin(c) + 2*(a*b*cos(2*d*x^3)*cos(2*c) - 2*a^2*cos(c)*sin(d*x^3) - a*b*sin(2*d*x^3)*sin(2*c) - 2*a^2*cos(d*x^3)*sin(c) - a*b)*cos(d*x^3 + c) - 3*(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x*cos(d*x^3) - (a^2*b^2 - b^4)*d*x*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x*sin(d*x^3) + (a^2*b^2 - b^4)*d*x*sin(2*c))*sin(2*d*x^3))*integrate(-2/3*(2*a*b*cos(d*x^3)*cos(c) + b^2*cos(2*c)*sin(2*d*x^3) + b^2*cos(2*d*x^3)*sin(2*c) - 2*a*b*sin(d*x^3)*sin(c) - (a*b - (3*a*b*d*x^3*sin(2*c) + a*b*cos(2*c))*cos(2*d*x^3) - 2*(3*a^2*d*x^3*cos(c) - a^2*sin(c))*cos(d*x^3) - (3*a*b*d*x^3*cos(2*c) - a*b*sin(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + a^2*cos(c))*sin(d*x^3))*cos(d*x^3 + c) + (3*a*b*d*x^3 - (3*a*b*d*x^3*cos(2*c) - a*b*sin(2*c))*cos(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + a^2*cos(c))*cos(d*x^3) + (3*a*b*d*x^3*sin(2*c) + a*b*cos(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*cos(c) - a^2*sin(c))*sin(d*x^3))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^2 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^2*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^2*sin(2*c))*sin(2*d*x^3)), x) + 2*(2*a^2*cos(d*x^3)*cos(c) + a*b*cos(2*c)*sin(2*d*x^3) + a*b*cos(2*d*x^3)*sin(2*c) - 2*a^2*sin(d*x^3)*sin(c))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x*cos(d*x^3) - (a^2*b^2 - b^4)*d*x*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x*sin(d*x^3) + (a^2*b^2 - b^4)*d*x*sin(2*c))*sin(2*d*x^3))","F",0
94,0,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) + 2 \, {\left(a b \cos\left(2 \, d x^{3}\right) \cos\left(2 \, c\right) - 2 \, a^{2} \cos\left(c\right) \sin\left(d x^{3}\right) - a b \sin\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \cos\left(d x^{3}\right) \sin\left(c\right) - a b\right)} \cos\left(d x^{3} + c\right) + 2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{4} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{4} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{4} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{4} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{4} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{4} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)} \int \frac{8 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 4 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 4 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 8 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) - {\left(4 \, a b - {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 4 \, a b \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) - 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 4 \, a^{2} \sin\left(c\right)\right)} \cos\left(d x^{3}\right) - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 4 \, a b \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 4 \, a^{2} \cos\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \cos\left(d x^{3} + c\right) + {\left(3 \, a b d x^{3} - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 4 \, a b \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 4 \, a^{2} \cos\left(c\right)\right)} \cos\left(d x^{3}\right) + {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 4 \, a b \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 4 \, a^{2} \sin\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \sin\left(d x^{3} + c\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)}\,{d x} + 2 \, {\left(2 \, a^{2} \cos\left(d x^{3}\right) \cos\left(c\right) + a b \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + a b \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \sin\left(d x^{3}\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + c\right)}{3 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{4} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{4} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{4} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{4} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{4} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{4} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{4} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{4} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)}}"," ",0,"1/3*(4*a*b*cos(d*x^3)*cos(c) + 2*b^2*cos(2*c)*sin(2*d*x^3) + 2*b^2*cos(2*d*x^3)*sin(2*c) - 4*a*b*sin(d*x^3)*sin(c) + 2*(a*b*cos(2*d*x^3)*cos(2*c) - 2*a^2*cos(c)*sin(d*x^3) - a*b*sin(2*d*x^3)*sin(2*c) - 2*a^2*cos(d*x^3)*sin(c) - a*b)*cos(d*x^3 + c) - 3*(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^4*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^4*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^4*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^4*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^4*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^4*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^4 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^4*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^4*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^4*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^4*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^4*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^4*sin(2*c))*sin(2*d*x^3))*integrate(-2/3*(8*a*b*cos(d*x^3)*cos(c) + 4*b^2*cos(2*c)*sin(2*d*x^3) + 4*b^2*cos(2*d*x^3)*sin(2*c) - 8*a*b*sin(d*x^3)*sin(c) - (4*a*b - (3*a*b*d*x^3*sin(2*c) + 4*a*b*cos(2*c))*cos(2*d*x^3) - 2*(3*a^2*d*x^3*cos(c) - 4*a^2*sin(c))*cos(d*x^3) - (3*a*b*d*x^3*cos(2*c) - 4*a*b*sin(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 4*a^2*cos(c))*sin(d*x^3))*cos(d*x^3 + c) + (3*a*b*d*x^3 - (3*a*b*d*x^3*cos(2*c) - 4*a*b*sin(2*c))*cos(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 4*a^2*cos(c))*cos(d*x^3) + (3*a*b*d*x^3*sin(2*c) + 4*a*b*cos(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*cos(c) - 4*a^2*sin(c))*sin(d*x^3))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^5 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^5*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^5*sin(2*c))*sin(2*d*x^3)), x) + 2*(2*a^2*cos(d*x^3)*cos(c) + a*b*cos(2*c)*sin(2*d*x^3) + a*b*cos(2*d*x^3)*sin(2*c) - 2*a^2*sin(d*x^3)*sin(c))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^4*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^4*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^4*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^4*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^4*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^4*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^4 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^4*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^4*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^4*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^4*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^4*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^4*sin(2*c))*sin(2*d*x^3))","F",0
95,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) + 2 \, {\left(a b \cos\left(2 \, d x^{3}\right) \cos\left(2 \, c\right) - 2 \, a^{2} \cos\left(c\right) \sin\left(d x^{3}\right) - a b \sin\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \cos\left(d x^{3}\right) \sin\left(c\right) - a b\right)} \cos\left(d x^{3} + c\right) + 2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)} \int \frac{4 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) - {\left(2 \, a b - {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 2 \, a b \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) - 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 2 \, a^{2} \sin\left(c\right)\right)} \cos\left(d x^{3}\right) - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 2 \, a b \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 2 \, a^{2} \cos\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \cos\left(d x^{3} + c\right) + {\left(3 \, a b d x^{3} - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 2 \, a b \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 2 \, a^{2} \cos\left(c\right)\right)} \cos\left(d x^{3}\right) + {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 2 \, a b \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 2 \, a^{2} \sin\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \sin\left(d x^{3} + c\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{3} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{3} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{3} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{3} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)}\,{d x} + 2 \, {\left(2 \, a^{2} \cos\left(d x^{3}\right) \cos\left(c\right) + a b \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + a b \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \sin\left(d x^{3}\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + c\right)}{3 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)}}"," ",0,"1/3*(4*a*b*cos(d*x^3)*cos(c) + 2*b^2*cos(2*c)*sin(2*d*x^3) + 2*b^2*cos(2*d*x^3)*sin(2*c) - 4*a*b*sin(d*x^3)*sin(c) + 2*(a*b*cos(2*d*x^3)*cos(2*c) - 2*a^2*cos(c)*sin(d*x^3) - a*b*sin(2*d*x^3)*sin(2*c) - 2*a^2*cos(d*x^3)*sin(c) - a*b)*cos(d*x^3 + c) - 3*(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^2 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^2*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^2*sin(2*c))*sin(2*d*x^3))*integrate(-2/3*(4*a*b*cos(d*x^3)*cos(c) + 2*b^2*cos(2*c)*sin(2*d*x^3) + 2*b^2*cos(2*d*x^3)*sin(2*c) - 4*a*b*sin(d*x^3)*sin(c) - (2*a*b - (3*a*b*d*x^3*sin(2*c) + 2*a*b*cos(2*c))*cos(2*d*x^3) - 2*(3*a^2*d*x^3*cos(c) - 2*a^2*sin(c))*cos(d*x^3) - (3*a*b*d*x^3*cos(2*c) - 2*a*b*sin(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 2*a^2*cos(c))*sin(d*x^3))*cos(d*x^3 + c) + (3*a*b*d*x^3 - (3*a*b*d*x^3*cos(2*c) - 2*a*b*sin(2*c))*cos(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 2*a^2*cos(c))*cos(d*x^3) + (3*a*b*d*x^3*sin(2*c) + 2*a*b*cos(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*cos(c) - 2*a^2*sin(c))*sin(d*x^3))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^3*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^3*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^3*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^3*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^3*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^3*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^3 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^3*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^3*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^3*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^3*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^3*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^3*sin(2*c))*sin(2*d*x^3)), x) + 2*(2*a^2*cos(d*x^3)*cos(c) + a*b*cos(2*c)*sin(2*d*x^3) + a*b*cos(2*d*x^3)*sin(2*c) - 2*a^2*sin(d*x^3)*sin(c))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^2 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^2*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^2*sin(2*c))*sin(2*d*x^3))","F",0
96,0,0,0,0.000000," ","integrate(1/x^3/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) + 2 \, {\left(a b \cos\left(2 \, d x^{3}\right) \cos\left(2 \, c\right) - 2 \, a^{2} \cos\left(c\right) \sin\left(d x^{3}\right) - a b \sin\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \cos\left(d x^{3}\right) \sin\left(c\right) - a b\right)} \cos\left(d x^{3} + c\right) + 2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)} \int \frac{10 \, a b \cos\left(d x^{3}\right) \cos\left(c\right) + 5 \, b^{2} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 5 \, b^{2} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 10 \, a b \sin\left(d x^{3}\right) \sin\left(c\right) - {\left(5 \, a b - {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 5 \, a b \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) - 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 5 \, a^{2} \sin\left(c\right)\right)} \cos\left(d x^{3}\right) - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 5 \, a b \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 5 \, a^{2} \cos\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \cos\left(d x^{3} + c\right) + {\left(3 \, a b d x^{3} - {\left(3 \, a b d x^{3} \cos\left(2 \, c\right) - 5 \, a b \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \sin\left(c\right) + 5 \, a^{2} \cos\left(c\right)\right)} \cos\left(d x^{3}\right) + {\left(3 \, a b d x^{3} \sin\left(2 \, c\right) + 5 \, a b \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d x^{3} \cos\left(c\right) - 5 \, a^{2} \sin\left(c\right)\right)} \sin\left(d x^{3}\right)\right)} \sin\left(d x^{3} + c\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{6} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{6} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{6} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{6} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{6} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{6} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{6} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{6} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{6} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{6} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{6} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{6} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{6} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)}\,{d x} + 2 \, {\left(2 \, a^{2} \cos\left(d x^{3}\right) \cos\left(c\right) + a b \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + a b \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} \sin\left(d x^{3}\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + c\right)}{3 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{5} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{5} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{5} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{5} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{5} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)}}"," ",0,"1/3*(4*a*b*cos(d*x^3)*cos(c) + 2*b^2*cos(2*c)*sin(2*d*x^3) + 2*b^2*cos(2*d*x^3)*sin(2*c) - 4*a*b*sin(d*x^3)*sin(c) + 2*(a*b*cos(2*d*x^3)*cos(2*c) - 2*a^2*cos(c)*sin(d*x^3) - a*b*sin(2*d*x^3)*sin(2*c) - 2*a^2*cos(d*x^3)*sin(c) - a*b)*cos(d*x^3 + c) - 3*(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^5 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^5*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^5*sin(2*c))*sin(2*d*x^3))*integrate(-2/3*(10*a*b*cos(d*x^3)*cos(c) + 5*b^2*cos(2*c)*sin(2*d*x^3) + 5*b^2*cos(2*d*x^3)*sin(2*c) - 10*a*b*sin(d*x^3)*sin(c) - (5*a*b - (3*a*b*d*x^3*sin(2*c) + 5*a*b*cos(2*c))*cos(2*d*x^3) - 2*(3*a^2*d*x^3*cos(c) - 5*a^2*sin(c))*cos(d*x^3) - (3*a*b*d*x^3*cos(2*c) - 5*a*b*sin(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 5*a^2*cos(c))*sin(d*x^3))*cos(d*x^3 + c) + (3*a*b*d*x^3 - (3*a*b*d*x^3*cos(2*c) - 5*a*b*sin(2*c))*cos(2*d*x^3) + 2*(3*a^2*d*x^3*sin(c) + 5*a^2*cos(c))*cos(d*x^3) + (3*a*b*d*x^3*sin(2*c) + 5*a*b*cos(2*c))*sin(2*d*x^3) + 2*(3*a^2*d*x^3*cos(c) - 5*a^2*sin(c))*sin(d*x^3))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^6*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^6*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^6*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^6*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^6*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^6*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^6 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^6*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^6*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^6*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^6*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^6*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^6*sin(2*c))*sin(2*d*x^3)), x) + 2*(2*a^2*cos(d*x^3)*cos(c) + a*b*cos(2*c)*sin(2*d*x^3) + a*b*cos(2*d*x^3)*sin(2*c) - 2*a^2*sin(d*x^3)*sin(c))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^5*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^5*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^5*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^5 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^5*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^5*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^5*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^5*sin(2*c))*sin(2*d*x^3))","F",0
97,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \sin\left(d x^{3} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sin(d*x^3 + c) + a)^p, x)","F",0
98,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^3,x, algorithm=""maxima"")","\frac{\left(e x\right)^{m + 1} a^{3}}{e {\left(m + 1\right)}} + \frac{\frac{{\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m \cos\left(c\right) + {\left(4 \, a^{2} b + b^{3}\right)} e^{m} \cos\left(c\right)\right)} d x^{4} x^{m} \Gamma\left(\frac{1}{6} \, m + \frac{2}{3}\right) \,_1F_2\left(\begin{matrix} \frac{1}{6} \, m + \frac{2}{3} \\ \frac{3}{2},\frac{1}{6} \, m + \frac{5}{3} \end{matrix} ; -\frac{1}{4} \, d^{2} x^{6} \right)}{2 \, \Gamma\left(\frac{1}{6} \, m + \frac{5}{3}\right)} + 12 \, a b^{2} e^{m} x x^{m} + \frac{{\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m \sin\left(c\right) + {\left(4 \, a^{2} b + b^{3}\right)} e^{m} \sin\left(c\right)\right)} x x^{m} \Gamma\left(\frac{1}{6} \, m + \frac{1}{6}\right) \,_1F_2\left(\begin{matrix} \frac{1}{6} \, m + \frac{1}{6} \\ \frac{1}{2},\frac{1}{6} \, m + \frac{7}{6} \end{matrix} ; -\frac{1}{4} \, d^{2} x^{6} \right)}{2 \, \Gamma\left(\frac{1}{6} \, m + \frac{7}{6}\right)} - 12 \, {\left(a b^{2} e^{m} m + a b^{2} e^{m}\right)} \int x^{m} \cos\left(2 \, d x^{3} + 2 \, c\right)\,{d x} - 2 \, {\left(b^{3} e^{m} m + b^{3} e^{m}\right)} \int x^{m} \sin\left(3 \, d x^{3} + 3 \, c\right)\,{d x} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{m} m + {\left(4 \, a^{2} b + b^{3}\right)} e^{m}\right)} \int x^{m} \sin\left(d x^{3} + c\right)\,{d x}}{8 \, {\left(m + 1\right)}}"," ",0,"(e*x)^(m + 1)*a^3/(e*(m + 1)) + 1/8*(12*a*b^2*e^m*x*x^m - 12*(a*b^2*e^m*m + a*b^2*e^m)*integrate(x^m*cos(2*d*x^3 + 2*c), x) + 3*((4*a^2*b + b^3)*e^m*m*sin(c) + (4*a^2*b + b^3)*e^m*sin(c))*integrate(x^m*cos(d*x^3), x) - 2*(b^3*e^m*m + b^3*e^m)*integrate(x^m*sin(3*d*x^3 + 3*c), x) + 3*((4*a^2*b + b^3)*e^m*m + (4*a^2*b + b^3)*e^m)*integrate(x^m*sin(d*x^3 + c), x) + 3*((4*a^2*b + b^3)*e^m*m*cos(c) + (4*a^2*b + b^3)*e^m*cos(c))*integrate(x^m*sin(d*x^3), x))/(m + 1)","F",0
99,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{m + 1} a^{2}}{e {\left(m + 1\right)}} + \frac{b^{2} e^{m} x x^{m} - {\left(b^{2} e^{m} m + b^{2} e^{m}\right)} \int x^{m} \cos\left(2 \, d x^{3} + 2 \, c\right)\,{d x} + 4 \, {\left(a b e^{m} m + a b e^{m}\right)} \int x^{m} \sin\left(d x^{3} + c\right)\,{d x}}{2 \, {\left(m + 1\right)}}"," ",0,"(e*x)^(m + 1)*a^2/(e*(m + 1)) + 1/2*(b^2*e^m*x*x^m - (b^2*e^m*m + b^2*e^m)*integrate(x^m*cos(2*d*x^3 + 2*c), x) + 4*(a*b*e^m*m + a*b*e^m)*integrate(x^m*sin(d*x^3 + c), x))/(m + 1)","F",0
100,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","b e^{m} \int x^{m} \sin\left(d x^{3} + c\right)\,{d x} + \frac{\left(e x\right)^{m + 1} a}{e {\left(m + 1\right)}}"," ",0,"b*e^m*integrate(x^m*sin(d*x^3 + c), x) + (e*x)^(m + 1)*a/(e*(m + 1))","F",0
101,0,0,0,0.000000," ","integrate((e*x)^m/(a+b*sin(d*x^3+c)),x, algorithm=""maxima"")","\int \frac{\left(e x\right)^{m}}{b \sin\left(d x^{3} + c\right) + a}\,{d x}"," ",0,"integrate((e*x)^m/(b*sin(d*x^3 + c) + a), x)","F",0
102,0,0,0,0.000000," ","integrate((e*x)^m/(a+b*sin(d*x^3+c))^2,x, algorithm=""maxima"")","\frac{4 \, a b e^{m} x^{m} \cos\left(d x^{3}\right) \cos\left(c\right) + 2 \, b^{2} e^{m} x^{m} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + 2 \, b^{2} e^{m} x^{m} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 4 \, a b e^{m} x^{m} \sin\left(d x^{3}\right) \sin\left(c\right) + 2 \, {\left(a b e^{m} x^{m} \cos\left(2 \, d x^{3}\right) \cos\left(2 \, c\right) - 2 \, a^{2} e^{m} x^{m} \cos\left(c\right) \sin\left(d x^{3}\right) - a b e^{m} x^{m} \sin\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} e^{m} x^{m} \cos\left(d x^{3}\right) \sin\left(c\right) - a b e^{m} x^{m}\right)} \cos\left(d x^{3} + c\right) - 2 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)} \int \frac{{\left(b^{2} e^{m} m \sin\left(2 \, c\right) - 2 \, b^{2} e^{m} \sin\left(2 \, c\right)\right)} x^{m} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(a b e^{m} m \cos\left(c\right) - 2 \, a b e^{m} \cos\left(c\right)\right)} x^{m} \cos\left(d x^{3}\right) + {\left(b^{2} e^{m} m \cos\left(2 \, c\right) - 2 \, b^{2} e^{m} \cos\left(2 \, c\right)\right)} x^{m} \sin\left(2 \, d x^{3}\right) - 2 \, {\left(a b e^{m} m \sin\left(c\right) - 2 \, a b e^{m} \sin\left(c\right)\right)} x^{m} \sin\left(d x^{3}\right) - {\left({\left(3 \, a b d e^{m} x^{3} \sin\left(2 \, c\right) - a b e^{m} m \cos\left(2 \, c\right) + 2 \, a b e^{m} \cos\left(2 \, c\right)\right)} x^{m} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d e^{m} x^{3} \cos\left(c\right) + a^{2} e^{m} m \sin\left(c\right) - 2 \, a^{2} e^{m} \sin\left(c\right)\right)} x^{m} \cos\left(d x^{3}\right) + {\left(3 \, a b d e^{m} x^{3} \cos\left(2 \, c\right) + a b e^{m} m \sin\left(2 \, c\right) - 2 \, a b e^{m} \sin\left(2 \, c\right)\right)} x^{m} \sin\left(2 \, d x^{3}\right) - 2 \, {\left(3 \, a^{2} d e^{m} x^{3} \sin\left(c\right) - a^{2} e^{m} m \cos\left(c\right) + 2 \, a^{2} e^{m} \cos\left(c\right)\right)} x^{m} \sin\left(d x^{3}\right) + {\left(a b e^{m} m - 2 \, a b e^{m}\right)} x^{m}\right)} \cos\left(d x^{3} + c\right) - {\left(3 \, a b d e^{m} x^{m + 3} - {\left(3 \, a b d e^{m} x^{3} \cos\left(2 \, c\right) + a b e^{m} m \sin\left(2 \, c\right) - 2 \, a b e^{m} \sin\left(2 \, c\right)\right)} x^{m} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d e^{m} x^{3} \sin\left(c\right) - a^{2} e^{m} m \cos\left(c\right) + 2 \, a^{2} e^{m} \cos\left(c\right)\right)} x^{m} \cos\left(d x^{3}\right) + {\left(3 \, a b d e^{m} x^{3} \sin\left(2 \, c\right) - a b e^{m} m \cos\left(2 \, c\right) + 2 \, a b e^{m} \cos\left(2 \, c\right)\right)} x^{m} \sin\left(2 \, d x^{3}\right) + 2 \, {\left(3 \, a^{2} d e^{m} x^{3} \cos\left(c\right) + a^{2} e^{m} m \sin\left(c\right) - 2 \, a^{2} e^{m} \sin\left(c\right)\right)} x^{m} \sin\left(d x^{3}\right)\right)} \sin\left(d x^{3} + c\right)}{{\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{3} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{3} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{3} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{3} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{3} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{3} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)}\,{d x} + 2 \, {\left(2 \, a^{2} e^{m} x^{m} \cos\left(d x^{3}\right) \cos\left(c\right) + a b e^{m} x^{m} \cos\left(2 \, c\right) \sin\left(2 \, d x^{3}\right) + a b e^{m} x^{m} \cos\left(2 \, d x^{3}\right) \sin\left(2 \, c\right) - 2 \, a^{2} e^{m} x^{m} \sin\left(d x^{3}\right) \sin\left(c\right)\right)} \sin\left(d x^{3} + c\right)}{3 \, {\left({\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{3}\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \cos\left(d x^{3}\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(c\right) \sin\left(d x^{3}\right) + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(c\right)^{2}\right)} d x^{2} \sin\left(d x^{3}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{2} \cos\left(d x^{3}\right) \sin\left(c\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) - {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \cos\left(2 \, c\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right)\right)} \cos\left(2 \, d x^{3}\right) + 2 \, {\left(2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \cos\left(c\right) + {\left(a^{3} b - a b^{3}\right)} \sin\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \cos\left(d x^{3}\right) + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(c\right) \sin\left(2 \, c\right) - {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, c\right) \sin\left(c\right)\right)} d x^{2} \sin\left(d x^{3}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d x^{2} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{3}\right)\right)}}"," ",0,"1/3*(4*a*b*e^m*x^m*cos(d*x^3)*cos(c) + 2*b^2*e^m*x^m*cos(2*c)*sin(2*d*x^3) + 2*b^2*e^m*x^m*cos(2*d*x^3)*sin(2*c) - 4*a*b*e^m*x^m*sin(d*x^3)*sin(c) + 2*(a*b*e^m*x^m*cos(2*d*x^3)*cos(2*c) - 2*a^2*e^m*x^m*cos(c)*sin(d*x^3) - a*b*e^m*x^m*sin(2*d*x^3)*sin(2*c) - 2*a^2*e^m*x^m*cos(d*x^3)*sin(c) - a*b*e^m*x^m)*cos(d*x^3 + c) - 3*(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^2 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^2*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^2*sin(2*c))*sin(2*d*x^3))*integrate(2/3*((b^2*e^m*m*sin(2*c) - 2*b^2*e^m*sin(2*c))*x^m*cos(2*d*x^3) + 2*(a*b*e^m*m*cos(c) - 2*a*b*e^m*cos(c))*x^m*cos(d*x^3) + (b^2*e^m*m*cos(2*c) - 2*b^2*e^m*cos(2*c))*x^m*sin(2*d*x^3) - 2*(a*b*e^m*m*sin(c) - 2*a*b*e^m*sin(c))*x^m*sin(d*x^3) - ((3*a*b*d*e^m*x^3*sin(2*c) - a*b*e^m*m*cos(2*c) + 2*a*b*e^m*cos(2*c))*x^m*cos(2*d*x^3) + 2*(3*a^2*d*e^m*x^3*cos(c) + a^2*e^m*m*sin(c) - 2*a^2*e^m*sin(c))*x^m*cos(d*x^3) + (3*a*b*d*e^m*x^3*cos(2*c) + a*b*e^m*m*sin(2*c) - 2*a*b*e^m*sin(2*c))*x^m*sin(2*d*x^3) - 2*(3*a^2*d*e^m*x^3*sin(c) - a^2*e^m*m*cos(c) + 2*a^2*e^m*cos(c))*x^m*sin(d*x^3) + (a*b*e^m*m - 2*a*b*e^m)*x^m)*cos(d*x^3 + c) - (3*a*b*d*e^m*x^3*x^m - (3*a*b*d*e^m*x^3*cos(2*c) + a*b*e^m*m*sin(2*c) - 2*a*b*e^m*sin(2*c))*x^m*cos(2*d*x^3) + 2*(3*a^2*d*e^m*x^3*sin(c) - a^2*e^m*m*cos(c) + 2*a^2*e^m*cos(c))*x^m*cos(d*x^3) + (3*a*b*d*e^m*x^3*sin(2*c) - a*b*e^m*m*cos(2*c) + 2*a*b*e^m*cos(2*c))*x^m*sin(2*d*x^3) + 2*(3*a^2*d*e^m*x^3*cos(c) + a^2*e^m*m*sin(c) - 2*a^2*e^m*sin(c))*x^m*sin(d*x^3))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^3*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^3*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^3*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^3*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^3*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^3*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^3 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^3*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^3*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^3*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^3*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^3*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^3*sin(2*c))*sin(2*d*x^3)), x) + 2*(2*a^2*e^m*x^m*cos(d*x^3)*cos(c) + a*b*e^m*x^m*cos(2*c)*sin(2*d*x^3) + a*b*e^m*x^m*cos(2*d*x^3)*sin(2*c) - 2*a^2*e^m*x^m*sin(d*x^3)*sin(c))*sin(d*x^3 + c))/(((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*cos(2*d*x^3)^2 + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*cos(d*x^3)^2 + ((a^2*b^2 - b^4)*cos(2*c)^2 + (a^2*b^2 - b^4)*sin(2*c)^2)*d*x^2*sin(2*d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(c)*sin(d*x^3) + 4*((a^4 - a^2*b^2)*cos(c)^2 + (a^4 - a^2*b^2)*sin(c)^2)*d*x^2*sin(d*x^3)^2 + 4*(a^3*b - a*b^3)*d*x^2*cos(d*x^3)*sin(c) + (a^2*b^2 - b^4)*d*x^2 + 2*(2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*cos(d*x^3) - (a^2*b^2 - b^4)*d*x^2*cos(2*c) - 2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*sin(d*x^3))*cos(2*d*x^3) + 2*(2*((a^3*b - a*b^3)*cos(2*c)*cos(c) + (a^3*b - a*b^3)*sin(2*c)*sin(c))*d*x^2*cos(d*x^3) + 2*((a^3*b - a*b^3)*cos(c)*sin(2*c) - (a^3*b - a*b^3)*cos(2*c)*sin(c))*d*x^2*sin(d*x^3) + (a^2*b^2 - b^4)*d*x^2*sin(2*c))*sin(2*d*x^3))","F",0
103,1,86,0,0.442181," ","integrate(x^2*sin(a+b/x),x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left({\rm Ei}\left(\frac{i \, b}{x}\right) + {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{x}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \sin\left(a\right)\right)} b^{3} + \frac{1}{6} \, b x^{2} \cos\left(\frac{a x + b}{x}\right) - \frac{1}{6} \, {\left(b^{2} x - 2 \, x^{3}\right)} \sin\left(\frac{a x + b}{x}\right)"," ",0,"1/12*((Ei(I*b/x) + Ei(-I*b/x))*cos(a) + (I*Ei(I*b/x) - I*Ei(-I*b/x))*sin(a))*b^3 + 1/6*b*x^2*cos((a*x + b)/x) - 1/6*(b^2*x - 2*x^3)*sin((a*x + b)/x)","C",0
104,1,76,0,0.393359," ","integrate(x*sin(a+b/x),x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{x}\right) + {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \sin\left(a\right)\right)} b^{2} + \frac{1}{2} \, b x \cos\left(\frac{a x + b}{x}\right) + \frac{1}{2} \, x^{2} \sin\left(\frac{a x + b}{x}\right)"," ",0,"1/4*((-I*Ei(I*b/x) + I*Ei(-I*b/x))*cos(a) + (Ei(I*b/x) + Ei(-I*b/x))*sin(a))*b^2 + 1/2*b*x*cos((a*x + b)/x) + 1/2*x^2*sin((a*x + b)/x)","C",0
105,1,58,0,0.380067," ","integrate(sin(a+b/x),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left({\rm Ei}\left(\frac{i \, b}{x}\right) + {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \cos\left(a\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, b}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \sin\left(a\right)\right)} b + x \sin\left(\frac{a x + b}{x}\right)"," ",0,"-1/2*((Ei(I*b/x) + Ei(-I*b/x))*cos(a) - (-I*Ei(I*b/x) + I*Ei(-I*b/x))*sin(a))*b + x*sin((a*x + b)/x)","C",0
106,1,43,0,0.364635," ","integrate(sin(a+b/x)/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(i \, {\rm Ei}\left(\frac{i \, b}{x}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \cos\left(a\right) - \frac{1}{2} \, {\left({\rm Ei}\left(\frac{i \, b}{x}\right) + {\rm Ei}\left(-\frac{i \, b}{x}\right)\right)} \sin\left(a\right)"," ",0,"1/2*(I*Ei(I*b/x) - I*Ei(-I*b/x))*cos(a) - 1/2*(Ei(I*b/x) + Ei(-I*b/x))*sin(a)","C",0
107,1,12,0,0.295063," ","integrate(sin(a+b/x)/x^2,x, algorithm=""maxima"")","\frac{\cos\left(a + \frac{b}{x}\right)}{b}"," ",0,"cos(a + b/x)/b","A",0
108,1,50,0,0.359066," ","integrate(sin(a+b/x)/x^3,x, algorithm=""maxima"")","-\frac{{\left(i \, \Gamma\left(2, \frac{i \, b}{x}\right) - i \, \Gamma\left(2, -\frac{i \, b}{x}\right)\right)} \cos\left(a\right) + {\left(\Gamma\left(2, \frac{i \, b}{x}\right) + \Gamma\left(2, -\frac{i \, b}{x}\right)\right)} \sin\left(a\right)}{2 \, b^{2}}"," ",0,"-1/2*((I*gamma(2, I*b/x) - I*gamma(2, -I*b/x))*cos(a) + (gamma(2, I*b/x) + gamma(2, -I*b/x))*sin(a))/b^2","C",0
109,1,51,0,0.393890," ","integrate(sin(a+b/x)/x^4,x, algorithm=""maxima"")","-\frac{{\left(\Gamma\left(3, \frac{i \, b}{x}\right) + \Gamma\left(3, -\frac{i \, b}{x}\right)\right)} \cos\left(a\right) - {\left(i \, \Gamma\left(3, \frac{i \, b}{x}\right) - i \, \Gamma\left(3, -\frac{i \, b}{x}\right)\right)} \sin\left(a\right)}{2 \, b^{3}}"," ",0,"-1/2*((gamma(3, I*b/x) + gamma(3, -I*b/x))*cos(a) - (I*gamma(3, I*b/x) - I*gamma(3, -I*b/x))*sin(a))/b^3","C",0
110,1,50,0,0.420266," ","integrate(sin(a+b/x)/x^5,x, algorithm=""maxima"")","\frac{{\left(i \, \Gamma\left(4, \frac{i \, b}{x}\right) - i \, \Gamma\left(4, -\frac{i \, b}{x}\right)\right)} \cos\left(a\right) + {\left(\Gamma\left(4, \frac{i \, b}{x}\right) + \Gamma\left(4, -\frac{i \, b}{x}\right)\right)} \sin\left(a\right)}{2 \, b^{4}}"," ",0,"1/2*((I*gamma(4, I*b/x) - I*gamma(4, -I*b/x))*cos(a) + (gamma(4, I*b/x) + gamma(4, -I*b/x))*sin(a))/b^4","C",0
111,1,99,0,0.450961," ","integrate(x^2*sin(a+b/x)^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(-2 i \, {\rm Ei}\left(\frac{2 i \, b}{x}\right) + 2 i \, {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) + 2 \, {\left({\rm Ei}\left(\frac{2 i \, b}{x}\right) + {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} b^{3} + \frac{1}{6} \, b x^{2} \sin\left(\frac{2 \, {\left(a x + b\right)}}{x}\right) + \frac{1}{6} \, x^{3} + \frac{1}{6} \, {\left(2 \, b^{2} x - x^{3}\right)} \cos\left(\frac{2 \, {\left(a x + b\right)}}{x}\right)"," ",0,"1/6*((-2*I*Ei(2*I*b/x) + 2*I*Ei(-2*I*b/x))*cos(2*a) + 2*(Ei(2*I*b/x) + Ei(-2*I*b/x))*sin(2*a))*b^3 + 1/6*b*x^2*sin(2*(a*x + b)/x) + 1/6*x^3 + 1/6*(2*b^2*x - x^3)*cos(2*(a*x + b)/x)","C",0
112,1,89,0,0.389126," ","integrate(x*sin(a+b/x)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(2 \, {\left({\rm Ei}\left(\frac{2 i \, b}{x}\right) + {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) - {\left(-2 i \, {\rm Ei}\left(\frac{2 i \, b}{x}\right) + 2 i \, {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} b^{2} - \frac{1}{4} \, x^{2} \cos\left(\frac{2 \, {\left(a x + b\right)}}{x}\right) + \frac{1}{2} \, b x \sin\left(\frac{2 \, {\left(a x + b\right)}}{x}\right) + \frac{1}{4} \, x^{2}"," ",0,"-1/4*(2*(Ei(2*I*b/x) + Ei(-2*I*b/x))*cos(2*a) - (-2*I*Ei(2*I*b/x) + 2*I*Ei(-2*I*b/x))*sin(2*a))*b^2 - 1/4*x^2*cos(2*(a*x + b)/x) + 1/2*b*x*sin(2*(a*x + b)/x) + 1/4*x^2","C",0
113,1,66,0,0.405570," ","integrate(sin(a+b/x)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(-i \, {\rm Ei}\left(\frac{2 i \, b}{x}\right) + i \, {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) + {\left({\rm Ei}\left(\frac{2 i \, b}{x}\right) + {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} b - \frac{1}{2} \, x \cos\left(\frac{2 \, {\left(a x + b\right)}}{x}\right) + \frac{1}{2} \, x"," ",0,"-1/2*((-I*Ei(2*I*b/x) + I*Ei(-2*I*b/x))*cos(2*a) + (Ei(2*I*b/x) + Ei(-2*I*b/x))*sin(2*a))*b - 1/2*x*cos(2*(a*x + b)/x) + 1/2*x","C",0
114,1,51,0,0.426276," ","integrate(sin(a+b/x)^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\rm Ei}\left(\frac{2 i \, b}{x}\right) + {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) + \frac{1}{4} \, {\left(i \, {\rm Ei}\left(\frac{2 i \, b}{x}\right) - i \, {\rm Ei}\left(-\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"1/4*(Ei(2*I*b/x) + Ei(-2*I*b/x))*cos(2*a) + 1/4*(I*Ei(2*I*b/x) - I*Ei(-2*I*b/x))*sin(2*a) + 1/2*log(x)","C",0
115,1,25,0,0.316820," ","integrate(sin(a+b/x)^2/x^2,x, algorithm=""maxima"")","\frac{x \sin\left(\frac{2 \, {\left(a x + b\right)}}{x}\right) - 2 \, b}{4 \, b x}"," ",0,"1/4*(x*sin(2*(a*x + b)/x) - 2*b)/(b*x)","A",0
116,1,68,0,0.373209," ","integrate(sin(a+b/x)^2/x^3,x, algorithm=""maxima"")","\frac{{\left({\left(\Gamma\left(2, \frac{2 i \, b}{x}\right) + \Gamma\left(2, -\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) - {\left(i \, \Gamma\left(2, \frac{2 i \, b}{x}\right) - i \, \Gamma\left(2, -\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} x^{2} - 4 \, b^{2}}{16 \, b^{2} x^{2}}"," ",0,"1/16*(((gamma(2, 2*I*b/x) + gamma(2, -2*I*b/x))*cos(2*a) - (I*gamma(2, 2*I*b/x) - I*gamma(2, -2*I*b/x))*sin(2*a))*x^2 - 4*b^2)/(b^2*x^2)","C",0
117,1,68,0,0.385202," ","integrate(sin(a+b/x)^2/x^4,x, algorithm=""maxima"")","-\frac{{\left({\left(3 i \, \Gamma\left(3, \frac{2 i \, b}{x}\right) - 3 i \, \Gamma\left(3, -\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) + 3 \, {\left(\Gamma\left(3, \frac{2 i \, b}{x}\right) + \Gamma\left(3, -\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} x^{3} + 16 \, b^{3}}{96 \, b^{3} x^{3}}"," ",0,"-1/96*(((3*I*gamma(3, 2*I*b/x) - 3*I*gamma(3, -2*I*b/x))*cos(2*a) + 3*(gamma(3, 2*I*b/x) + gamma(3, -2*I*b/x))*sin(2*a))*x^3 + 16*b^3)/(b^3*x^3)","C",0
118,1,68,0,0.369140," ","integrate(sin(a+b/x)^2/x^5,x, algorithm=""maxima"")","-\frac{{\left({\left(\Gamma\left(4, \frac{2 i \, b}{x}\right) + \Gamma\left(4, -\frac{2 i \, b}{x}\right)\right)} \cos\left(2 \, a\right) - {\left(i \, \Gamma\left(4, \frac{2 i \, b}{x}\right) - i \, \Gamma\left(4, -\frac{2 i \, b}{x}\right)\right)} \sin\left(2 \, a\right)\right)} x^{4} + 8 \, b^{4}}{64 \, b^{4} x^{4}}"," ",0,"-1/64*(((gamma(4, 2*I*b/x) + gamma(4, -2*I*b/x))*cos(2*a) - (I*gamma(4, 2*I*b/x) - I*gamma(4, -2*I*b/x))*sin(2*a))*x^4 + 8*b^4)/(b^4*x^4)","C",0
119,1,127,0,0.394366," ","integrate(sin(a+b/x^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(2 \, \sqrt{2} b x^{2} \sqrt{\frac{1}{x^{4}}} \sin\left(\frac{a x^{2} + b}{x^{2}}\right) + {\left({\left(\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{x^{2}}}\right) - 1\right)} - \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{x^{2}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{x^{2}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{x^{2}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b \left(\frac{b^{2}}{x^{4}}\right)^{\frac{1}{4}}\right)} \sqrt{x^{4}}}{4 \, b x}"," ",0,"1/4*sqrt(2)*(2*sqrt(2)*b*x^2*sqrt(x^(-4))*sin((a*x^2 + b)/x^2) + (((I - 1)*sqrt(pi)*(erf(sqrt(I*b/x^2)) - 1) - (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/x^2)) - 1))*cos(a) + ((I + 1)*sqrt(pi)*(erf(sqrt(I*b/x^2)) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/x^2)) - 1))*sin(a))*b*(b^2/x^4)^(1/4))*sqrt(x^4)/(b*x)","C",0
120,1,43,0,0.365996," ","integrate(sin(a+b/x^2)/x,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(i \, {\rm Ei}\left(\frac{i \, b}{x^{2}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{x^{2}}\right)\right)} \cos\left(a\right) - \frac{1}{4} \, {\left({\rm Ei}\left(\frac{i \, b}{x^{2}}\right) + {\rm Ei}\left(-\frac{i \, b}{x^{2}}\right)\right)} \sin\left(a\right)"," ",0,"1/4*(I*Ei(I*b/x^2) - I*Ei(-I*b/x^2))*cos(a) - 1/4*(Ei(I*b/x^2) + Ei(-I*b/x^2))*sin(a)","C",0
121,1,98,0,0.419724," ","integrate(sin(a+b/x^2)/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{x^{4}} {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{x^{2}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{x^{2}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{x^{2}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{x^{2}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} \left(\frac{b^{2}}{x^{4}}\right)^{\frac{1}{4}}}{8 \, b x}"," ",0,"-1/8*sqrt(2)*(((I + 1)*sqrt(pi)*(erf(sqrt(I*b/x^2)) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/x^2)) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/x^2)) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/x^2)) - 1))*sin(a))*sqrt(x^4)*(b^2/x^4)^(1/4)/(b*x)","C",0
122,1,13,0,0.356454," ","integrate(sin(a+b/x^2)/x^3,x, algorithm=""maxima"")","\frac{\cos\left(a + \frac{b}{x^{2}}\right)}{2 \, b}"," ",0,"1/2*cos(a + b/x^2)/b","A",0
123,1,74,0,0.399444," ","integrate(sin(a+b/x^2)/x^4,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(x^{4}\right)}^{\frac{3}{2}} {\left({\left(\left(i - 1\right) \, \Gamma\left(\frac{3}{2}, \frac{i \, b}{x^{2}}\right) - \left(i + 1\right) \, \Gamma\left(\frac{3}{2}, -\frac{i \, b}{x^{2}}\right)\right)} \cos\left(a\right) + {\left(\left(i + 1\right) \, \Gamma\left(\frac{3}{2}, \frac{i \, b}{x^{2}}\right) - \left(i - 1\right) \, \Gamma\left(\frac{3}{2}, -\frac{i \, b}{x^{2}}\right)\right)} \sin\left(a\right)\right)} \left(\frac{b^{2}}{x^{4}}\right)^{\frac{3}{4}}}{8 \, b^{3} x^{3}}"," ",0,"-1/8*sqrt(2)*(((I - 1)*gamma(3/2, I*b/x^2) - (I + 1)*gamma(3/2, -I*b/x^2))*cos(a) + ((I + 1)*gamma(3/2, I*b/x^2) - (I - 1)*gamma(3/2, -I*b/x^2))*sin(a))*(x^4)^(3/2)*(b^2/x^4)^(3/4)/(b^3*x^3)","C",0
124,1,6,0,0.310853," ","integrate(sin(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","-2 \, \cos\left(\sqrt{x}\right)"," ",0,"-2*cos(sqrt(x))","A",0
125,1,15,0,0.302041," ","integrate(sin(x^(1/2))^3/x^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, \cos\left(\sqrt{x}\right)^{3} - 2 \, \cos\left(\sqrt{x}\right)"," ",0,"2/3*cos(sqrt(x))^3 - 2*cos(sqrt(x))","A",0
126,1,16,0,0.471098," ","integrate(sin(x^(1/2)),x, algorithm=""maxima"")","-2 \, \sqrt{x} \cos\left(\sqrt{x}\right) + 2 \, \sin\left(\sqrt{x}\right)"," ",0,"-2*sqrt(x)*cos(sqrt(x)) + 2*sin(sqrt(x))","A",0
127,1,30,0,0.435767," ","integrate(sin(x^(1/3))^2,x, algorithm=""maxima"")","-\frac{3}{8} \, {\left(2 \, x^{\frac{2}{3}} - 1\right)} \sin\left(2 \, x^{\frac{1}{3}}\right) - \frac{3}{4} \, x^{\frac{1}{3}} \cos\left(2 \, x^{\frac{1}{3}}\right) + \frac{1}{2} \, x"," ",0,"-3/8*(2*x^(2/3) - 1)*sin(2*x^(1/3)) - 3/4*x^(1/3)*cos(2*x^(1/3)) + 1/2*x","A",0
128,1,47,0,0.330255," ","integrate(sin(x^(1/3))^3,x, algorithm=""maxima"")","\frac{1}{36} \, {\left(9 \, x^{\frac{2}{3}} - 2\right)} \cos\left(3 \, x^{\frac{1}{3}}\right) - \frac{9}{4} \, {\left(x^{\frac{2}{3}} - 2\right)} \cos\left(x^{\frac{1}{3}}\right) - \frac{1}{6} \, x^{\frac{1}{3}} \sin\left(3 \, x^{\frac{1}{3}}\right) + \frac{9}{2} \, x^{\frac{1}{3}} \sin\left(x^{\frac{1}{3}}\right)"," ",0,"1/36*(9*x^(2/3) - 2)*cos(3*x^(1/3)) - 9/4*(x^(2/3) - 2)*cos(x^(1/3)) - 1/6*x^(1/3)*sin(3*x^(1/3)) + 9/2*x^(1/3)*sin(x^(1/3))","A",0
129,0,0,0,0.000000," ","integrate((e*x)^m*(b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} \left(b \sin\left(d x^{n} + c\right)\right)^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sin(d*x^n + c))^p, x)","F",0
130,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sin(d*x^n + c) + a)^p, x)","F",0
131,0,0,0,0.000000," ","integrate((e*x)^(-1+n)*(b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{n - 1} \left(b \sin\left(d x^{n} + c\right)\right)^{p}\,{d x}"," ",0,"integrate((e*x)^(n - 1)*(b*sin(d*x^n + c))^p, x)","F",0
132,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{2 \, n - 1} \left(b \sin\left(d x^{n} + c\right)\right)^{p}\,{d x}"," ",0,"integrate((e*x)^(2*n - 1)*(b*sin(d*x^n + c))^p, x)","F",0
133,0,0,0,0.000000," ","integrate((e*x)^(-1+n)*(a+b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{n - 1} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^(n - 1)*(b*sin(d*x^n + c) + a)^p, x)","F",0
134,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(a+b*sin(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{2 \, n - 1} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^(2*n - 1)*(b*sin(d*x^n + c) + a)^p, x)","F",0
135,1,91,0,1.021393," ","integrate(sin(a+b*x^n)/x,x, algorithm=""maxima"")","-\frac{{\left(i \, {\rm Ei}\left(i \, b x^{n}\right) - i \, {\rm Ei}\left(-i \, b x^{n}\right) + i \, {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) - i \, {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(i \, b x^{n}\right) + {\rm Ei}\left(-i \, b x^{n}\right) + {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(a\right)}{4 \, n}"," ",0,"-1/4*((I*Ei(I*b*x^n) - I*Ei(-I*b*x^n) + I*Ei(I*b*e^(n*conjugate(log(x)))) - I*Ei(-I*b*e^(n*conjugate(log(x)))))*cos(a) - (Ei(I*b*x^n) + Ei(-I*b*x^n) + Ei(I*b*e^(n*conjugate(log(x)))) + Ei(-I*b*e^(n*conjugate(log(x)))))*sin(a))/n","C",0
136,1,100,0,3.103101," ","integrate(sin(a+b*x^n)^2/x,x, algorithm=""maxima"")","-\frac{{\left({\rm Ei}\left(2 i \, b x^{n}\right) + {\rm Ei}\left(-2 i \, b x^{n}\right) + {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(2 \, a\right) - 4 \, n \log\left(x\right) - {\left(-i \, {\rm Ei}\left(2 i \, b x^{n}\right) + i \, {\rm Ei}\left(-2 i \, b x^{n}\right) - i \, {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + i \, {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(2 \, a\right)}{8 \, n}"," ",0,"-1/8*((Ei(2*I*b*x^n) + Ei(-2*I*b*x^n) + Ei(2*I*b*e^(n*conjugate(log(x)))) + Ei(-2*I*b*e^(n*conjugate(log(x)))))*cos(2*a) - 4*n*log(x) - (-I*Ei(2*I*b*x^n) + I*Ei(-2*I*b*x^n) - I*Ei(2*I*b*e^(n*conjugate(log(x)))) + I*Ei(-2*I*b*e^(n*conjugate(log(x)))))*sin(2*a))/n","C",0
137,1,180,0,3.802066," ","integrate(sin(a+b*x^n)^3/x,x, algorithm=""maxima"")","\frac{{\left(i \, {\rm Ei}\left(3 i \, b x^{n}\right) - i \, {\rm Ei}\left(-3 i \, b x^{n}\right) + i \, {\rm Ei}\left(3 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) - i \, {\rm Ei}\left(-3 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(3 \, a\right) + {\left(-3 i \, {\rm Ei}\left(i \, b x^{n}\right) + 3 i \, {\rm Ei}\left(-i \, b x^{n}\right) - 3 i \, {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + 3 i \, {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(3 i \, b x^{n}\right) + {\rm Ei}\left(-3 i \, b x^{n}\right) + {\rm Ei}\left(3 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-3 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(3 \, a\right) + 3 \, {\left({\rm Ei}\left(i \, b x^{n}\right) + {\rm Ei}\left(-i \, b x^{n}\right) + {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(a\right)}{16 \, n}"," ",0,"1/16*((I*Ei(3*I*b*x^n) - I*Ei(-3*I*b*x^n) + I*Ei(3*I*b*e^(n*conjugate(log(x)))) - I*Ei(-3*I*b*e^(n*conjugate(log(x)))))*cos(3*a) + (-3*I*Ei(I*b*x^n) + 3*I*Ei(-I*b*x^n) - 3*I*Ei(I*b*e^(n*conjugate(log(x)))) + 3*I*Ei(-I*b*e^(n*conjugate(log(x)))))*cos(a) - (Ei(3*I*b*x^n) + Ei(-3*I*b*x^n) + Ei(3*I*b*e^(n*conjugate(log(x)))) + Ei(-3*I*b*e^(n*conjugate(log(x)))))*sin(3*a) + 3*(Ei(I*b*x^n) + Ei(-I*b*x^n) + Ei(I*b*e^(n*conjugate(log(x)))) + Ei(-I*b*e^(n*conjugate(log(x)))))*sin(a))/n","C",0
138,1,188,0,1.321716," ","integrate(sin(a+b*x^n)^4/x,x, algorithm=""maxima"")","\frac{{\left({\rm Ei}\left(4 i \, b x^{n}\right) + {\rm Ei}\left(-4 i \, b x^{n}\right) + {\rm Ei}\left(4 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-4 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(4 \, a\right) - 4 \, {\left({\rm Ei}\left(2 i \, b x^{n}\right) + {\rm Ei}\left(-2 i \, b x^{n}\right) + {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(2 \, a\right) + 12 \, n \log\left(x\right) + {\left(i \, {\rm Ei}\left(4 i \, b x^{n}\right) - i \, {\rm Ei}\left(-4 i \, b x^{n}\right) + i \, {\rm Ei}\left(4 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) - i \, {\rm Ei}\left(-4 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(4 \, a\right) + {\left(-4 i \, {\rm Ei}\left(2 i \, b x^{n}\right) + 4 i \, {\rm Ei}\left(-2 i \, b x^{n}\right) - 4 i \, {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + 4 i \, {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(2 \, a\right)}{32 \, n}"," ",0,"1/32*((Ei(4*I*b*x^n) + Ei(-4*I*b*x^n) + Ei(4*I*b*e^(n*conjugate(log(x)))) + Ei(-4*I*b*e^(n*conjugate(log(x)))))*cos(4*a) - 4*(Ei(2*I*b*x^n) + Ei(-2*I*b*x^n) + Ei(2*I*b*e^(n*conjugate(log(x)))) + Ei(-2*I*b*e^(n*conjugate(log(x)))))*cos(2*a) + 12*n*log(x) + (I*Ei(4*I*b*x^n) - I*Ei(-4*I*b*x^n) + I*Ei(4*I*b*e^(n*conjugate(log(x)))) - I*Ei(-4*I*b*e^(n*conjugate(log(x)))))*sin(4*a) + (-4*I*Ei(2*I*b*x^n) + 4*I*Ei(-2*I*b*x^n) - 4*I*Ei(2*I*b*e^(n*conjugate(log(x)))) + 4*I*Ei(-2*I*b*e^(n*conjugate(log(x)))))*sin(2*a))/n","C",0
139,0,0,0,0.000000," ","integrate(sin(a+b*x^n),x, algorithm=""maxima"")","\int \sin\left(b x^{n} + a\right)\,{d x}"," ",0,"integrate(sin(b*x^n + a), x)","F",0
140,0,0,0,0.000000," ","integrate(sin(a+b*x^n)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x - \frac{1}{2} \, \int \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}"," ",0,"1/2*x - 1/2*integrate(cos(2*b*x^n + 2*a), x)","F",0
141,0,0,0,0.000000," ","integrate(sin(a+b*x^n)^3,x, algorithm=""maxima"")","\int \sin\left(b x^{n} + a\right)^{3}\,{d x}"," ",0,"integrate(sin(b*x^n + a)^3, x)","F",0
142,0,0,0,0.000000," ","integrate(x^m*sin(a+b*x^n),x, algorithm=""maxima"")","\int x^{m} \sin\left(b x^{n} + a\right)\,{d x}"," ",0,"integrate(x^m*sin(b*x^n + a), x)","F",0
143,0,0,0,0.000000," ","integrate(x^m*sin(a+b*x^n)^2,x, algorithm=""maxima"")","\frac{x x^{m} - {\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}}{2 \, {\left(m + 1\right)}}"," ",0,"1/2*(x*x^m - (m + 1)*integrate(x^m*cos(2*b*x^n + 2*a), x))/(m + 1)","F",0
144,0,0,0,0.000000," ","integrate(x^m*sin(a+b*x^n)^3,x, algorithm=""maxima"")","\int x^{m} \sin\left(b x^{n} + a\right)^{3}\,{d x}"," ",0,"integrate(x^m*sin(b*x^n + a)^3, x)","F",0
145,1,32,0,0.372113," ","integrate(x^(-1+2*n)*sin(a+b*x^n),x, algorithm=""maxima"")","-\frac{b x^{n} \cos\left(b x^{n} + a\right) - \sin\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"-(b*x^n*cos(b*x^n + a) - sin(b*x^n + a))/(b^2*n)","A",0
146,1,29,0,0.406916," ","integrate(x^(-1+2*n)*cos(a+b*x^n),x, algorithm=""maxima"")","\frac{b x^{n} \sin\left(b x^{n} + a\right) + \cos\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"(b*x^n*sin(b*x^n + a) + cos(b*x^n + a))/(b^2*n)","A",0
147,0,0,0,0.000000," ","integrate(x^(-1-n)*sin(a+b*x^n),x, algorithm=""maxima"")","\int x^{-n - 1} \sin\left(b x^{n} + a\right)\,{d x}"," ",0,"integrate(x^(-n - 1)*sin(b*x^n + a), x)","F",0
148,0,0,0,0.000000," ","integrate(x^(-1-n)*sin(a+b*x^n)^2,x, algorithm=""maxima"")","-\frac{n x^{n} \int \frac{\cos\left(2 \, b x^{n} + 2 \, a\right)}{x x^{n}}\,{d x} + 1}{2 \, n x^{n}}"," ",0,"-1/2*(n*x^n*integrate(cos(2*b*x^n + 2*a)/(x*x^n), x) + 1)/(n*x^n)","F",0
149,0,0,0,0.000000," ","integrate(x^(-1-n)*sin(a+b*x^n)^3,x, algorithm=""maxima"")","\int x^{-n - 1} \sin\left(b x^{n} + a\right)^{3}\,{d x}"," ",0,"integrate(x^(-n - 1)*sin(b*x^n + a)^3, x)","F",0
150,0,0,0,0.000000," ","integrate(x^(-1-2*n)*sin(a+b*x^n),x, algorithm=""maxima"")","\int x^{-2 \, n - 1} \sin\left(b x^{n} + a\right)\,{d x}"," ",0,"integrate(x^(-2*n - 1)*sin(b*x^n + a), x)","F",0
151,0,0,0,0.000000," ","integrate(x^(-1-2*n)*sin(a+b*x^n)^2,x, algorithm=""maxima"")","-\frac{2 \, n x^{2 \, n} \int \frac{\cos\left(2 \, b x^{n} + 2 \, a\right)}{x x^{2 \, n}}\,{d x} + 1}{4 \, n x^{2 \, n}}"," ",0,"-1/4*(2*n*x^(2*n)*integrate(cos(2*b*x^n + 2*a)/(x*x^(2*n)), x) + 1)/(n*x^(2*n))","F",0
152,0,0,0,0.000000," ","integrate(x^(-1-2*n)*sin(a+b*x^n)^3,x, algorithm=""maxima"")","\int x^{-2 \, n - 1} \sin\left(b x^{n} + a\right)^{3}\,{d x}"," ",0,"integrate(x^(-2*n - 1)*sin(b*x^n + a)^3, x)","F",0
153,1,972,0,2.275396," ","integrate((f*x+e)^3*sin(b*(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} e^{3} {\left(\left(i + 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + \left(i - 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)}}{8 \, \sqrt{b} d} - \frac{3 \, {\left(2 \, d x {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} c + 2 \, c {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)}\right)} e^{2} f}{8 \, {\left(b d^{3} x + b c d^{2}\right)}} + \frac{3 \, {\left(4 \, b c d x {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} + 4 \, b c^{2} {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} b c^{2} - \left(i - 1\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + \left(i + 1\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)}\right)} e f^{2}}{8 \, {\left(b^{2} d^{4} x + b^{2} c d^{3}\right)}} - \frac{{\left(12 \, b c^{3} {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} + {\left(12 \, b c^{2} {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - 4 i \, \Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + 4 i \, \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} d x - c {\left(4 i \, \Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - 4 i \, \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} - 2 \, {\left({\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} b c^{3} + {\left(-\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} c\right)} \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}}\right)} f^{3}}{16 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}"," ",0,"1/8*sqrt(2)*sqrt(pi)*e^3*((I + 1)*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (I - 1)*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))/(sqrt(b)*d) - 3/8*(2*d*x*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*c + 2*c*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)))*e^2*f/(b*d^3*x + b*c*d^2) + 3/8*(4*b*c*d*x*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) + 4*b*c^2*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*((-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*b*c^2 - (I - 1)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + (I + 1)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)))*e*f^2/(b^2*d^4*x + b^2*c*d^3) - 1/16*(12*b*c^3*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) + (12*b*c^2*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 4*I*gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + 4*I*gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*d*x - c*(4*I*gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 4*I*gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 2*((-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*b*c^3 + (-(3*I - 3)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + (3*I + 3)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*c)*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2))*f^3/(b^2*d^5*x + b^2*c*d^4)","C",0
154,1,564,0,1.613270," ","integrate((f*x+e)^2*sin(b*(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} e^{2} {\left(\left(i + 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + \left(i - 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)}}{8 \, \sqrt{b} d} - \frac{{\left(2 \, d x {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} c + 2 \, c {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)}\right)} e f}{4 \, {\left(b d^{3} x + b c d^{2}\right)}} + \frac{{\left(4 \, b c d x {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} + 4 \, b c^{2} {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} b c^{2} - \left(i - 1\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + \left(i + 1\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)}\right)} f^{2}}{8 \, {\left(b^{2} d^{4} x + b^{2} c d^{3}\right)}}"," ",0,"1/8*sqrt(2)*sqrt(pi)*e^2*((I + 1)*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (I - 1)*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))/(sqrt(b)*d) - 1/4*(2*d*x*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*c + 2*c*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)))*e*f/(b*d^3*x + b*c*d^2) + 1/8*(4*b*c*d*x*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) + 4*b*c^2*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*((-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*b*c^2 - (I - 1)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + (I + 1)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)))*f^2/(b^2*d^4*x + b^2*c*d^3)","C",0
155,1,271,0,0.856602," ","integrate((f*x+e)*sin(b*(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} e {\left(\left(i + 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + \left(i - 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)}}{8 \, \sqrt{b} d} - \frac{{\left(2 \, d x {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} - \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left(-\left(i + 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(i - 1\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} c + 2 \, c {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)}\right)} f}{8 \, {\left(b d^{3} x + b c d^{2}\right)}}"," ",0,"1/8*sqrt(2)*sqrt(pi)*e*((I + 1)*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (I - 1)*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))/(sqrt(b)*d) - 1/8*(2*d*x*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(-(I + 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (I - 1)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*c + 2*c*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)))*f/(b*d^3*x + b*c*d^2)","C",0
156,1,53,0,0.374146," ","integrate(sin(b*(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} {\left(\left(i + 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + \left(i - 1\right) \, \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)}}{8 \, \sqrt{b} d}"," ",0,"1/8*sqrt(2)*sqrt(pi)*((I + 1)*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (I - 1)*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))/(sqrt(b)*d)","C",0
157,0,0,0,0.000000," ","integrate(sin(b*(d*x+c)^2)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{2} b\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^2*b)/(f*x + e), x)","F",0
158,0,0,0,0.000000," ","integrate(sin(b*(d*x+c)^2)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{2} b\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^2*b)/(f*x + e)^2, x)","F",0
159,0,0,0,0.000000," ","integrate((f*x+e)^3*sin(b/(d*x+c)^2),x, algorithm=""maxima"")","-\frac{-{\left(\frac{4 \, c^{3} e f^{2} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{3}} - \frac{3 \, c^{4} f^{3} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{4}} - 2 \, \int -\frac{2 \, {\left(3 \, {\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} x^{2} + 2 \, {\left(b d^{3} e^{3} - 3 \, b c^{2} d e f^{2} + 2 \, b c^{3} f^{3}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - {\left(b^{2} d f^{3} x^{2} + 2 \, {\left(4 \, b^{2} d e f^{2} - 3 \, b^{2} c f^{3}\right)} x\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left(d^{5} x^{3} + 3 \, c d^{4} x^{2} + 3 \, c^{2} d^{3} x + c^{3} d^{2}\right)}}\,{d x} - 2 \, \int -\frac{2 \, {\left(3 \, {\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} x^{2} + 2 \, {\left(b d^{3} e^{3} - 3 \, b c^{2} d e f^{2} + 2 \, b c^{3} f^{3}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - {\left(b^{2} d f^{3} x^{2} + 2 \, {\left(4 \, b^{2} d e f^{2} - 3 \, b^{2} c f^{3}\right)} x\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left({\left(d^{5} x^{3} + 3 \, c d^{4} x^{2} + 3 \, c^{2} d^{3} x + c^{3} d^{2}\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{5} x^{3} + 3 \, c d^{4} x^{2} + 3 \, c^{2} d^{3} x + c^{3} d^{2}\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}\right)}}\,{d x}\right)} d^{3} - {\left(b d f^{3} x^{2} + 2 \, {\left(4 \, b d e f^{2} - 3 \, b c f^{3}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - {\left(d^{3} f^{3} x^{4} + 4 \, d^{3} e f^{2} x^{3} + 6 \, d^{3} e^{2} f x^{2} + 4 \, d^{3} e^{3} x\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{4 \, d^{3}}"," ",0,"-1/4*(4*d^3*integrate(1/4*((4*b*c^3*d*e*f^2 - 3*b*c^4*f^3 - 6*(b*d^4*e^2*f - 2*b*c*d^3*e*f^2 + b*c^2*d^2*f^3)*x^2 - 4*(b*d^4*e^3 - 3*b*c^2*d^2*e*f^2 + 2*b*c^3*d*f^3)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b^2*d^2*f^3*x^2 + 2*(4*b^2*d^2*e*f^2 - 3*b^2*c*d*f^3)*x)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3), x) + 4*d^3*integrate(1/4*((4*b*c^3*d*e*f^2 - 3*b*c^4*f^3 - 6*(b*d^4*e^2*f - 2*b*c*d^3*e*f^2 + b*c^2*d^2*f^3)*x^2 - 4*(b*d^4*e^3 - 3*b*c^2*d^2*e*f^2 + 2*b*c^3*d*f^3)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b^2*d^2*f^3*x^2 + 2*(4*b^2*d^2*e*f^2 - 3*b^2*c*d*f^3)*x)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sin(b/(d^2*x^2 + 2*c*d*x + c^2))^2), x) - (b*d*f^3*x^2 + 2*(4*b*d*e*f^2 - 3*b*c*f^3)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) - (d^3*f^3*x^4 + 4*d^3*e*f^2*x^3 + 6*d^3*e^2*f*x^2 + 4*d^3*e^3*x)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d^3","F",0
160,0,0,0,0.000000," ","integrate((f*x+e)^2*sin(b/(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, b f^{2} x \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(\frac{c^{3} f^{2} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{3}} - 2 \, \int \frac{2 \, b^{2} f^{2} x \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left({\left(b d^{2} e f - b c d f^{2}\right)} x^{2} + {\left(b d^{2} e^{2} - b c^{2} f^{2}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)}}\,{d x} - 2 \, \int \frac{2 \, b^{2} f^{2} x \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left({\left(b d^{2} e f - b c d f^{2}\right)} x^{2} + {\left(b d^{2} e^{2} - b c^{2} f^{2}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left({\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}\right)}}\,{d x}\right)} d^{2} + {\left(d^{2} f^{2} x^{3} + 3 \, d^{2} e f x^{2} + 3 \, d^{2} e^{2} x\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{3 \, d^{2}}"," ",0,"1/3*(2*b*f^2*x*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*d^2*integrate(1/3*(2*b^2*d*f^2*x*sin(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b*c^3*f^2 - 3*(b*d^3*e*f - b*c*d^2*f^2)*x^2 - 3*(b*d^3*e^2 - b*c^2*d*f^2)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)))/(d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2), x) - 3*d^2*integrate(1/3*(2*b^2*d*f^2*x*sin(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b*c^3*f^2 - 3*(b*d^3*e*f - b*c*d^2*f^2)*x^2 - 3*(b*d^3*e^2 - b*c^2*d*f^2)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)))/((d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2)*sin(b/(d^2*x^2 + 2*c*d*x + c^2))^2), x) + (d^2*f^2*x^3 + 3*d^2*e*f*x^2 + 3*d^2*e^2*x)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d^2","F",0
161,0,0,0,0.000000," ","integrate((f*x+e)*sin(b/(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \int \frac{{\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)}}\,{d x} + \int \frac{{\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left({\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}\right)}}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)) + integrate(1/2*(b*d*f*x^2 + 2*b*d*e*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x) + integrate(1/2*(b*d*f*x^2 + 2*b*d*e*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))/((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*sin(b/(d^2*x^2 + 2*c*d*x + c^2))^2), x)","F",0
162,0,0,0,0.000000," ","integrate(sin(b/(d*x+c)^2),x, algorithm=""maxima"")","b d \int \frac{x \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\,{d x} + b d \int \frac{x \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}}\,{d x} + x \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)"," ",0,"b*d*integrate(x*cos(b/(d^2*x^2 + 2*c*d*x + c^2))/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x) + b*d*integrate(x*cos(b/(d^2*x^2 + 2*c*d*x + c^2))/((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos(b/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*sin(b/(d^2*x^2 + 2*c*d*x + c^2))^2), x) + x*sin(b/(d^2*x^2 + 2*c*d*x + c^2))","F",0
163,0,0,0,0.000000," ","integrate(sin(b/(d*x+c)^2)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(\frac{b}{{\left(d x + c\right)}^{2}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(b/(d*x + c)^2)/(f*x + e), x)","F",0
164,0,0,0,0.000000," ","integrate(sin(b/(d*x+c)^2)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(\frac{b}{{\left(d x + c\right)}^{2}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(b/(d*x + c)^2)/(f*x + e)^2, x)","F",0
165,1,1815,0,3.972686," ","integrate((f*x+e)^3*sin(a+b*(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(a\right) + \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + {\left(-\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)} e^{3}}{8 \, \sqrt{b} d} - \frac{3 \, {\left({\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} d x + 2 \, \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} c + {\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} c\right)} e^{2} f}{4096 \, {\left(b d^{3} x + b c d^{2}\right)}} + \frac{3 \, {\left({\left(2048 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(2048 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 2048 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c d x + {\left(2048 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(2048 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 2048 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c^{2} + 2 \, \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b c^{2} + {\left(\left(256 i - 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(256 i + 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \cos\left(a\right) + {\left(\left(256 i + 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(256 i - 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \sin\left(a\right)\right)}\right)} e f^{2}}{4096 \, {\left(b^{2} d^{4} x + b^{2} c d^{3}\right)}} - \frac{{\left({\left(3072 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(3072 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 3072 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c^{3} + {\left({\left(3072 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(3072 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 3072 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c^{2} + {\left(-1024 i \, \Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + 1024 i \, \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \cos\left(a\right) - 1024 \, {\left(\Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \sin\left(a\right)\right)} d x + {\left({\left(-1024 i \, \Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + 1024 i \, \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \cos\left(a\right) - 1024 \, {\left(\Gamma\left(2, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) + \Gamma\left(2, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \sin\left(a\right)\right)} c + 2 \, {\left({\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b c^{3} + {\left({\left(\left(768 i - 768\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(768 i + 768\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \cos\left(a\right) + {\left(\left(768 i + 768\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(768 i - 768\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \sin\left(a\right)\right)} c\right)} \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}}\right)} f^{3}}{4096 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}"," ",0,"-1/8*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(a) + (I - 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (-(I - 1)*cos(a) + (I + 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))*e^3/(sqrt(b)*d) - 3/4096*((1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*d*x + 2*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*c + (1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*c)*e^2*f/(b*d^3*x + b*c*d^2) + 3/4096*((2048*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (2048*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 2048*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c*d*x + (2048*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (2048*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 2048*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c^2 + 2*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*((((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*b*c^2 + ((256*I - 256)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (256*I + 256)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + ((256*I + 256)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (256*I - 256)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a)))*e*f^2/(b^2*d^4*x + b^2*c*d^3) - 1/4096*((3072*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (3072*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 3072*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c^3 + ((3072*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (3072*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 3072*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c^2 + (-1024*I*gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + 1024*I*gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) - 1024*(gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*d*x + ((-1024*I*gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + 1024*I*gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) - 1024*(gamma(2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + gamma(2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*c + 2*((((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*b*c^3 + (((768*I - 768)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (768*I + 768)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + ((768*I + 768)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (768*I - 768)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*c)*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2))*f^3/(b^2*d^5*x + b^2*c*d^4)","C",0
166,1,1034,0,2.279819," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(a\right) + \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + {\left(-\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)} e^{2}}{8 \, \sqrt{b} d} - \frac{{\left({\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} d x + 2 \, \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} c + {\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} c\right)} e f}{2048 \, {\left(b d^{3} x + b c d^{2}\right)}} + \frac{{\left({\left(2048 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(2048 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 2048 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c d x + {\left(2048 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(2048 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 2048 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} b c^{2} + 2 \, \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b c^{2} + {\left(\left(256 i - 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(256 i + 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \cos\left(a\right) + {\left(\left(256 i + 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right) - \left(256 i - 256\right) \, \sqrt{2} \Gamma\left(\frac{3}{2}, -i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)\right)} \sin\left(a\right)\right)}\right)} f^{2}}{4096 \, {\left(b^{2} d^{4} x + b^{2} c d^{3}\right)}}"," ",0,"-1/8*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(a) + (I - 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (-(I - 1)*cos(a) + (I + 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))*e^2/(sqrt(b)*d) - 1/2048*((1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*d*x + 2*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*c + (1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*c)*e*f/(b*d^3*x + b*c*d^2) + 1/4096*((2048*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (2048*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 2048*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c*d*x + (2048*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (2048*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 2048*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*b*c^2 + 2*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*((((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*b*c^2 + ((256*I - 256)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (256*I + 256)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + ((256*I + 256)*sqrt(2)*gamma(3/2, I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - (256*I - 256)*sqrt(2)*gamma(3/2, -I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a)))*f^2/(b^2*d^4*x + b^2*c*d^3)","C",0
167,1,481,0,1.215688," ","integrate((f*x+e)*sin(a+b*(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(a\right) + \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + {\left(-\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)} e}{8 \, \sqrt{b} d} - \frac{{\left({\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} d x + 2 \, \sqrt{b d^{2} x^{2} + 2 \, b c d x + b c^{2}} {\left({\left(\left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} - \left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(256 i - 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}}\right) - 1\right)} + \left(256 i + 256\right) \, \sqrt{2} \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} c + {\left(1024 \, {\left(e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} + e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \cos\left(a\right) + {\left(1024 i \, e^{\left(i \, b d^{2} x^{2} + 2 i \, b c d x + i \, b c^{2}\right)} - 1024 i \, e^{\left(-i \, b d^{2} x^{2} - 2 i \, b c d x - i \, b c^{2}\right)}\right)} \sin\left(a\right)\right)} c\right)} f}{4096 \, {\left(b d^{3} x + b c d^{2}\right)}}"," ",0,"-1/8*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(a) + (I - 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (-(I - 1)*cos(a) + (I + 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))*e/(sqrt(b)*d) - 1/4096*((1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*d*x + 2*sqrt(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(((256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) - (256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*cos(a) + (-(256*I - 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2)) - 1) + (256*I + 256)*sqrt(2)*sqrt(pi)*(erf(sqrt(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2)) - 1))*sin(a))*c + (1024*(e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) + e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*cos(a) + (1024*I*e^(I*b*d^2*x^2 + 2*I*b*c*d*x + I*b*c^2) - 1024*I*e^(-I*b*d^2*x^2 - 2*I*b*c*d*x - I*b*c^2))*sin(a))*c)*f/(b*d^3*x + b*c*d^2)","C",0
168,1,69,0,0.514553," ","integrate(sin(a+b*(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(a\right) + \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{i \, b}}\right) + {\left(-\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\frac{i \, b d x + i \, b c}{\sqrt{-i \, b}}\right)\right)}}{8 \, \sqrt{b} d}"," ",0,"-1/8*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(a) + (I - 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(I*b)) + (-(I - 1)*cos(a) + (I + 1)*sin(a))*erf((I*b*d*x + I*b*c)/sqrt(-I*b)))/(sqrt(b)*d)","C",0
169,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^2)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{2} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^2*b + a)/(f*x + e), x)","F",0
170,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^2)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{2} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^2*b + a)/(f*x + e)^2, x)","F",0
171,0,0,0,0.000000," ","integrate((f*x+e)^3*sin(a+b*(d*x+c)^3),x, algorithm=""maxima"")","\int {\left(f x + e\right)}^{3} \sin\left({\left(d x + c\right)}^{3} b + a\right)\,{d x}"," ",0,"integrate((f*x + e)^3*sin((d*x + c)^3*b + a), x)","F",0
172,0,0,0,0.000000," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^3),x, algorithm=""maxima"")","\int {\left(f x + e\right)}^{2} \sin\left({\left(d x + c\right)}^{3} b + a\right)\,{d x}"," ",0,"integrate((f*x + e)^2*sin((d*x + c)^3*b + a), x)","F",0
173,0,0,0,0.000000," ","integrate((f*x+e)*sin(a+b*(d*x+c)^3),x, algorithm=""maxima"")","\int {\left(f x + e\right)} \sin\left({\left(d x + c\right)}^{3} b + a\right)\,{d x}"," ",0,"integrate((f*x + e)*sin((d*x + c)^3*b + a), x)","F",0
174,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^3),x, algorithm=""maxima"")","\int \sin\left({\left(d x + c\right)}^{3} b + a\right)\,{d x}"," ",0,"integrate(sin((d*x + c)^3*b + a), x)","F",0
175,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^3)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{3} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^3*b + a)/(f*x + e), x)","F",0
176,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^3)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{3} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^3*b + a)/(f*x + e)^2, x)","F",0
177,0,0,0,0.000000," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, b f^{2} x \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(\frac{c^{3} f^{2} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{3}} - 2 \, \int \frac{2 \, b^{2} f^{2} x \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left({\left(b d^{2} e f - b c d f^{2}\right)} x^{2} + {\left(b d^{2} e^{2} - b c^{2} f^{2}\right)} x\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)}}\,{d x} - 2 \, \int \frac{2 \, b^{2} f^{2} x \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left({\left(b d^{2} e f - b c d f^{2}\right)} x^{2} + {\left(b d^{2} e^{2} - b c^{2} f^{2}\right)} x\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left({\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}\right)}}\,{d x}\right)} d^{2} + {\left(d^{2} f^{2} x^{3} + 3 \, d^{2} e f x^{2} + 3 \, d^{2} e^{2} x\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{3 \, d^{2}}"," ",0,"1/3*(2*b*f^2*x*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)) - 3*d^2*integrate(1/3*(2*b^2*d*f^2*x*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)) + (b*c^3*f^2 - 3*(b*d^3*e*f - b*c*d^2*f^2)*x^2 - 3*(b*d^3*e^2 - b*c^2*d*f^2)*x)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/(d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2), x) - 3*d^2*integrate(1/3*(2*b^2*d*f^2*x*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)) + (b*c^3*f^2 - 3*(b*d^3*e*f - b*c*d^2*f^2)*x^2 - 3*(b*d^3*e^2 - b*c^2*d*f^2)*x)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/((d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^5*x^3 + 3*c*d^4*x^2 + 3*c^2*d^3*x + c^3*d^2)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2), x) + (d^2*f^2*x^3 + 3*d^2*e*f*x^2 + 3*d^2*e^2*x)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/d^2","F",0
178,0,0,0,0.000000," ","integrate((f*x+e)*sin(a+b/(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \int \frac{{\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)}}\,{d x} + \int \frac{{\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, {\left({\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}\right)}}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)) + integrate(1/2*(b*d*f*x^2 + 2*b*d*e*x)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x) + integrate(1/2*(b*d*f*x^2 + 2*b*d*e*x)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2), x)","F",0
179,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^2),x, algorithm=""maxima"")","b d \int \frac{x \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\,{d x} + b d \int \frac{x \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2} + {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}}\,{d x} + x \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)"," ",0,"b*d*integrate(x*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x) + b*d*integrate(x*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))^2), x) + x*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))","F",0
180,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^2)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{2}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^2)/(f*x + e), x)","F",0
181,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^2)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{2}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^2)/(f*x + e)^2, x)","F",0
182,0,0,0,0.000000," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^3),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + \int \frac{{\left(b d f^{2} x^{3} + 3 \, b d e f x^{2} + 3 \, b d e^{2} x\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{2 \, {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)}}\,{d x} + \int \frac{{\left(b d f^{2} x^{3} + 3 \, b d e f x^{2} + 3 \, b d e^{2} x\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{2 \, {\left({\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2} + {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2}\right)}}\,{d x}"," ",0,"1/3*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + integrate(1/2*(b*d*f^2*x^3 + 3*b*d*e*f*x^2 + 3*b*d*e^2*x)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4), x) + integrate(1/2*(b*d*f^2*x^3 + 3*b*d*e*f*x^2 + 3*b*d*e^2*x)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/((d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2 + (d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2), x)","F",0
183,0,0,0,0.000000," ","integrate((f*x+e)*sin(a+b/(d*x+c)^3),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + \int \frac{3 \, {\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{4 \, {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)}}\,{d x} + \int \frac{3 \, {\left(b d f x^{2} + 2 \, b d e x\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{4 \, {\left({\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2} + {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2}\right)}}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + integrate(3/4*(b*d*f*x^2 + 2*b*d*e*x)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4), x) + integrate(3/4*(b*d*f*x^2 + 2*b*d*e*x)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/((d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2 + (d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2), x)","F",0
184,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^3),x, algorithm=""maxima"")","3 \, b d \int \frac{x \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{2 \, {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)}}\,{d x} + 3 \, b d \int \frac{x \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{2 \, {\left({\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \cos\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2} + {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)^{2}\right)}}\,{d x} + x \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)"," ",0,"3*b*d*integrate(1/2*x*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4), x) + 3*b*d*integrate(1/2*x*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/((d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*cos((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2 + (d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))^2), x) + x*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))","F",0
185,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^3)/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{3}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^3)/(f*x + e), x)","F",0
186,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^3)/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{3}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^3)/(f*x + e)^2, x)","F",0
187,1,1101,0,0.407318," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{2 \, {\left(a e^{2} \cos\left(\sqrt{d x + c} b + a\right) - \frac{2 \, a c e f \cos\left(\sqrt{d x + c} b + a\right)}{d} + \frac{a c^{2} f^{2} \cos\left(\sqrt{d x + c} b + a\right)}{d^{2}} - {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} e^{2} + \frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} c e f}{d} - \frac{{\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} c^{2} f^{2}}{d^{2}} + \frac{2 \, a^{3} e f \cos\left(\sqrt{d x + c} b + a\right)}{b^{2} d} - \frac{2 \, a^{3} c f^{2} \cos\left(\sqrt{d x + c} b + a\right)}{b^{2} d^{2}} - \frac{6 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{2} e f}{b^{2} d} + \frac{6 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{2} c f^{2}}{b^{2} d^{2}} + \frac{a^{5} f^{2} \cos\left(\sqrt{d x + c} b + a\right)}{b^{4} d^{2}} + \frac{6 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \cos\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(\sqrt{d x + c} b + a\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a e f}{b^{2} d} - \frac{5 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{4} f^{2}}{b^{4} d^{2}} - \frac{6 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \cos\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(\sqrt{d x + c} b + a\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a c f^{2}}{b^{2} d^{2}} - \frac{2 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{3} - 6 \, \sqrt{d x + c} b - 6 \, a\right)} \cos\left(\sqrt{d x + c} b + a\right) - 3 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} e f}{b^{2} d} + \frac{10 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \cos\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(\sqrt{d x + c} b + a\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{3} f^{2}}{b^{4} d^{2}} + \frac{2 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{3} - 6 \, \sqrt{d x + c} b - 6 \, a\right)} \cos\left(\sqrt{d x + c} b + a\right) - 3 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} c f^{2}}{b^{2} d^{2}} - \frac{10 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{3} - 6 \, \sqrt{d x + c} b - 6 \, a\right)} \cos\left(\sqrt{d x + c} b + a\right) - 3 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{2} f^{2}}{b^{4} d^{2}} + \frac{5 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{4} - 12 \, {\left(\sqrt{d x + c} b + a\right)}^{2} + 24\right)} \cos\left(\sqrt{d x + c} b + a\right) - 4 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{3} - 6 \, \sqrt{d x + c} b - 6 \, a\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a f^{2}}{b^{4} d^{2}} - \frac{{\left({\left({\left(\sqrt{d x + c} b + a\right)}^{5} - 20 \, {\left(\sqrt{d x + c} b + a\right)}^{3} + 120 \, \sqrt{d x + c} b + 120 \, a\right)} \cos\left(\sqrt{d x + c} b + a\right) - 5 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{4} - 12 \, {\left(\sqrt{d x + c} b + a\right)}^{2} + 24\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} f^{2}}{b^{4} d^{2}}\right)}}{b^{2} d}"," ",0,"2*(a*e^2*cos(sqrt(d*x + c)*b + a) - 2*a*c*e*f*cos(sqrt(d*x + c)*b + a)/d + a*c^2*f^2*cos(sqrt(d*x + c)*b + a)/d^2 - ((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*e^2 + 2*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*c*e*f/d - ((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*c^2*f^2/d^2 + 2*a^3*e*f*cos(sqrt(d*x + c)*b + a)/(b^2*d) - 2*a^3*c*f^2*cos(sqrt(d*x + c)*b + a)/(b^2*d^2) - 6*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*a^2*e*f/(b^2*d) + 6*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*a^2*c*f^2/(b^2*d^2) + a^5*f^2*cos(sqrt(d*x + c)*b + a)/(b^4*d^2) + 6*(((sqrt(d*x + c)*b + a)^2 - 2)*cos(sqrt(d*x + c)*b + a) - 2*(sqrt(d*x + c)*b + a)*sin(sqrt(d*x + c)*b + a))*a*e*f/(b^2*d) - 5*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*a^4*f^2/(b^4*d^2) - 6*(((sqrt(d*x + c)*b + a)^2 - 2)*cos(sqrt(d*x + c)*b + a) - 2*(sqrt(d*x + c)*b + a)*sin(sqrt(d*x + c)*b + a))*a*c*f^2/(b^2*d^2) - 2*(((sqrt(d*x + c)*b + a)^3 - 6*sqrt(d*x + c)*b - 6*a)*cos(sqrt(d*x + c)*b + a) - 3*((sqrt(d*x + c)*b + a)^2 - 2)*sin(sqrt(d*x + c)*b + a))*e*f/(b^2*d) + 10*(((sqrt(d*x + c)*b + a)^2 - 2)*cos(sqrt(d*x + c)*b + a) - 2*(sqrt(d*x + c)*b + a)*sin(sqrt(d*x + c)*b + a))*a^3*f^2/(b^4*d^2) + 2*(((sqrt(d*x + c)*b + a)^3 - 6*sqrt(d*x + c)*b - 6*a)*cos(sqrt(d*x + c)*b + a) - 3*((sqrt(d*x + c)*b + a)^2 - 2)*sin(sqrt(d*x + c)*b + a))*c*f^2/(b^2*d^2) - 10*(((sqrt(d*x + c)*b + a)^3 - 6*sqrt(d*x + c)*b - 6*a)*cos(sqrt(d*x + c)*b + a) - 3*((sqrt(d*x + c)*b + a)^2 - 2)*sin(sqrt(d*x + c)*b + a))*a^2*f^2/(b^4*d^2) + 5*(((sqrt(d*x + c)*b + a)^4 - 12*(sqrt(d*x + c)*b + a)^2 + 24)*cos(sqrt(d*x + c)*b + a) - 4*((sqrt(d*x + c)*b + a)^3 - 6*sqrt(d*x + c)*b - 6*a)*sin(sqrt(d*x + c)*b + a))*a*f^2/(b^4*d^2) - (((sqrt(d*x + c)*b + a)^5 - 20*(sqrt(d*x + c)*b + a)^3 + 120*sqrt(d*x + c)*b + 120*a)*cos(sqrt(d*x + c)*b + a) - 5*((sqrt(d*x + c)*b + a)^4 - 12*(sqrt(d*x + c)*b + a)^2 + 24)*sin(sqrt(d*x + c)*b + a))*f^2/(b^4*d^2))/(b^2*d)","B",0
188,1,348,0,0.329643," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{2 \, {\left(a e \cos\left(\sqrt{d x + c} b + a\right) - \frac{a c f \cos\left(\sqrt{d x + c} b + a\right)}{d} - {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} e + \frac{{\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} c f}{d} + \frac{a^{3} f \cos\left(\sqrt{d x + c} b + a\right)}{b^{2} d} - \frac{3 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)} a^{2} f}{b^{2} d} + \frac{3 \, {\left({\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \cos\left(\sqrt{d x + c} b + a\right) - 2 \, {\left(\sqrt{d x + c} b + a\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} a f}{b^{2} d} - \frac{{\left({\left({\left(\sqrt{d x + c} b + a\right)}^{3} - 6 \, \sqrt{d x + c} b - 6 \, a\right)} \cos\left(\sqrt{d x + c} b + a\right) - 3 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} - 2\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)} f}{b^{2} d}\right)}}{b^{2} d}"," ",0,"2*(a*e*cos(sqrt(d*x + c)*b + a) - a*c*f*cos(sqrt(d*x + c)*b + a)/d - ((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*e + ((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*c*f/d + a^3*f*cos(sqrt(d*x + c)*b + a)/(b^2*d) - 3*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))*a^2*f/(b^2*d) + 3*(((sqrt(d*x + c)*b + a)^2 - 2)*cos(sqrt(d*x + c)*b + a) - 2*(sqrt(d*x + c)*b + a)*sin(sqrt(d*x + c)*b + a))*a*f/(b^2*d) - (((sqrt(d*x + c)*b + a)^3 - 6*sqrt(d*x + c)*b - 6*a)*cos(sqrt(d*x + c)*b + a) - 3*((sqrt(d*x + c)*b + a)^2 - 2)*sin(sqrt(d*x + c)*b + a))*f/(b^2*d))/(b^2*d)","B",0
189,1,62,0,0.328657," ","integrate(sin(a+b*(d*x+c)^(1/2)),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)} \cos\left(\sqrt{d x + c} b + a\right) - a \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)}}{b^{2} d}"," ",0,"-2*((sqrt(d*x + c)*b + a)*cos(sqrt(d*x + c)*b + a) - a*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))/(b^2*d)","A",0
190,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(1/2))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(\sqrt{d x + c} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(sqrt(d*x + c)*b + a)/(f*x + e), x)","F",0
191,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(1/2))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(\sqrt{d x + c} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(sqrt(d*x + c)*b + a)/(f*x + e)^2, x)","F",0
192,1,694,0,1.202656," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(3/2)),x, algorithm=""maxima"")","-\frac{\frac{3 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)} e^{2}}{\sqrt{d x + c} b} - \frac{6 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)} c e f}{\sqrt{d x + c} b d} + \frac{3 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)} c^{2} f^{2}}{\sqrt{d x + c} b d^{2}} + \frac{2 \, {\left(12 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} \sqrt{d x + c} \cos\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right) + \sqrt{d x + c} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)}\right)} e f}{\left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} b d} - \frac{2 \, {\left(12 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} \sqrt{d x + c} \cos\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right) + \sqrt{d x + c} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)}\right)} c f^{2}}{\left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} b d^{2}} + \frac{12 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} b \cos\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right)\right)} f^{2}}{b^{2} d^{2}}}{18 \, d}"," ",0,"-1/18*(3*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))*e^2/(sqrt(d*x + c)*b) - 6*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))*c*e*f/(sqrt(d*x + c)*b*d) + 3*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))*c^2*f^2/(sqrt(d*x + c)*b*d^2) + 2*(12*((d*x + c)^(3/2)*b)^(1/3)*sqrt(d*x + c)*cos((d*x + c)^(3/2)*b + a) + sqrt(d*x + c)*(((sqrt(3) - I)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (I*sqrt(3) - 1)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*sin(a)))*e*f/(((d*x + c)^(3/2)*b)^(1/3)*b*d) - 2*(12*((d*x + c)^(3/2)*b)^(1/3)*sqrt(d*x + c)*cos((d*x + c)^(3/2)*b + a) + sqrt(d*x + c)*(((sqrt(3) - I)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (I*sqrt(3) - 1)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*sin(a)))*c*f^2/(((d*x + c)^(3/2)*b)^(1/3)*b*d^2) + 12*((d*x + c)^(3/2)*b*cos((d*x + c)^(3/2)*b + a) - sin((d*x + c)^(3/2)*b + a))*f^2/(b^2*d^2))/d","B",0
193,1,375,0,0.978166," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(3/2)),x, algorithm=""maxima"")","-\frac{\frac{3 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)} e}{\sqrt{d x + c} b} - \frac{3 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)} c f}{\sqrt{d x + c} b d} + \frac{{\left(12 \, \left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} \sqrt{d x + c} \cos\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right) + \sqrt{d x + c} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)}\right)} f}{\left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} b d}}{18 \, d}"," ",0,"-1/18*(3*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))*e/(sqrt(d*x + c)*b) - 3*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))*c*f/(sqrt(d*x + c)*b*d) + (12*((d*x + c)^(3/2)*b)^(1/3)*sqrt(d*x + c)*cos((d*x + c)^(3/2)*b + a) + sqrt(d*x + c)*(((sqrt(3) - I)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*(d*x + c)^(3/2)*b) + (I*sqrt(3) - 1)*gamma(1/3, -I*(d*x + c)^(3/2)*b))*sin(a)))*f/(((d*x + c)^(3/2)*b)^(1/3)*b*d))/d","A",0
194,1,112,0,0.575995," ","integrate(sin(a+b*(d*x+c)^(3/2)),x, algorithm=""maxima"")","-\frac{\left({\left(d x + c\right)}^{\frac{3}{2}} b\right)^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \cos\left(a\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -i \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)\right)} \sin\left(a\right)\right)}}{6 \, \sqrt{d x + c} b d}"," ",0,"-1/6*((d*x + c)^(3/2)*b)^(1/3)*(((sqrt(3) + I)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*cos(a) - ((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)^(3/2)*b) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)^(3/2)*b))*sin(a))/(sqrt(d*x + c)*b*d)","A",0
195,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(3/2))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^(3/2)*b + a)/(f*x + e), x)","F",0
196,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(3/2))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{3}{2}} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^(3/2)*b + a)/(f*x + e)^2, x)","F",0
197,1,877,0,1.068516," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{360 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} e^{2} - \frac{720 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} c e f}{d} + \frac{360 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} c^{2} f^{2}}{d^{2}} + \frac{60 \, {\left({\left({\left(i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{4} - 2 \, {\left(\sqrt{d x + c} b^{3} - 2 \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)} \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) - 2 \, {\left({\left(d x + c\right)} b^{2} - 6 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} e f}{d} - \frac{60 \, {\left({\left({\left(i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{4} - 2 \, {\left(\sqrt{d x + c} b^{3} - 2 \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)} \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) - 2 \, {\left({\left(d x + c\right)} b^{2} - 6 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} c f^{2}}{d^{2}} + \frac{{\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{6} + 2 \, {\left(\sqrt{d x + c} b^{5} - 2 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} + 24 \, {\left(d x + c\right)}^{\frac{5}{2}} b\right)} \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left({\left(d x + c\right)} b^{4} - 6 \, {\left(d x + c\right)}^{2} b^{2} + 120 \, {\left(d x + c\right)}^{3}\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} f^{2}}{d^{2}}}{720 \, d}"," ",0,"1/720*(360*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*e^2 - 720*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*c*e*f/d + 360*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*c^2*f^2/d^2 + 60*(((I*Ei(I*b/sqrt(d*x + c)) - I*Ei(-I*b/sqrt(d*x + c)))*cos(a) - (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^4 - 2*(sqrt(d*x + c)*b^3 - 2*(d*x + c)^(3/2)*b)*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) - 2*((d*x + c)*b^2 - 6*(d*x + c)^2)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*e*f/d - 60*(((I*Ei(I*b/sqrt(d*x + c)) - I*Ei(-I*b/sqrt(d*x + c)))*cos(a) - (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^4 - 2*(sqrt(d*x + c)*b^3 - 2*(d*x + c)^(3/2)*b)*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) - 2*((d*x + c)*b^2 - 6*(d*x + c)^2)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*c*f^2/d^2 + (((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^6 + 2*(sqrt(d*x + c)*b^5 - 2*(d*x + c)^(3/2)*b^3 + 24*(d*x + c)^(5/2)*b)*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*((d*x + c)*b^4 - 6*(d*x + c)^2*b^2 + 120*(d*x + c)^3)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*f^2/d^2)/d","C",0
198,1,407,0,0.716562," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{12 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} e - \frac{12 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} c f}{d} + \frac{{\left({\left({\left(i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{4} - 2 \, {\left(\sqrt{d x + c} b^{3} - 2 \, {\left(d x + c\right)}^{\frac{3}{2}} b\right)} \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) - 2 \, {\left({\left(d x + c\right)} b^{2} - 6 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)\right)} f}{d}}{24 \, d}"," ",0,"1/24*(12*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*e - 12*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*c*f/d + (((I*Ei(I*b/sqrt(d*x + c)) - I*Ei(-I*b/sqrt(d*x + c)))*cos(a) - (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^4 - 2*(sqrt(d*x + c)*b^3 - 2*(d*x + c)^(3/2)*b)*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) - 2*((d*x + c)*b^2 - 6*(d*x + c)^2)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))*f/d)/d","C",0
199,1,124,0,0.592674," ","integrate(sin(a+b/(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{{\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) + {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 2 \, \sqrt{d x + c} b \cos\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{\sqrt{d x + c} a + b}{\sqrt{d x + c}}\right)}{2 \, d}"," ",0,"1/2*(((-I*Ei(I*b/sqrt(d*x + c)) + I*Ei(-I*b/sqrt(d*x + c)))*cos(a) + (Ei(I*b/sqrt(d*x + c)) + Ei(-I*b/sqrt(d*x + c)))*sin(a))*b^2 + 2*sqrt(d*x + c)*b*cos((sqrt(d*x + c)*a + b)/sqrt(d*x + c)) + 2*(d*x + c)*sin((sqrt(d*x + c)*a + b)/sqrt(d*x + c)))/d","C",0
200,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(1/2))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{\sqrt{d x + c}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/sqrt(d*x + c))/(f*x + e), x)","F",0
201,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(1/2))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{\sqrt{d x + c}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/sqrt(d*x + c))/(f*x + e)^2, x)","F",0
202,1,1003,0,1.204069," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(3/2)),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b\right)} e^{2}}{\sqrt{d x + c} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}} - \frac{6 \, {\left(4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b\right)} c e f}{\sqrt{d x + c} d \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}} + \frac{3 \, {\left(4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b\right)} c^{2} f^{2}}{\sqrt{d x + c} d^{2} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}} + \frac{2 \, {\left(2 \, {\left(d x + c\right)}^{3} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + 2 \, {\left(d x + c\right)}^{\frac{3}{2}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b^{2}\right)} f^{2}}{d^{2}} + \frac{3 \, {\left(4 \, {\left(d x + c\right)}^{3} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + 12 \, {\left(d x + c\right)}^{\frac{3}{2}} b \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \cos\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) - {\left({\left({\left(3 \, \sqrt{3} + 3 i\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(3 \, \sqrt{3} - 3 i\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + 3 \, {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b^{2}\right)} e f}{{\left(d x + c\right)} d \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}}} - \frac{3 \, {\left(4 \, {\left(d x + c\right)}^{3} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + 12 \, {\left(d x + c\right)}^{\frac{3}{2}} b \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \cos\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) - {\left({\left({\left(3 \, \sqrt{3} + 3 i\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(3 \, \sqrt{3} - 3 i\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + 3 \, {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b^{2}\right)} c f^{2}}{{\left(d x + c\right)} d^{2} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}}}}{12 \, d}"," ",0,"1/12*(3*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)*e^2/(sqrt(d*x + c)*(b/(d*x + c)^(3/2))^(1/3)) - 6*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)*c*e*f/(sqrt(d*x + c)*d*(b/(d*x + c)^(3/2))^(1/3)) + 3*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)*c^2*f^2/(sqrt(d*x + c)*d^2*(b/(d*x + c)^(3/2))^(1/3)) + 2*(2*(d*x + c)^3*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + 2*(d*x + c)^(3/2)*b*cos(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + ((-I*Ei(I*b/(d*x + c)^(3/2)) + I*Ei(-I*b/(d*x + c)^(3/2)))*cos(a) + (Ei(I*b/(d*x + c)^(3/2)) + Ei(-I*b/(d*x + c)^(3/2)))*sin(a))*b^2)*f^2/d^2 + 3*(4*(d*x + c)^3*(b/(d*x + c)^(3/2))^(2/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + 12*(d*x + c)^(3/2)*b*(b/(d*x + c)^(3/2))^(2/3)*cos(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) - (((3*sqrt(3) + 3*I)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (3*sqrt(3) - 3*I)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*cos(a) + 3*((-I*sqrt(3) + 1)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) + 1)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b^2)*e*f/((d*x + c)*d*(b/(d*x + c)^(3/2))^(2/3)) - 3*(4*(d*x + c)^3*(b/(d*x + c)^(3/2))^(2/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + 12*(d*x + c)^(3/2)*b*(b/(d*x + c)^(3/2))^(2/3)*cos(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) - (((3*sqrt(3) + 3*I)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (3*sqrt(3) - 3*I)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*cos(a) + 3*((-I*sqrt(3) + 1)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) + 1)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b^2)*c*f^2/((d*x + c)*d^2*(b/(d*x + c)^(3/2))^(2/3)))/d","B",0
203,1,508,0,1.999824," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(3/2)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b\right)} e}{\sqrt{d x + c} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}} - \frac{2 \, {\left(4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b\right)} c f}{\sqrt{d x + c} d \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}} + \frac{{\left(4 \, {\left(d x + c\right)}^{3} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + 12 \, {\left(d x + c\right)}^{\frac{3}{2}} b \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}} \cos\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) - {\left({\left({\left(3 \, \sqrt{3} + 3 i\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(3 \, \sqrt{3} - 3 i\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + 3 \, {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b^{2}\right)} f}{{\left(d x + c\right)} d \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}}}}{8 \, d}"," ",0,"1/8*(2*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)*e/(sqrt(d*x + c)*(b/(d*x + c)^(3/2))^(1/3)) - 2*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)*c*f/(sqrt(d*x + c)*d*(b/(d*x + c)^(3/2))^(1/3)) + (4*(d*x + c)^3*(b/(d*x + c)^(3/2))^(2/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + 12*(d*x + c)^(3/2)*b*(b/(d*x + c)^(3/2))^(2/3)*cos(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) - (((3*sqrt(3) + 3*I)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (3*sqrt(3) - 3*I)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*cos(a) + 3*((-I*sqrt(3) + 1)*gamma(2/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) + 1)*gamma(2/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b^2)*f/((d*x + c)*d*(b/(d*x + c)^(3/2))^(2/3)))/d","B",0
204,1,151,0,0.603867," ","integrate(sin(a+b/(d*x+c)^(3/2)),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)}^{\frac{3}{2}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{3}{2}} a + b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \cos\left(a\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)\right)} \sin\left(a\right)\right)} b}{4 \, \sqrt{d x + c} d \left(\frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)^{\frac{1}{3}}}"," ",0,"1/4*(4*(d*x + c)^(3/2)*(b/(d*x + c)^(3/2))^(1/3)*sin(((d*x + c)^(3/2)*a + b)/(d*x + c)^(3/2)) + (((sqrt(3) - I)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (sqrt(3) + I)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*cos(a) + ((-I*sqrt(3) - 1)*gamma(1/3, I*b/(d*x + c)^(3/2)) + (I*sqrt(3) - 1)*gamma(1/3, -I*b/(d*x + c)^(3/2)))*sin(a))*b)/(sqrt(d*x + c)*d*(b/(d*x + c)^(3/2))^(1/3))","A",0
205,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(3/2))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(3/2))/(f*x + e), x)","F",0
206,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(3/2))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{3}{2}}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(3/2))/(f*x + e)^2, x)","F",0
207,1,2151,0,0.472882," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} e^{2} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \frac{2 \, a^{2} c e f \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d} + \frac{a^{2} c^{2} f^{2} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d^{2}} - 2 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a e^{2} + \frac{4 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a c e f}{d} - \frac{2 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a c^{2} f^{2}}{d^{2}} - \frac{2 \, a^{5} e f \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b^{3} d} + \frac{2 \, a^{5} c f^{2} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b^{3} d^{2}} + {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} e^{2} + \frac{10 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{4} e f}{b^{3} d} - \frac{2 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} c e f}{d} - \frac{10 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{4} c f^{2}}{b^{3} d^{2}} + \frac{{\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} c^{2} f^{2}}{d^{2}} + \frac{a^{8} f^{2} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b^{6} d^{2}} - \frac{20 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{3} e f}{b^{3} d} - \frac{8 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{7} f^{2}}{b^{6} d^{2}} + \frac{20 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{3} c f^{2}}{b^{3} d^{2}} + \frac{20 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{2} e f}{b^{3} d} + \frac{28 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{6} f^{2}}{b^{6} d^{2}} - \frac{20 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{2} c f^{2}}{b^{3} d^{2}} - \frac{10 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 4 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a e f}{b^{3} d} - \frac{56 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{5} f^{2}}{b^{6} d^{2}} + \frac{10 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 4 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a c f^{2}}{b^{3} d^{2}} + \frac{2 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} - 20 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} + 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b + 120 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 5 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} e f}{b^{3} d} + \frac{70 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 4 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{4} f^{2}}{b^{6} d^{2}} - \frac{2 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} - 20 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} + 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b + 120 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 5 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} c f^{2}}{b^{3} d^{2}} - \frac{56 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} - 20 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} + 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b + 120 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 5 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{3} f^{2}}{b^{6} d^{2}} + \frac{28 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{6} - 30 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} + 360 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 720\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 6 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} - 20 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} + 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b + 120 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{2} f^{2}}{b^{6} d^{2}} - \frac{8 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{7} - 42 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} + 840 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 5040 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 5040 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 7 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{6} - 30 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} + 360 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 720\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a f^{2}}{b^{6} d^{2}} + \frac{{\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{8} - 56 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{6} + 1680 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 20160 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 40320\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 8 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{7} - 42 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} + 840 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 5040 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 5040 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} f^{2}}{b^{6} d^{2}}\right)}}{b^{3} d}"," ",0,"-3*(a^2*e^2*cos((d*x + c)^(1/3)*b + a) - 2*a^2*c*e*f*cos((d*x + c)^(1/3)*b + a)/d + a^2*c^2*f^2*cos((d*x + c)^(1/3)*b + a)/d^2 - 2*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a*e^2 + 4*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a*c*e*f/d - 2*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a*c^2*f^2/d^2 - 2*a^5*e*f*cos((d*x + c)^(1/3)*b + a)/(b^3*d) + 2*a^5*c*f^2*cos((d*x + c)^(1/3)*b + a)/(b^3*d^2) + ((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*e^2 + 10*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a^4*e*f/(b^3*d) - 2*((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*c*e*f/d - 10*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a^4*c*f^2/(b^3*d^2) + ((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*c^2*f^2/d^2 + a^8*f^2*cos((d*x + c)^(1/3)*b + a)/(b^6*d^2) - 20*((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*a^3*e*f/(b^3*d) - 8*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a^7*f^2/(b^6*d^2) + 20*((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*a^3*c*f^2/(b^3*d^2) + 20*((((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*cos((d*x + c)^(1/3)*b + a) - 3*(((d*x + c)^(1/3)*b + a)^2 - 2)*sin((d*x + c)^(1/3)*b + a))*a^2*e*f/(b^3*d) + 28*((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*a^6*f^2/(b^6*d^2) - 20*((((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*cos((d*x + c)^(1/3)*b + a) - 3*(((d*x + c)^(1/3)*b + a)^2 - 2)*sin((d*x + c)^(1/3)*b + a))*a^2*c*f^2/(b^3*d^2) - 10*((((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*cos((d*x + c)^(1/3)*b + a) - 4*(((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*sin((d*x + c)^(1/3)*b + a))*a*e*f/(b^3*d) - 56*((((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*cos((d*x + c)^(1/3)*b + a) - 3*(((d*x + c)^(1/3)*b + a)^2 - 2)*sin((d*x + c)^(1/3)*b + a))*a^5*f^2/(b^6*d^2) + 10*((((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*cos((d*x + c)^(1/3)*b + a) - 4*(((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*sin((d*x + c)^(1/3)*b + a))*a*c*f^2/(b^3*d^2) + 2*((((d*x + c)^(1/3)*b + a)^5 - 20*((d*x + c)^(1/3)*b + a)^3 + 120*(d*x + c)^(1/3)*b + 120*a)*cos((d*x + c)^(1/3)*b + a) - 5*(((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*sin((d*x + c)^(1/3)*b + a))*e*f/(b^3*d) + 70*((((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*cos((d*x + c)^(1/3)*b + a) - 4*(((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*sin((d*x + c)^(1/3)*b + a))*a^4*f^2/(b^6*d^2) - 2*((((d*x + c)^(1/3)*b + a)^5 - 20*((d*x + c)^(1/3)*b + a)^3 + 120*(d*x + c)^(1/3)*b + 120*a)*cos((d*x + c)^(1/3)*b + a) - 5*(((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*sin((d*x + c)^(1/3)*b + a))*c*f^2/(b^3*d^2) - 56*((((d*x + c)^(1/3)*b + a)^5 - 20*((d*x + c)^(1/3)*b + a)^3 + 120*(d*x + c)^(1/3)*b + 120*a)*cos((d*x + c)^(1/3)*b + a) - 5*(((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*sin((d*x + c)^(1/3)*b + a))*a^3*f^2/(b^6*d^2) + 28*((((d*x + c)^(1/3)*b + a)^6 - 30*((d*x + c)^(1/3)*b + a)^4 + 360*((d*x + c)^(1/3)*b + a)^2 - 720)*cos((d*x + c)^(1/3)*b + a) - 6*(((d*x + c)^(1/3)*b + a)^5 - 20*((d*x + c)^(1/3)*b + a)^3 + 120*(d*x + c)^(1/3)*b + 120*a)*sin((d*x + c)^(1/3)*b + a))*a^2*f^2/(b^6*d^2) - 8*((((d*x + c)^(1/3)*b + a)^7 - 42*((d*x + c)^(1/3)*b + a)^5 + 840*((d*x + c)^(1/3)*b + a)^3 - 5040*(d*x + c)^(1/3)*b - 5040*a)*cos((d*x + c)^(1/3)*b + a) - 7*(((d*x + c)^(1/3)*b + a)^6 - 30*((d*x + c)^(1/3)*b + a)^4 + 360*((d*x + c)^(1/3)*b + a)^2 - 720)*sin((d*x + c)^(1/3)*b + a))*a*f^2/(b^6*d^2) + ((((d*x + c)^(1/3)*b + a)^8 - 56*((d*x + c)^(1/3)*b + a)^6 + 1680*((d*x + c)^(1/3)*b + a)^4 - 20160*((d*x + c)^(1/3)*b + a)^2 + 40320)*cos((d*x + c)^(1/3)*b + a) - 8*(((d*x + c)^(1/3)*b + a)^7 - 42*((d*x + c)^(1/3)*b + a)^5 + 840*((d*x + c)^(1/3)*b + a)^3 - 5040*(d*x + c)^(1/3)*b - 5040*a)*sin((d*x + c)^(1/3)*b + a))*f^2/(b^6*d^2))/(b^3*d)","B",0
208,1,681,0,0.448174," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} e \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \frac{a^{2} c f \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d} - 2 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a e + \frac{2 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a c f}{d} - \frac{a^{5} f \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b^{3} d} + {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} e + \frac{5 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{4} f}{b^{3} d} - \frac{{\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} c f}{d} - \frac{10 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{3} f}{b^{3} d} + \frac{10 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a^{2} f}{b^{3} d} - \frac{5 \, {\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 4 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} - 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b - 6 \, a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a f}{b^{3} d} + \frac{{\left({\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{5} - 20 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{3} + 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b + 120 \, a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 5 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{4} - 12 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} + 24\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} f}{b^{3} d}\right)}}{b^{3} d}"," ",0,"-3*(a^2*e*cos((d*x + c)^(1/3)*b + a) - a^2*c*f*cos((d*x + c)^(1/3)*b + a)/d - 2*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a*e + 2*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a*c*f/d - a^5*f*cos((d*x + c)^(1/3)*b + a)/(b^3*d) + ((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*e + 5*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a^4*f/(b^3*d) - ((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*c*f/d - 10*((((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))*a^3*f/(b^3*d) + 10*((((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*cos((d*x + c)^(1/3)*b + a) - 3*(((d*x + c)^(1/3)*b + a)^2 - 2)*sin((d*x + c)^(1/3)*b + a))*a^2*f/(b^3*d) - 5*((((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*cos((d*x + c)^(1/3)*b + a) - 4*(((d*x + c)^(1/3)*b + a)^3 - 6*(d*x + c)^(1/3)*b - 6*a)*sin((d*x + c)^(1/3)*b + a))*a*f/(b^3*d) + ((((d*x + c)^(1/3)*b + a)^5 - 20*((d*x + c)^(1/3)*b + a)^3 + 120*(d*x + c)^(1/3)*b + 120*a)*cos((d*x + c)^(1/3)*b + a) - 5*(((d*x + c)^(1/3)*b + a)^4 - 12*((d*x + c)^(1/3)*b + a)^2 + 24)*sin((d*x + c)^(1/3)*b + a))*f/(b^3*d))/(b^3*d)","B",0
209,1,120,0,0.544327," ","integrate(sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} a + {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{3} d}"," ",0,"-3*(a^2*cos((d*x + c)^(1/3)*b + a) - 2*(((d*x + c)^(1/3)*b + a)*cos((d*x + c)^(1/3)*b + a) - sin((d*x + c)^(1/3)*b + a))*a + (((d*x + c)^(1/3)*b + a)^2 - 2)*cos((d*x + c)^(1/3)*b + a) - 2*((d*x + c)^(1/3)*b + a)*sin((d*x + c)^(1/3)*b + a))/(b^3*d)","A",0
210,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(1/3))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^(1/3)*b + a)/(f*x + e), x)","F",0
211,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(1/3))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^(1/3)*b + a)/(f*x + e)^2, x)","F",0
212,1,559,0,0.504204," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(\frac{8 \, {\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} e^{2}}{b^{3}} - \frac{16 \, {\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} c e f}{b^{3} d} + \frac{8 \, {\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} c^{2} f^{2}}{b^{3} d^{2}} - \frac{128 \, {\left(2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - {\left({\left(d x + c\right)}^{\frac{4}{3}} b^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} e f}{b^{3} d} + \frac{128 \, {\left(2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - {\left({\left(d x + c\right)}^{\frac{4}{3}} b^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} c f^{2}}{b^{3} d^{2}} + \frac{{\left(\sqrt{2} \sqrt{\pi} {\left({\left(-\left(105 i + 105\right) \, \cos\left(a\right) + \left(105 i - 105\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(\left(105 i - 105\right) \, \cos\left(a\right) - \left(105 i + 105\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 16 \, {\left(4 \, {\left(d x + c\right)}^{\frac{7}{3}} b^{5} - 35 \, {\left(d x + c\right)} b^{3}\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - 56 \, {\left(4 \, {\left(d x + c\right)}^{\frac{5}{3}} b^{4} - 15 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2}\right)} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} f^{2}}{b^{6} d^{2}}\right)}}{128 \, d}"," ",0,"-3/128*(8*(sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))*e^2/b^3 - 16*(sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))*c*e*f/(b^3*d) + 8*(sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))*c^2*f^2/(b^3*d^2) - 128*(2*(d*x + c)^(2/3)*b*sin((d*x + c)^(2/3)*b + a) - ((d*x + c)^(4/3)*b^2 - 2)*cos((d*x + c)^(2/3)*b + a))*e*f/(b^3*d) + 128*(2*(d*x + c)^(2/3)*b*sin((d*x + c)^(2/3)*b + a) - ((d*x + c)^(4/3)*b^2 - 2)*cos((d*x + c)^(2/3)*b + a))*c*f^2/(b^3*d^2) + (sqrt(2)*sqrt(pi)*((-(105*I + 105)*cos(a) + (105*I - 105)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + ((105*I - 105)*cos(a) - (105*I + 105)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 16*(4*(d*x + c)^(7/3)*b^5 - 35*(d*x + c)*b^3)*cos((d*x + c)^(2/3)*b + a) - 56*(4*(d*x + c)^(5/3)*b^4 - 15*(d*x + c)^(1/3)*b^2)*sin((d*x + c)^(2/3)*b + a))*f^2/(b^6*d^2))/d","C",0
213,1,248,0,0.366174," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(\frac{{\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} e}{b^{3}} - \frac{{\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} c f}{b^{3} d} - \frac{8 \, {\left(2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - {\left({\left(d x + c\right)}^{\frac{4}{3}} b^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)} f}{b^{3} d}\right)}}{16 \, d}"," ",0,"-3/16*((sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))*e/b^3 - (sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))*c*f/(b^3*d) - 8*(2*(d*x + c)^(2/3)*b*sin((d*x + c)^(2/3)*b + a) - ((d*x + c)^(4/3)*b^2 - 2)*cos((d*x + c)^(2/3)*b + a))*f/(b^3*d))/d","C",0
214,1,92,0,0.334804," ","integrate(sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(\sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{i \, b}\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left({\left(d x + c\right)}^{\frac{1}{3}} \sqrt{-i \, b}\right)\right)} b^{\frac{3}{2}} + 8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{2} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)}}{16 \, b^{3} d}"," ",0,"-3/16*(sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(I*b)) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf((d*x + c)^(1/3)*sqrt(-I*b)))*b^(3/2) + 8*(d*x + c)^(1/3)*b^2*cos((d*x + c)^(2/3)*b + a))/(b^3*d)","C",0
215,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(2/3))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{f x + e}\,{d x}"," ",0,"integrate(sin((d*x + c)^(2/3)*b + a)/(f*x + e), x)","F",0
216,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^(2/3))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^(2/3)*b + a)/(f*x + e)^2, x)","F",0
217,1,1003,0,1.924352," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""maxima"")","\frac{60480 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} e^{2} - \frac{120960 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} c e f}{d} + \frac{60480 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} c^{2} f^{2}}{d^{2}} + \frac{1008 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{6} + 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{5} - 2 \, {\left(d x + c\right)} b^{3} + 24 \, {\left(d x + c\right)}^{\frac{5}{3}} b\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{4} - 6 \, {\left(d x + c\right)}^{\frac{4}{3}} b^{2} + 120 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} e f}{d} - \frac{1008 \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{6} + 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{5} - 2 \, {\left(d x + c\right)} b^{3} + 24 \, {\left(d x + c\right)}^{\frac{5}{3}} b\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{4} - 6 \, {\left(d x + c\right)}^{\frac{4}{3}} b^{2} + 120 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} c f^{2}}{d^{2}} - \frac{{\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{9} + 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{7} - 6 \, {\left(d x + c\right)}^{\frac{4}{3}} b^{5} + 120 \, {\left(d x + c\right)}^{2} b^{3} - 5040 \, {\left(d x + c\right)}^{\frac{8}{3}} b\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{8} - 2 \, {\left(d x + c\right)} b^{6} + 24 \, {\left(d x + c\right)}^{\frac{5}{3}} b^{4} - 720 \, {\left(d x + c\right)}^{\frac{7}{3}} b^{2} + 40320 \, {\left(d x + c\right)}^{3}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} f^{2}}{d^{2}}}{241920 \, d}"," ",0,"1/241920*(60480*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*e^2 - 120960*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*c*e*f/d + 60480*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*c^2*f^2/d^2 + 1008*(((-I*Ei(I*b/(d*x + c)^(1/3)) + I*Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^6 + 2*((d*x + c)^(1/3)*b^5 - 2*(d*x + c)*b^3 + 24*(d*x + c)^(5/3)*b)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + 2*((d*x + c)^(2/3)*b^4 - 6*(d*x + c)^(4/3)*b^2 + 120*(d*x + c)^2)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*e*f/d - 1008*(((-I*Ei(I*b/(d*x + c)^(1/3)) + I*Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^6 + 2*((d*x + c)^(1/3)*b^5 - 2*(d*x + c)*b^3 + 24*(d*x + c)^(5/3)*b)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + 2*((d*x + c)^(2/3)*b^4 - 6*(d*x + c)^(4/3)*b^2 + 120*(d*x + c)^2)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*c*f^2/d^2 - (((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) - (-I*Ei(I*b/(d*x + c)^(1/3)) + I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^9 + 2*((d*x + c)^(2/3)*b^7 - 6*(d*x + c)^(4/3)*b^5 + 120*(d*x + c)^2*b^3 - 5040*(d*x + c)^(8/3)*b)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^8 - 2*(d*x + c)*b^6 + 24*(d*x + c)^(5/3)*b^4 - 720*(d*x + c)^(7/3)*b^2 + 40320*(d*x + c)^3)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*f^2/d^2)/d","C",0
218,1,458,0,0.737934," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""maxima"")","\frac{120 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} e - \frac{120 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} c f}{d} + \frac{{\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{6} + 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{5} - 2 \, {\left(d x + c\right)} b^{3} + 24 \, {\left(d x + c\right)}^{\frac{5}{3}} b\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{4} - 6 \, {\left(d x + c\right)}^{\frac{4}{3}} b^{2} + 120 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} f}{d}}{480 \, d}"," ",0,"1/480*(120*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*e - 120*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*c*f/d + (((-I*Ei(I*b/(d*x + c)^(1/3)) + I*Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^6 + 2*((d*x + c)^(1/3)*b^5 - 2*(d*x + c)*b^3 + 24*(d*x + c)^(5/3)*b)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + 2*((d*x + c)^(2/3)*b^4 - 6*(d*x + c)^(4/3)*b^2 + 120*(d*x + c)^2)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*f/d)/d","C",0
219,1,138,0,0.464025," ","integrate(sin(a+b/(d*x+c)^(1/3)),x, algorithm=""maxima"")","\frac{{\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{4 \, d}"," ",0,"1/4*(((Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(1/3)) - I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b^3 + 2*(d*x + c)^(2/3)*b*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))/d","C",0
220,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(1/3))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(1/3))/(f*x + e), x)","F",0
221,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(1/3))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(1/3))/(f*x + e)^2, x)","F",0
222,1,1258,0,1.369629," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{\frac{630 \, \sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} e^{2}}{{\left(d x + c\right)}^{\frac{1}{3}} b} - \frac{1260 \, \sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} c e f}{{\left(d x + c\right)}^{\frac{1}{3}} b d} + \frac{630 \, \sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} c^{2} f^{2}}{{\left(d x + c\right)}^{\frac{1}{3}} b d^{2}} + \frac{315 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{4}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{2} - 2 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} e f}{d} - \frac{315 \, {\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{4}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{2} - 2 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} c f^{2}}{d^{2}} + \frac{2 \, \sqrt{2} {\left({\left({\left(\left(8 i - 8\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(8 i + 8\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(\left(8 i + 8\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(8 i - 8\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{5} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}} - 2 \, {\left(4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{4} - 15 \, \sqrt{2} {\left(d x + c\right)}^{\frac{8}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2}\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left(16 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{5} - 12 \, \sqrt{2} {\left(d x + c\right)}^{2} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{3} + 105 \, \sqrt{2} {\left(d x + c\right)}^{\frac{10}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} f^{2}}{{\left(d x + c\right)}^{\frac{1}{3}} b d^{2}}}{1260 \, d}"," ",0,"1/1260*(630*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))*e^2/((d*x + c)^(1/3)*b) - 1260*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))*c*e*f/((d*x + c)^(1/3)*b*d) + 630*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))*c^2*f^2/((d*x + c)^(1/3)*b*d^2) + 315*(((Ei(I*b/(d*x + c)^(2/3)) + Ei(-I*b/(d*x + c)^(2/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(2/3)) - I*Ei(-I*b/(d*x + c)^(2/3)))*sin(a))*b^3 + 2*(d*x + c)^(4/3)*b*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) - 2*((d*x + c)^(2/3)*b^2 - 2*(d*x + c)^2)*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)))*e*f/d - 315*(((Ei(I*b/(d*x + c)^(2/3)) + Ei(-I*b/(d*x + c)^(2/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(2/3)) - I*Ei(-I*b/(d*x + c)^(2/3)))*sin(a))*b^3 + 2*(d*x + c)^(4/3)*b*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) - 2*((d*x + c)^(2/3)*b^2 - 2*(d*x + c)^2)*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)))*c*f^2/d^2 + 2*sqrt(2)*((((8*I - 8)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (8*I + 8)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + ((8*I + 8)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (8*I - 8)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^5*(b^2/(d*x + c)^(4/3))^(1/4) - 2*(4*sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b^4 - 15*sqrt(2)*(d*x + c)^(8/3)*sqrt((d*x + c)^(-4/3))*b^2)*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (16*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^5 - 12*sqrt(2)*(d*x + c)^2*sqrt((d*x + c)^(-4/3))*b^3 + 105*sqrt(2)*(d*x + c)^(10/3)*sqrt((d*x + c)^(-4/3))*b)*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)))*sqrt((d*x + c)^(4/3))*f^2/((d*x + c)^(1/3)*b*d^2))/d","C",0
223,1,584,0,0.774088," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} e}{{\left(d x + c\right)}^{\frac{1}{3}} b} - \frac{4 \, \sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}} c f}{{\left(d x + c\right)}^{\frac{1}{3}} b d} + \frac{{\left({\left({\left({\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) + {\left(i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{3} + 2 \, {\left(d x + c\right)}^{\frac{4}{3}} b \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{2} - 2 \, {\left(d x + c\right)}^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} f}{d}}{8 \, d}"," ",0,"1/8*(4*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))*e/((d*x + c)^(1/3)*b) - 4*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))*c*f/((d*x + c)^(1/3)*b*d) + (((Ei(I*b/(d*x + c)^(2/3)) + Ei(-I*b/(d*x + c)^(2/3)))*cos(a) + (I*Ei(I*b/(d*x + c)^(2/3)) - I*Ei(-I*b/(d*x + c)^(2/3)))*sin(a))*b^3 + 2*(d*x + c)^(4/3)*b*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) - 2*((d*x + c)^(2/3)*b^2 - 2*(d*x + c)^2)*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)))*f/d)/d","C",0
224,1,219,0,0.486499," ","integrate(sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(2 \, \sqrt{2} {\left(d x + c\right)}^{\frac{2}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b^{2} \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \sqrt{2} {\left(d x + c\right)}^{\frac{4}{3}} \sqrt{\frac{1}{{\left(d x + c\right)}^{\frac{4}{3}}}} b \sin\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + {\left({\left(\left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - \left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(a\right) + {\left(-\left(i - 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \left(i + 1\right) \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(a\right)\right)} b^{2} \left(\frac{b^{2}}{{\left(d x + c\right)}^{\frac{4}{3}}}\right)^{\frac{1}{4}}\right)} \sqrt{{\left(d x + c\right)}^{\frac{4}{3}}}}{2 \, {\left(d x + c\right)}^{\frac{1}{3}} b d}"," ",0,"1/2*sqrt(2)*(2*sqrt(2)*(d*x + c)^(2/3)*sqrt((d*x + c)^(-4/3))*b^2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + sqrt(2)*(d*x + c)^(4/3)*sqrt((d*x + c)^(-4/3))*b*sin(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3)) + (((I + 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) - (I - 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(a) + (-(I - 1)*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1) + (I + 1)*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(a))*b^2*(b^2/(d*x + c)^(4/3))^(1/4))*sqrt((d*x + c)^(4/3))/((d*x + c)^(1/3)*b*d)","C",0
225,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(2/3))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)}{f x + e}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(2/3))/(f*x + e), x)","F",0
226,0,0,0,0.000000," ","integrate(sin(a+b/(d*x+c)^(2/3))/(f*x+e)^2,x, algorithm=""maxima"")","\int \frac{\sin\left(a + \frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)}{{\left(f x + e\right)}^{2}}\,{d x}"," ",0,"integrate(sin(a + b/(d*x + c)^(2/3))/(f*x + e)^2, x)","F",0
227,1,176,0,0.632456," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","\frac{{\left({\left(9 \, {\left(\Gamma\left(6, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(6, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) - {\left(9 i \, \Gamma\left(6, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 9 i \, \Gamma\left(6, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 9 i \, \Gamma\left(6, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 9 i \, \Gamma\left(6, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} e - 6 \, {\left(b^{6} d^{2} e x^{2} + 2 \, b^{6} c d e x + b^{6} c^{2} e\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)} e^{\frac{1}{3}}}{2 \, b^{7} d}"," ",0,"1/2*((9*(gamma(6, I*b*conjugate((d*x + c)^(1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(1/3))) + gamma(6, I*(d*x + c)^(1/3)*b) + gamma(6, -I*(d*x + c)^(1/3)*b))*cos(a) - (9*I*gamma(6, I*b*conjugate((d*x + c)^(1/3))) - 9*I*gamma(6, -I*b*conjugate((d*x + c)^(1/3))) + 9*I*gamma(6, I*(d*x + c)^(1/3)*b) - 9*I*gamma(6, -I*(d*x + c)^(1/3)*b))*sin(a))*e - 6*(b^6*d^2*e*x^2 + 2*b^6*c*d*e*x + b^6*c^2*e)*cos((d*x + c)^(1/3)*b + a))*e^(1/3)/(b^7*d)","C",0
228,1,193,0,0.630503," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","-\frac{3 \, {\left(b^{4} d x + b^{4} c\right)} {\left(d x + c\right)}^{\frac{1}{3}} e^{\frac{2}{3}} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + {\left(9 \, {\left(\Gamma\left(3, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(3, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(3, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(3, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) - 12 \, {\left(b^{3} d x + b^{3} c\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + {\left(-9 i \, \Gamma\left(3, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 9 i \, \Gamma\left(3, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 9 i \, \Gamma\left(3, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + 9 i \, \Gamma\left(3, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} e^{\frac{2}{3}}}{b^{5} d}"," ",0,"-(3*(b^4*d*x + b^4*c)*(d*x + c)^(1/3)*e^(2/3)*cos((d*x + c)^(1/3)*b + a) + (9*(gamma(3, I*b*conjugate((d*x + c)^(1/3))) + gamma(3, -I*b*conjugate((d*x + c)^(1/3))) + gamma(3, I*(d*x + c)^(1/3)*b) + gamma(3, -I*(d*x + c)^(1/3)*b))*cos(a) - 12*(b^3*d*x + b^3*c)*sin((d*x + c)^(1/3)*b + a) + (-9*I*gamma(3, I*b*conjugate((d*x + c)^(1/3))) + 9*I*gamma(3, -I*b*conjugate((d*x + c)^(1/3))) - 9*I*gamma(3, I*(d*x + c)^(1/3)*b) + 9*I*gamma(3, -I*(d*x + c)^(1/3)*b))*sin(a))*e^(2/3))/(b^5*d)","C",0
229,1,155,0,0.616503," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""maxima"")","-\frac{{\left(12 \, {\left(b^{3} d x + b^{3} c\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + {\left(9 i \, \Gamma\left(3, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 9 i \, \Gamma\left(3, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 9 i \, \Gamma\left(3, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 9 i \, \Gamma\left(3, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) + 9 \, {\left(\Gamma\left(3, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(3, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(3, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(3, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} e^{\frac{1}{3}}}{4 \, b^{4} d}"," ",0,"-1/4*(12*(b^3*d*x + b^3*c)*cos((d*x + c)^(1/3)*b + a) + (9*I*gamma(3, I*b*conjugate((d*x + c)^(1/3))) - 9*I*gamma(3, -I*b*conjugate((d*x + c)^(1/3))) + 9*I*gamma(3, I*(d*x + c)^(1/3)*b) - 9*I*gamma(3, -I*(d*x + c)^(1/3)*b))*cos(a) + 9*(gamma(3, I*b*conjugate((d*x + c)^(1/3))) + gamma(3, -I*b*conjugate((d*x + c)^(1/3))) + gamma(3, I*(d*x + c)^(1/3)*b) + gamma(3, -I*(d*x + c)^(1/3)*b))*sin(a))*e^(1/3)/(b^4*d)","C",0
230,1,129,0,0.617115," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(1/3),x, algorithm=""maxima"")","\frac{{\left(3 i \, \Gamma\left(2, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(2, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 3 i \, \Gamma\left(2, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 3 i \, \Gamma\left(2, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(2, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(2, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(2, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(2, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)}{4 \, b^{2} d e^{\frac{1}{3}}}"," ",0,"1/4*((3*I*gamma(2, I*b*conjugate((d*x + c)^(1/3))) - 3*I*gamma(2, -I*b*conjugate((d*x + c)^(1/3))) + 3*I*gamma(2, I*(d*x + c)^(1/3)*b) - 3*I*gamma(2, -I*(d*x + c)^(1/3)*b))*cos(a) + 3*(gamma(2, I*b*conjugate((d*x + c)^(1/3))) + gamma(2, -I*b*conjugate((d*x + c)^(1/3))) + gamma(2, I*(d*x + c)^(1/3)*b) + gamma(2, -I*(d*x + c)^(1/3)*b))*sin(a))/(b^2*d*e^(1/3))","C",0
231,1,23,0,0.349551," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(2/3),x, algorithm=""maxima"")","-\frac{3 \, \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b d e^{\frac{2}{3}}}"," ",0,"-3*cos((d*x + c)^(1/3)*b + a)/(b*d*e^(2/3))","A",0
232,1,128,0,0.617125," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(4/3),x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(\Gamma\left(-1, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-1, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-1, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(-1, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) - {\left(3 i \, \Gamma\left(-1, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(-1, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 3 i \, \Gamma\left(-1, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 3 i \, \Gamma\left(-1, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} b}{4 \, d e^{\frac{4}{3}}}"," ",0,"1/4*(3*(gamma(-1, I*b*conjugate((d*x + c)^(1/3))) + gamma(-1, -I*b*conjugate((d*x + c)^(1/3))) + gamma(-1, I*(d*x + c)^(1/3)*b) + gamma(-1, -I*(d*x + c)^(1/3)*b))*cos(a) - (3*I*gamma(-1, I*b*conjugate((d*x + c)^(1/3))) - 3*I*gamma(-1, -I*b*conjugate((d*x + c)^(1/3))) + 3*I*gamma(-1, I*(d*x + c)^(1/3)*b) - 3*I*gamma(-1, -I*(d*x + c)^(1/3)*b))*sin(a))*b/(d*e^(4/3))","C",0
233,1,129,0,0.624264," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(5/3),x, algorithm=""maxima"")","\frac{{\left({\left(3 i \, \Gamma\left(-2, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(-2, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 3 i \, \Gamma\left(-2, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 3 i \, \Gamma\left(-2, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(-2, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-2, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-2, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(-2, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} b^{2}}{4 \, d e^{\frac{5}{3}}}"," ",0,"1/4*((3*I*gamma(-2, I*b*conjugate((d*x + c)^(1/3))) - 3*I*gamma(-2, -I*b*conjugate((d*x + c)^(1/3))) + 3*I*gamma(-2, I*(d*x + c)^(1/3)*b) - 3*I*gamma(-2, -I*(d*x + c)^(1/3)*b))*cos(a) + 3*(gamma(-2, I*b*conjugate((d*x + c)^(1/3))) + gamma(-2, -I*b*conjugate((d*x + c)^(1/3))) + gamma(-2, I*(d*x + c)^(1/3)*b) + gamma(-2, -I*(d*x + c)^(1/3)*b))*sin(a))*b^2/(d*e^(5/3))","C",0
234,1,129,0,0.696473," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(7/3),x, algorithm=""maxima"")","-\frac{{\left({\left(3 i \, \Gamma\left(-4, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(-4, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 3 i \, \Gamma\left(-4, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) - 3 i \, \Gamma\left(-4, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(-4, i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-4, -i \, b \overline{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-4, i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right) + \Gamma\left(-4, -i \, {\left(d x + c\right)}^{\frac{1}{3}} b\right)\right)} \sin\left(a\right)\right)} b^{4}}{4 \, d e^{\frac{7}{3}}}"," ",0,"-1/4*((3*I*gamma(-4, I*b*conjugate((d*x + c)^(1/3))) - 3*I*gamma(-4, -I*b*conjugate((d*x + c)^(1/3))) + 3*I*gamma(-4, I*(d*x + c)^(1/3)*b) - 3*I*gamma(-4, -I*(d*x + c)^(1/3)*b))*cos(a) + 3*(gamma(-4, I*b*conjugate((d*x + c)^(1/3))) + gamma(-4, -I*b*conjugate((d*x + c)^(1/3))) + gamma(-4, I*(d*x + c)^(1/3)*b) + gamma(-4, -I*(d*x + c)^(1/3)*b))*sin(a))*b^4/(d*e^(7/3))","C",0
235,1,386,0,0.783118," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(-3 i \, \Gamma\left(\frac{7}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 3 i \, \Gamma\left(\frac{7}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(\frac{7}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{7}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{7}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(\frac{7}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{7}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(\frac{7}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{7}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{7}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{7}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(\frac{7}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(\frac{7}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} \sqrt{{\left(d x + c\right)}^{\frac{2}{3}} b} e^{\frac{4}{3}}}{8 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{4} d}"," ",0,"-1/8*(((-3*I*gamma(7/2, -I*b*conjugate((d*x + c)^(2/3))) + 3*I*gamma(7/2, I*(d*x + c)^(2/3)*b))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(7/2, I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(7/2, -I*(d*x + c)^(2/3)*b))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(7/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(7/2, I*(d*x + c)^(2/3)*b))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) - 3*(gamma(7/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(7/2, -I*(d*x + c)^(2/3)*b))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(7/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(7/2, I*(d*x + c)^(2/3)*b))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(7/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(7/2, -I*(d*x + c)^(2/3)*b))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(7/2, -I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(7/2, I*(d*x + c)^(2/3)*b))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(7/2, I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(7/2, -I*(d*x + c)^(2/3)*b))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*sin(a))*sqrt((d*x + c)^(2/3)*b)*e^(4/3)/((d*x + c)^(1/3)*b^4*d)","C",0
236,1,429,0,0.818777," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{{\left(d x + c\right)}^{\frac{2}{3}} {\left({\left(9 \, {\left(\Gamma\left(\frac{3}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{3}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) + 9 \, {\left(\Gamma\left(\frac{3}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{3}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) - {\left(-9 i \, \Gamma\left(\frac{3}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 9 i \, \Gamma\left(\frac{3}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) - {\left(-9 i \, \Gamma\left(\frac{3}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 9 i \, \Gamma\left(\frac{3}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) - {\left({\left(-9 i \, \Gamma\left(\frac{3}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 9 i \, \Gamma\left(\frac{3}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) + {\left(9 i \, \Gamma\left(\frac{3}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 9 i \, \Gamma\left(\frac{3}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) + 9 \, {\left(\Gamma\left(\frac{3}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{3}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right) - 9 \, {\left(\Gamma\left(\frac{3}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(\frac{3}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{3}{4} \, \pi + \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} \sqrt{{\left(d x + c\right)}^{\frac{2}{3}} b} e^{\frac{2}{3}} + 24 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} e^{\frac{2}{3}} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{16 \, {\left(b^{3} d^{2} x + b^{3} c d\right)}}"," ",0,"-1/16*((d*x + c)^(2/3)*((9*(gamma(3/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(3/2, I*(d*x + c)^(2/3)*b))*cos(3/4*pi + arctan2(0, d*x + c)) + 9*(gamma(3/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(3/2, -I*(d*x + c)^(2/3)*b))*cos(-3/4*pi + arctan2(0, d*x + c)) - (-9*I*gamma(3/2, -I*b*conjugate((d*x + c)^(2/3))) + 9*I*gamma(3/2, I*(d*x + c)^(2/3)*b))*sin(3/4*pi + arctan2(0, d*x + c)) - (-9*I*gamma(3/2, I*b*conjugate((d*x + c)^(2/3))) + 9*I*gamma(3/2, -I*(d*x + c)^(2/3)*b))*sin(-3/4*pi + arctan2(0, d*x + c)))*cos(a) - ((-9*I*gamma(3/2, -I*b*conjugate((d*x + c)^(2/3))) + 9*I*gamma(3/2, I*(d*x + c)^(2/3)*b))*cos(3/4*pi + arctan2(0, d*x + c)) + (9*I*gamma(3/2, I*b*conjugate((d*x + c)^(2/3))) - 9*I*gamma(3/2, -I*(d*x + c)^(2/3)*b))*cos(-3/4*pi + arctan2(0, d*x + c)) + 9*(gamma(3/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(3/2, I*(d*x + c)^(2/3)*b))*sin(3/4*pi + arctan2(0, d*x + c)) - 9*(gamma(3/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(3/2, -I*(d*x + c)^(2/3)*b))*sin(-3/4*pi + arctan2(0, d*x + c)))*sin(a))*sqrt((d*x + c)^(2/3)*b)*e^(2/3) + 24*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*e^(2/3)*cos((d*x + c)^(2/3)*b + a))/(b^3*d^2*x + b^3*c*d)","C",0
237,1,129,0,1.338188," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{{\left({\left(3 i \, \Gamma\left(2, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(2, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 3 i \, \Gamma\left(2, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right) - 3 i \, \Gamma\left(2, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(2, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(2, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(2, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right) + \Gamma\left(2, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(a\right)\right)} e^{\frac{1}{3}}}{8 \, b^{2} d}"," ",0,"1/8*((3*I*gamma(2, I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(2, -I*b*conjugate((d*x + c)^(2/3))) + 3*I*gamma(2, I*(d*x + c)^(2/3)*b) - 3*I*gamma(2, -I*(d*x + c)^(2/3)*b))*cos(a) + 3*(gamma(2, I*b*conjugate((d*x + c)^(2/3))) + gamma(2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(2, I*(d*x + c)^(2/3)*b) + gamma(2, -I*(d*x + c)^(2/3)*b))*sin(a))*e^(1/3)/(b^2*d)","C",0
238,1,23,0,0.340749," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(1/3),x, algorithm=""maxima"")","-\frac{3 \, \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{2 \, b d e^{\frac{1}{3}}}"," ",0,"-3/2*cos((d*x + c)^(2/3)*b + a)/(b*d*e^(1/3))","A",0
239,1,493,0,1.602106," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(2/3),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} - 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) - {\left(3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b}\right) - 1\right)}\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} \sqrt{{\left(d x + c\right)}^{\frac{2}{3}} b}}{8 \, {\left(d x + c\right)}^{\frac{1}{3}} b d e^{\frac{2}{3}}}"," ",0,"-1/8*(((3*I*sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(2/3)))) - 1) - 3*I*sqrt(pi)*(erf(sqrt(I*(d*x + c)^(2/3)*b)) - 1))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(-I*(d*x + c)^(2/3)*b)) - 1))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) - 3*(sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(2/3)))) - 1) + sqrt(pi)*(erf(sqrt(I*(d*x + c)^(2/3)*b)) - 1))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(2/3)))) - 1) + sqrt(pi)*(erf(sqrt(-I*(d*x + c)^(2/3)*b)) - 1))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*cos(a) - (3*(sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(2/3)))) - 1) + sqrt(pi)*(erf(sqrt(I*(d*x + c)^(2/3)*b)) - 1))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(2/3)))) - 1) + sqrt(pi)*(erf(sqrt(-I*(d*x + c)^(2/3)*b)) - 1))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) - (-3*I*sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(I*(d*x + c)^(2/3)*b)) - 1))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) - (-3*I*sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(-I*(d*x + c)^(2/3)*b)) - 1))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*sin(a))*sqrt((d*x + c)^(2/3)*b)/((d*x + c)^(1/3)*b*d*e^(2/3))","C",0
240,1,386,0,1.343043," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(4/3),x, algorithm=""maxima"")","\frac{{\left({\left({\left(3 i \, \Gamma\left(-\frac{1}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{1}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 3 i \, \Gamma\left(-\frac{1}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{1}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-\frac{1}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{1}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-\frac{1}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) - {\left(3 \, {\left(\Gamma\left(-\frac{1}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-\frac{1}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{1}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-\frac{1}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(-\frac{1}{2}, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(-\frac{1}{2}, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} \sqrt{{\left(d x + c\right)}^{\frac{2}{3}} b}}{8 \, {\left(d x + c\right)}^{\frac{1}{3}} d e^{\frac{4}{3}}}"," ",0,"1/8*(((3*I*gamma(-1/2, -I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(-1/2, I*(d*x + c)^(2/3)*b))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*gamma(-1/2, I*b*conjugate((d*x + c)^(2/3))) + 3*I*gamma(-1/2, -I*(d*x + c)^(2/3)*b))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(gamma(-1/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(-1/2, I*(d*x + c)^(2/3)*b))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) - 3*(gamma(-1/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(-1/2, -I*(d*x + c)^(2/3)*b))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*cos(a) - (3*(gamma(-1/2, -I*b*conjugate((d*x + c)^(2/3))) + gamma(-1/2, I*(d*x + c)^(2/3)*b))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(gamma(-1/2, I*b*conjugate((d*x + c)^(2/3))) + gamma(-1/2, -I*(d*x + c)^(2/3)*b))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) - (3*I*gamma(-1/2, -I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(-1/2, I*(d*x + c)^(2/3)*b))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) - (3*I*gamma(-1/2, I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(-1/2, -I*(d*x + c)^(2/3)*b))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*sin(a))*sqrt((d*x + c)^(2/3)*b)/((d*x + c)^(1/3)*d*e^(4/3))","C",0
241,1,128,0,0.696819," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(5/3),x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(\Gamma\left(-1, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-1, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-1, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right) + \Gamma\left(-1, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \cos\left(a\right) - {\left(3 i \, \Gamma\left(-1, i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-1, -i \, b \overline{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 3 i \, \Gamma\left(-1, i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right) - 3 i \, \Gamma\left(-1, -i \, {\left(d x + c\right)}^{\frac{2}{3}} b\right)\right)} \sin\left(a\right)\right)} b}{8 \, d e^{\frac{5}{3}}}"," ",0,"1/8*(3*(gamma(-1, I*b*conjugate((d*x + c)^(2/3))) + gamma(-1, -I*b*conjugate((d*x + c)^(2/3))) + gamma(-1, I*(d*x + c)^(2/3)*b) + gamma(-1, -I*(d*x + c)^(2/3)*b))*cos(a) - (3*I*gamma(-1, I*b*conjugate((d*x + c)^(2/3))) - 3*I*gamma(-1, -I*b*conjugate((d*x + c)^(2/3))) + 3*I*gamma(-1, I*(d*x + c)^(2/3)*b) - 3*I*gamma(-1, -I*(d*x + c)^(2/3)*b))*sin(a))*b/(d*e^(5/3))","C",0
242,1,129,0,1.780463," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""maxima"")","\frac{{\left({\left(3 i \, \Gamma\left(-4, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(-4, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(-4, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(-4, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(-4, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(-4, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(-4, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-4, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{4} e^{\frac{1}{3}}}{4 \, d}"," ",0,"1/4*((3*I*gamma(-4, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(-4, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(-4, I*b/(d*x + c)^(1/3)) - 3*I*gamma(-4, -I*b/(d*x + c)^(1/3)))*cos(a) + 3*(gamma(-4, I*b*conjugate((d*x + c)^(-1/3))) + gamma(-4, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(-4, I*b/(d*x + c)^(1/3)) + gamma(-4, -I*b/(d*x + c)^(1/3)))*sin(a))*b^4*e^(1/3)/d","C",0
243,1,172,0,0.616495," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(1/3),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{\frac{1}{3}} {\left({\left(3 i \, \Gamma\left(-1, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(-1, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(-1, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(-1, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(-1, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(-1, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(-1, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(-1, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{2} + 12 \, {\left(d x + c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{8 \, {\left(d x + c\right)}^{\frac{1}{3}} d e^{\frac{1}{3}}}"," ",0,"1/8*((d*x + c)^(1/3)*((3*I*gamma(-1, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(-1, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(-1, I*b/(d*x + c)^(1/3)) - 3*I*gamma(-1, -I*b/(d*x + c)^(1/3)))*cos(a) + 3*(gamma(-1, I*b*conjugate((d*x + c)^(-1/3))) + gamma(-1, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(-1, I*b/(d*x + c)^(1/3)) + gamma(-1, -I*b/(d*x + c)^(1/3)))*sin(a))*b^2 + 12*(d*x + c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))/((d*x + c)^(1/3)*d*e^(1/3))","C",0
244,1,157,0,0.590763," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left({\rm Ei}\left(i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + {\rm Ei}\left(-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) - {\left(-3 i \, {\rm Ei}\left(i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, {\rm Ei}\left(-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 3 i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)} b e^{\frac{1}{3}} - 12 \, {\left(d x + c\right)}^{\frac{1}{3}} e^{\frac{1}{3}} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{4 \, d e}"," ",0,"-1/4*((3*(Ei(I*b*conjugate((d*x + c)^(-1/3))) + Ei(-I*b*conjugate((d*x + c)^(-1/3))) + Ei(I*b/(d*x + c)^(1/3)) + Ei(-I*b/(d*x + c)^(1/3)))*cos(a) - (-3*I*Ei(I*b*conjugate((d*x + c)^(-1/3))) + 3*I*Ei(-I*b*conjugate((d*x + c)^(-1/3))) - 3*I*Ei(I*b/(d*x + c)^(1/3)) + 3*I*Ei(-I*b/(d*x + c)^(1/3)))*sin(a))*b*e^(1/3) - 12*(d*x + c)^(1/3)*e^(1/3)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))/(d*e)","C",0
245,1,31,0,0.341631," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(4/3),x, algorithm=""maxima"")","\frac{3 \, \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{b d e^{\frac{4}{3}}}"," ",0,"3*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))/(b*d*e^(4/3))","A",0
246,1,170,0,0.597444," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(5/3),x, algorithm=""maxima"")","-\frac{12 \, b^{2} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\left(d x + c\right)}^{\frac{2}{3}} {\left({\left(3 i \, \Gamma\left(3, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(3, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(3, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(3, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(3, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(3, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(3, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(3, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)\right)}}{8 \, {\left(d x + c\right)}^{\frac{2}{3}} b^{2} d e^{\frac{5}{3}}}"," ",0,"-1/8*(12*b^2*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + (d*x + c)^(2/3)*((3*I*gamma(3, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(3, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(3, I*b/(d*x + c)^(1/3)) - 3*I*gamma(3, -I*b/(d*x + c)^(1/3)))*cos(a) + 3*(gamma(3, I*b*conjugate((d*x + c)^(-1/3))) + gamma(3, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(3, I*b/(d*x + c)^(1/3)) + gamma(3, -I*b/(d*x + c)^(1/3)))*sin(a)))/((d*x + c)^(2/3)*b^2*d*e^(5/3))","C",0
247,1,1390,0,2.367780," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(7/3),x, algorithm=""maxima"")","-\frac{6 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 6 \, {\left(b^{4} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} \sin\left(a\right) + b^{4} \sin\left(a\right) \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} \cos\left(\frac{2 \, {\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 6 \, {\left(b^{4} \cos\left(a\right) \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + b^{4} \cos\left(a\right) \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} \sin\left(\frac{2 \, {\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - {\left({\left({\left({\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + {\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} d x + {\left({\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + {\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + {\left({\left({\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + {\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} d x + {\left({\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + {\left(3 i \, \Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 3 i \, \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 3 i \, \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 3 i \, \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 3 \, {\left(\Gamma\left(5, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(5, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(5, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} {\left(d x + c\right)}^{\frac{1}{3}}}{16 \, {\left({\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} d^{2} e^{2} x + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} c d e^{2}\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} d^{2} e^{2} x + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} c d e^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} {\left(d x + c\right)}^{\frac{1}{3}} e^{\frac{1}{3}}}"," ",0,"-1/16*(6*(cos(a)^2 + sin(a)^2)*b^4*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - 6*(b^4*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2*sin(a) + b^4*sin(a)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*cos((2*(d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + 6*(b^4*cos(a)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + b^4*cos(a)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*sin((2*(d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - ((((3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^3 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + (3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*d*x + ((3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^3 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + (3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + (((3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^3 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + (3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*d*x + ((3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^3 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + (3*I*gamma(5, I*b*conjugate((d*x + c)^(-1/3))) - 3*I*gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + 3*I*gamma(5, I*b/(d*x + c)^(1/3)) - 3*I*gamma(5, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 + 3*(gamma(5, I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(5, I*b/(d*x + c)^(1/3)) + gamma(5, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*(d*x + c)^(1/3))/((((cos(a)^2 + sin(a)^2)*b^4*d^2*e^2*x + (cos(a)^2 + sin(a)^2)*b^4*c*d*e^2)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + ((cos(a)^2 + sin(a)^2)*b^4*d^2*e^2*x + (cos(a)^2 + sin(a)^2)*b^4*c*d*e^2)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*(d*x + c)^(1/3)*e^(1/3))","C",0
248,1,1965,0,3.566126," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(8/3),x, algorithm=""maxima"")","-\frac{600 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - {\left(b^{5} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} \sin\left(a\right) + b^{5} \sin\left(a\right) \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} \cos\left(\frac{2 \, {\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\left(b^{5} \cos\left(a\right) \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + b^{5} \cos\left(a\right) \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} \sin\left(\frac{2 \, {\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} {\left(d x + c\right)}^{\frac{1}{3}} e^{\frac{1}{3}} - {\left({\left({\left(300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} d^{2} x^{2} + {\left(600 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(600 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 600 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 600 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 600 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 600 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(600 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 600 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 600 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 600 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c d x + {\left(300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c^{2}\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + {\left({\left(300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} d^{2} x^{2} + {\left(600 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(600 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 600 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 600 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 600 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 600 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(600 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 600 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 600 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 600 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c d x + {\left(300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{3} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right)^{2} \sin\left(a\right) + 300 \, {\left(\Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} - {\left(300 i \, \Gamma\left(6, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) - 300 i \, \Gamma\left(6, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{1}{3}}}}\right) + 300 i \, \Gamma\left(6, \frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 300 i \, \Gamma\left(6, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)\right)} \sin\left(a\right)^{3}\right)} c^{2}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)} e^{\frac{1}{3}}}{2000 \, {\left({\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} d^{3} e^{3} x^{2} + 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} c d^{2} e^{3} x + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} c^{2} d e^{3}\right)} \cos\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2} + {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} d^{3} e^{3} x^{2} + 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} c d^{2} e^{3} x + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{5} c^{2} d e^{3}\right)} \sin\left(\frac{{\left(d x + c\right)}^{\frac{1}{3}} a + b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)^{2}\right)}}"," ",0,"-1/2000*(600*((cos(a)^2 + sin(a)^2)*b^5*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) - (b^5*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2*sin(a) + b^5*sin(a)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*cos((2*(d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)) + (b^5*cos(a)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + b^5*cos(a)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*sin((2*(d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3)))*(d*x + c)^(1/3)*e^(1/3) - (((300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*d^2*x^2 + (600*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (600*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 600*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 600*I*gamma(6, I*b/(d*x + c)^(1/3)) - 600*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 600*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (600*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 600*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 600*I*gamma(6, I*b/(d*x + c)^(1/3)) - 600*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c*d*x + (300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c^2)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + ((300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*d^2*x^2 + (600*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (600*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 600*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 600*I*gamma(6, I*b/(d*x + c)^(1/3)) - 600*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 600*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (600*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 600*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 600*I*gamma(6, I*b/(d*x + c)^(1/3)) - 600*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c*d*x + (300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^3 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)^2*sin(a) + 300*(gamma(6, I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + gamma(6, I*b/(d*x + c)^(1/3)) + gamma(6, -I*b/(d*x + c)^(1/3)))*cos(a)*sin(a)^2 - (300*I*gamma(6, I*b*conjugate((d*x + c)^(-1/3))) - 300*I*gamma(6, -I*b*conjugate((d*x + c)^(-1/3))) + 300*I*gamma(6, I*b/(d*x + c)^(1/3)) - 300*I*gamma(6, -I*b/(d*x + c)^(1/3)))*sin(a)^3)*c^2)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)*e^(1/3))/(((cos(a)^2 + sin(a)^2)*b^5*d^3*e^3*x^2 + 2*(cos(a)^2 + sin(a)^2)*b^5*c*d^2*e^3*x + (cos(a)^2 + sin(a)^2)*b^5*c^2*d*e^3)*cos(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2 + ((cos(a)^2 + sin(a)^2)*b^5*d^3*e^3*x^2 + 2*(cos(a)^2 + sin(a)^2)*b^5*c*d^2*e^3*x + (cos(a)^2 + sin(a)^2)*b^5*c^2*d*e^3)*sin(((d*x + c)^(1/3)*a + b)/(d*x + c)^(1/3))^2)","C",0
249,1,1119,0,2.539796," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{{\left({\left({\left({\left(3 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} d^{2} e^{\frac{4}{3}} x^{2} + {\left({\left({\left(6 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 6 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-6 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 6 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - 6 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 6 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(6 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 6 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(6 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 6 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(6 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 6 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} c d e^{\frac{4}{3}} x + {\left({\left({\left(3 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} c^{2} e^{\frac{4}{3}}\right)} {\left(d x + c\right)}^{\frac{1}{3}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)^{\frac{7}{2}}}{8 \, d}"," ",0,"1/8*((((3*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + (-3*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) - 3*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*sin(a))*d^2*e^(4/3)*x^2 + (((6*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 6*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + (-6*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + 6*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) - 6*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + 6*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*cos(a) + (6*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + 6*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) + (6*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 6*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + (6*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) - 6*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*sin(a))*c*d*e^(4/3)*x + (((3*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + (-3*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) - 3*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(-7/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(-7/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*sin(a))*c^2*e^(4/3))*(d*x + c)^(1/3)*(b/(d*x + c)^(2/3))^(7/2)/d","C",0
250,1,749,0,2.047597," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","\frac{{\left({\left({\left({\left(3 i \, \Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} d e^{\frac{2}{3}} x + {\left({\left({\left(3 i \, \Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} c e^{\frac{2}{3}}\right)} {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)^{\frac{5}{2}}}{8 \, d}"," ",0,"1/8*((((3*I*gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + (-3*I*gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) - 3*(gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) + (3*I*gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) + (3*I*gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*sin(a))*d*e^(2/3)*x + (((3*I*gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + (-3*I*gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) - 3*(gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) + (3*I*gamma(-5/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) + (3*I*gamma(-5/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*sin(a))*c*e^(2/3))*(d*x + c)^(2/3)*(b/(d*x + c)^(2/3))^(5/2)/d","C",0
251,1,129,0,0.579917," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""maxima"")","-\frac{{\left({\left(3 i \, \Gamma\left(-2, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-2, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-2, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-2, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(-2, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-2, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-2, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-2, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)\right)} b^{2} e^{\frac{1}{3}}}{8 \, d}"," ",0,"-1/8*((3*I*gamma(-2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-2, I*b/(d*x + c)^(2/3)) - 3*I*gamma(-2, -I*b/(d*x + c)^(2/3)))*cos(a) + 3*(gamma(-2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-2, I*b/(d*x + c)^(2/3)) + gamma(-2, -I*b/(d*x + c)^(2/3)))*sin(a))*b^2*e^(1/3)/d","C",0
252,1,128,0,0.657796," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(1/3),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(\Gamma\left(-1, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-1, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-1, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(-1, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) - {\left(3 i \, \Gamma\left(-1, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-1, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-1, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(-1, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)\right)} b}{8 \, d e^{\frac{1}{3}}}"," ",0,"-1/8*(3*(gamma(-1, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1, I*b/(d*x + c)^(2/3)) + gamma(-1, -I*b/(d*x + c)^(2/3)))*cos(a) - (3*I*gamma(-1, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-1, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-1, I*b/(d*x + c)^(2/3)) - 3*I*gamma(-1, -I*b/(d*x + c)^(2/3)))*sin(a))*b/(d*e^(1/3))","C",0
253,1,383,0,1.534549," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(2/3),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{\frac{1}{3}} {\left({\left({\left(3 i \, \Gamma\left(-\frac{1}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \Gamma\left(-\frac{1}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(-\frac{1}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(-\frac{1}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{1}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{1}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{1}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\Gamma\left(-\frac{1}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{1}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(-\frac{1}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(-\frac{1}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{1}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(-\frac{1}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(-\frac{1}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} \sqrt{\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}}}{8 \, d e^{\frac{2}{3}}}"," ",0,"1/8*(d*x + c)^(1/3)*(((3*I*gamma(-1/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-1/2, -I*b/(d*x + c)^(2/3)))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*gamma(-1/2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(-1/2, I*b/(d*x + c)^(2/3)))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) - 3*(gamma(-1/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1/2, -I*b/(d*x + c)^(2/3)))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(gamma(-1/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1/2, I*b/(d*x + c)^(2/3)))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*cos(a) + (3*(gamma(-1/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1/2, -I*b/(d*x + c)^(2/3)))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(gamma(-1/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(-1/2, I*b/(d*x + c)^(2/3)))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) + (3*I*gamma(-1/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-1/2, -I*b/(d*x + c)^(2/3)))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) + (3*I*gamma(-1/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(-1/2, I*b/(d*x + c)^(2/3)))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*sin(a))*sqrt(b/(d*x + c)^(2/3))/(d*e^(2/3))","C",0
254,1,487,0,1.119014," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(4/3),x, algorithm=""maxima"")","-\frac{{\left({\left(3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} - 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) + {\left(3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \cos\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(-3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}}\right) - 1\right)} + 3 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 1\right)}\right)} \sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)}{8 \, {\left(d x + c\right)}^{\frac{1}{3}} d e^{\frac{4}{3}} \sqrt{\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}}}"," ",0,"-1/8*(((3*I*sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(-2/3)))) - 1) - 3*I*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(-2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(-2/3)))) - 1) + sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) - 3*(sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(-2/3)))) - 1) + sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*cos(a) + (3*(sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(-2/3)))) - 1) + sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*cos(1/4*pi + 1/3*arctan2(0, d*x + c)) + 3*(sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(-2/3)))) - 1) + sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1))*cos(-1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*sqrt(pi)*(erf(sqrt(I*b*conjugate((d*x + c)^(-2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(-I*b/(d*x + c)^(2/3))) - 1))*sin(1/4*pi + 1/3*arctan2(0, d*x + c)) + (-3*I*sqrt(pi)*(erf(sqrt(-I*b*conjugate((d*x + c)^(-2/3)))) - 1) + 3*I*sqrt(pi)*(erf(sqrt(I*b/(d*x + c)^(2/3))) - 1))*sin(-1/4*pi + 1/3*arctan2(0, d*x + c)))*sin(a))/((d*x + c)^(1/3)*d*e^(4/3)*sqrt(b/(d*x + c)^(2/3)))","C",0
255,1,31,0,0.335197," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(5/3),x, algorithm=""maxima"")","\frac{3 \, \cos\left(\frac{{\left(d x + c\right)}^{\frac{2}{3}} a + b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)}{2 \, b d e^{\frac{5}{3}}}"," ",0,"3/2*cos(((d*x + c)^(2/3)*a + b)/(d*x + c)^(2/3))/(b*d*e^(5/3))","A",0
256,1,129,0,0.663712," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(7/3),x, algorithm=""maxima"")","-\frac{{\left(3 i \, \Gamma\left(2, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(2, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(2, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 3 i \, \Gamma\left(2, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(a\right) + 3 \, {\left(\Gamma\left(2, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(2, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(2, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + \Gamma\left(2, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(a\right)}{8 \, b^{2} d e^{\frac{7}{3}}}"," ",0,"-1/8*((3*I*gamma(2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(2, -I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(2, I*b/(d*x + c)^(2/3)) - 3*I*gamma(2, -I*b/(d*x + c)^(2/3)))*cos(a) + 3*(gamma(2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(2, I*b/(d*x + c)^(2/3)) + gamma(2, -I*b/(d*x + c)^(2/3)))*sin(a))/(b^2*d*e^(7/3))","C",0
257,1,414,0,1.167324," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(8/3),x, algorithm=""maxima"")","-\frac{{\left(d x + c\right)}^{\frac{1}{3}} {\left({\left({\left(-3 i \, \Gamma\left(\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) - {\left(3 \, {\left(\Gamma\left(\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(\frac{5}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{5}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(\frac{5}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{5}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{5}{4} \, \pi + \frac{5}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)\right)} e^{\frac{1}{3}}}{8 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)} \left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)^{\frac{5}{2}}}"," ",0,"-1/8*(d*x + c)^(1/3)*(((-3*I*gamma(5/2, I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + (3*I*gamma(5/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) - 3*(gamma(5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*cos(a) - (3*(gamma(5/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(5/2, -I*b/(d*x + c)^(2/3)))*cos(5/4*pi + 5/3*arctan2(0, d*x + c)) + 3*(gamma(5/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(5/2, I*b/(d*x + c)^(2/3)))*cos(-5/4*pi + 5/3*arctan2(0, d*x + c)) - (3*I*gamma(5/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(5/2, -I*b/(d*x + c)^(2/3)))*sin(5/4*pi + 5/3*arctan2(0, d*x + c)) - (3*I*gamma(5/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(5/2, I*b/(d*x + c)^(2/3)))*sin(-5/4*pi + 5/3*arctan2(0, d*x + c)))*sin(a))*e^(1/3)/((d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)*(b/(d*x + c)^(2/3))^(5/2))","C",0
258,1,411,0,0.829754," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(10/3),x, algorithm=""maxima"")","-\frac{{\left({\left(-3 i \, \Gamma\left(\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + 3 i \, \Gamma\left(\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + {\left(3 i \, \Gamma\left(\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - 3 \, {\left(\Gamma\left(\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \cos\left(a\right) - {\left(3 \, {\left(\Gamma\left(\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) + 3 \, {\left(\Gamma\left(\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) + \Gamma\left(\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \cos\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(\frac{7}{2}, i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, -\frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right) - {\left(3 i \, \Gamma\left(\frac{7}{2}, -i \, b \overline{\frac{1}{{\left(d x + c\right)}^{\frac{2}{3}}}}\right) - 3 i \, \Gamma\left(\frac{7}{2}, \frac{i \, b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)\right)} \sin\left(-\frac{7}{4} \, \pi + \frac{7}{3} \, \arctan\left(0, d x + c\right)\right)\right)} \sin\left(a\right)}{8 \, {\left(d^{3} e^{\frac{10}{3}} x^{2} + 2 \, c d^{2} e^{\frac{10}{3}} x + c^{2} d e^{\frac{10}{3}}\right)} {\left(d x + c\right)}^{\frac{1}{3}} \left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right)^{\frac{7}{2}}}"," ",0,"-1/8*(((-3*I*gamma(7/2, I*b*conjugate((d*x + c)^(-2/3))) + 3*I*gamma(7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + (3*I*gamma(7/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) - 3*(gamma(7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*cos(a) - (3*(gamma(7/2, I*b*conjugate((d*x + c)^(-2/3))) + gamma(7/2, -I*b/(d*x + c)^(2/3)))*cos(7/4*pi + 7/3*arctan2(0, d*x + c)) + 3*(gamma(7/2, -I*b*conjugate((d*x + c)^(-2/3))) + gamma(7/2, I*b/(d*x + c)^(2/3)))*cos(-7/4*pi + 7/3*arctan2(0, d*x + c)) - (3*I*gamma(7/2, I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(7/2, -I*b/(d*x + c)^(2/3)))*sin(7/4*pi + 7/3*arctan2(0, d*x + c)) - (3*I*gamma(7/2, -I*b*conjugate((d*x + c)^(-2/3))) - 3*I*gamma(7/2, I*b/(d*x + c)^(2/3)))*sin(-7/4*pi + 7/3*arctan2(0, d*x + c)))*sin(a))/((d^3*e^(10/3)*x^2 + 2*c*d^2*e^(10/3)*x + c^2*d*e^(10/3))*(d*x + c)^(1/3)*(b/(d*x + c)^(2/3))^(7/2))","C",0
259,0,0,0,0.000000," ","integrate((e*x)^m*sin(a+b*(d*x+c)^n),x, algorithm=""maxima"")","\int \left(e x\right)^{m} \sin\left({\left(d x + c\right)}^{n} b + a\right)\,{d x}"," ",0,"integrate((e*x)^m*sin((d*x + c)^n*b + a), x)","F",0
260,0,0,0,0.000000," ","integrate(x^3*sin(a+b*(d*x+c)^n),x, algorithm=""maxima"")","\int x^{3} \sin\left({\left(d x + c\right)}^{n} b + a\right)\,{d x}"," ",0,"integrate(x^3*sin((d*x + c)^n*b + a), x)","F",0
261,0,0,0,0.000000," ","integrate(x^2*sin(a+b*(d*x+c)^n),x, algorithm=""maxima"")","\int x^{2} \sin\left({\left(d x + c\right)}^{n} b + a\right)\,{d x}"," ",0,"integrate(x^2*sin((d*x + c)^n*b + a), x)","F",0
262,0,0,0,0.000000," ","integrate(x*sin(a+b*(d*x+c)^n),x, algorithm=""maxima"")","\int x \sin\left({\left(d x + c\right)}^{n} b + a\right)\,{d x}"," ",0,"integrate(x*sin((d*x + c)^n*b + a), x)","F",0
263,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^n),x, algorithm=""maxima"")","\int \sin\left({\left(d x + c\right)}^{n} b + a\right)\,{d x}"," ",0,"integrate(sin((d*x + c)^n*b + a), x)","F",0
264,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^n)/x,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{n} b + a\right)}{x}\,{d x}"," ",0,"integrate(sin((d*x + c)^n*b + a)/x, x)","F",0
265,0,0,0,0.000000," ","integrate(sin(a+b*(d*x+c)^n)/x^2,x, algorithm=""maxima"")","\int \frac{\sin\left({\left(d x + c\right)}^{n} b + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(sin((d*x + c)^n*b + a)/x^2, x)","F",0
266,0,0,0,0.000000," ","integrate(x^3*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + b \int x^{3} \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"1/4*a*x^4 + b*integrate(x^3*sin((g*x + f)^n*d + c), x)","F",0
267,0,0,0,0.000000," ","integrate(x^2*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + b \int x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"1/3*a*x^3 + b*integrate(x^2*sin((g*x + f)^n*d + c), x)","F",0
268,0,0,0,0.000000," ","integrate(x*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + b \int x \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"1/2*a*x^2 + b*integrate(x*sin((g*x + f)^n*d + c), x)","F",0
269,0,0,0,0.000000," ","integrate(a+b*sin(c+d*(g*x+f)^n),x, algorithm=""maxima"")","a x + b \int \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"a*x + b*integrate(sin((g*x + f)^n*d + c), x)","F",0
270,0,0,0,0.000000," ","integrate((a+b*sin(c+d*(g*x+f)^n))/x,x, algorithm=""maxima"")","b \int \frac{\sin\left({\left(g x + f\right)}^{n} d + c\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(sin((g*x + f)^n*d + c)/x, x) + a*log(x)","F",0
271,0,0,0,0.000000," ","integrate((a+b*sin(c+d*(g*x+f)^n))/x^2,x, algorithm=""maxima"")","b \int \frac{\sin\left({\left(g x + f\right)}^{n} d + c\right)}{x^{2}}\,{d x} - \frac{a}{x}"," ",0,"b*integrate(sin((g*x + f)^n*d + c)/x^2, x) - a/x","F",0
272,0,0,0,0.000000," ","integrate(x^2*(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{6} \, b^{2} x^{3} - \frac{1}{2} \, b^{2} \int x^{2} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\,{d x} + 2 \, a b \int x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"1/3*a^2*x^3 + 1/6*b^2*x^3 - 1/2*b^2*integrate(x^2*cos(2*(g*x + f)^n*d + 2*c), x) + 2*a*b*integrate(x^2*sin((g*x + f)^n*d + c), x)","F",0
273,0,0,0,0.000000," ","integrate(x*(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{1}{4} \, b^{2} x^{2} - \frac{1}{2} \, b^{2} \int x \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\,{d x} + 2 \, a b \int x \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"1/2*a^2*x^2 + 1/4*b^2*x^2 - 1/2*b^2*integrate(x*cos(2*(g*x + f)^n*d + 2*c), x) + 2*a*b*integrate(x*sin((g*x + f)^n*d + c), x)","F",0
274,0,0,0,0.000000," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","a^{2} x + \frac{1}{2} \, b^{2} x - \frac{1}{2} \, b^{2} \int \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\,{d x} + 2 \, a b \int \sin\left({\left(g x + f\right)}^{n} d + c\right)\,{d x}"," ",0,"a^2*x + 1/2*b^2*x - 1/2*b^2*integrate(cos(2*(g*x + f)^n*d + 2*c), x) + 2*a*b*integrate(sin((g*x + f)^n*d + c), x)","F",0
275,0,0,0,0.000000," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2/x,x, algorithm=""maxima"")","-\frac{1}{2} \, b^{2} \int \frac{\cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{x}\,{d x} + 2 \, a b \int \frac{\sin\left({\left(g x + f\right)}^{n} d + c\right)}{x}\,{d x} + a^{2} \log\left(x\right) + \frac{1}{2} \, b^{2} \log\left(x\right)"," ",0,"-1/2*b^2*integrate(cos(2*(g*x + f)^n*d + 2*c)/x, x) + 2*a*b*integrate(sin((g*x + f)^n*d + c)/x, x) + a^2*log(x) + 1/2*b^2*log(x)","F",0
276,0,0,0,0.000000," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2/x^2,x, algorithm=""maxima"")","-\frac{a^{2}}{x} - \frac{b^{2} x \int \frac{\cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{x^{2}}\,{d x} - 4 \, a b x \int \frac{\sin\left({\left(g x + f\right)}^{n} d + c\right)}{x^{2}}\,{d x} + b^{2}}{2 \, x}"," ",0,"-a^2/x - 1/2*(b^2*x*integrate(cos(2*(g*x + f)^n*d + 2*c)/x^2, x) - 4*a*b*x*integrate(sin((g*x + f)^n*d + c)/x^2, x) + b^2)/x","F",0
277,0,0,0,0.000000," ","integrate(x^2/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\int \frac{x^{2}}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}\,{d x}"," ",0,"integrate(x^2/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
278,0,0,0,0.000000," ","integrate(x/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\int \frac{x}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}\,{d x}"," ",0,"integrate(x/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
279,0,0,0,0.000000," ","integrate(1/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
280,0,0,0,0.000000," ","integrate(1/x/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*sin((g*x + f)^n*d + c) + a)*x), x)","F",0
281,0,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*sin((g*x + f)^n*d + c) + a)*x^2), x)","F",0
282,0,0,0,0.000000," ","integrate(x^2/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a b g x^{3} + a b f x^{2}\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left(a b g x^{3} + a b f x^{2}\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\right)} \int \frac{2 \, {\left(g x + f\right)}^{n} a^{2} d g n x^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, {\left(g x + f\right)}^{n} a^{2} d g n x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + {\left(g x + f\right)}^{n} a b d g n x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left({\left(g x + f\right)}^{n} a b d g n x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(2 \, a b f x - {\left(a b g n - 3 \, a b g\right)} x^{2}\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right)\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) - {\left(2 \, a b f x - {\left(a b g n - 3 \, a b g\right)} x^{2}\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + {\left({\left(g x + f\right)}^{n} a b d g n x^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right) - 2 \, b^{2} f x + {\left(b^{2} g n - 3 \, b^{2} g\right)} x^{2} - {\left(2 \, a b f x - {\left(a b g n - 3 \, a b g\right)} x^{2}\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}\,{d x} + 2 \, {\left(b^{2} g x^{3} + b^{2} f x^{2} + {\left(a b g x^{3} + a b f x^{2}\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}"," ",0,"(2*(a*b*g*x^3 + a*b*f*x^2)*cos(2*(g*x + f)^n*d + 2*c)*cos((g*x + f)^n*d + c) + 2*(a*b*g*x^3 + a*b*f*x^2)*cos((g*x + f)^n*d + c) - ((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))*integrate(-2*(2*(g*x + f)^n*a^2*d*g*n*x^2*cos((g*x + f)^n*d + c)^2 + 2*(g*x + f)^n*a^2*d*g*n*x^2*sin((g*x + f)^n*d + c)^2 + (g*x + f)^n*a*b*d*g*n*x^2*sin((g*x + f)^n*d + c) - ((g*x + f)^n*a*b*d*g*n*x^2*sin((g*x + f)^n*d + c) + (2*a*b*f*x - (a*b*g*n - 3*a*b*g)*x^2)*cos((g*x + f)^n*d + c))*cos(2*(g*x + f)^n*d + 2*c) - (2*a*b*f*x - (a*b*g*n - 3*a*b*g)*x^2)*cos((g*x + f)^n*d + c) + ((g*x + f)^n*a*b*d*g*n*x^2*cos((g*x + f)^n*d + c) - 2*b^2*f*x + (b^2*g*n - 3*b^2*g)*x^2 - (2*a*b*f*x - (a*b*g*n - 3*a*b*g)*x^2)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c)), x) + 2*(b^2*g*x^3 + b^2*f*x^2 + (a*b*g*x^3 + a*b*f*x^2)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))","F",0
283,0,0,0,0.000000," ","integrate(x/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a b g x^{2} + a b f x\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left(a b g x^{2} + a b f x\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\right)} \int \frac{2 \, {\left(g x + f\right)}^{n} a^{2} d g n x \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, {\left(g x + f\right)}^{n} a^{2} d g n x \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + {\left(g x + f\right)}^{n} a b d g n x \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left({\left(g x + f\right)}^{n} a b d g n x \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a b f - {\left(a b g n - 2 \, a b g\right)} x\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right)\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) - {\left(a b f - {\left(a b g n - 2 \, a b g\right)} x\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + {\left({\left(g x + f\right)}^{n} a b d g n x \cos\left({\left(g x + f\right)}^{n} d + c\right) - b^{2} f + {\left(b^{2} g n - 2 \, b^{2} g\right)} x - {\left(a b f - {\left(a b g n - 2 \, a b g\right)} x\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}\,{d x} + 2 \, {\left(b^{2} g x^{2} + b^{2} f x + {\left(a b g x^{2} + a b f x\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}"," ",0,"(2*(a*b*g*x^2 + a*b*f*x)*cos(2*(g*x + f)^n*d + 2*c)*cos((g*x + f)^n*d + c) + 2*(a*b*g*x^2 + a*b*f*x)*cos((g*x + f)^n*d + c) - ((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))*integrate(-2*(2*(g*x + f)^n*a^2*d*g*n*x*cos((g*x + f)^n*d + c)^2 + 2*(g*x + f)^n*a^2*d*g*n*x*sin((g*x + f)^n*d + c)^2 + (g*x + f)^n*a*b*d*g*n*x*sin((g*x + f)^n*d + c) - ((g*x + f)^n*a*b*d*g*n*x*sin((g*x + f)^n*d + c) + (a*b*f - (a*b*g*n - 2*a*b*g)*x)*cos((g*x + f)^n*d + c))*cos(2*(g*x + f)^n*d + 2*c) - (a*b*f - (a*b*g*n - 2*a*b*g)*x)*cos((g*x + f)^n*d + c) + ((g*x + f)^n*a*b*d*g*n*x*cos((g*x + f)^n*d + c) - b^2*f + (b^2*g*n - 2*b^2*g)*x - (a*b*f - (a*b*g*n - 2*a*b*g)*x)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c)), x) + 2*(b^2*g*x^2 + b^2*f*x + (a*b*g*x^2 + a*b*f*x)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))","F",0
284,0,0,0,0.000000," ","integrate(1/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a b g x + a b f\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left(a b g x + a b f\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)\right)} \int \frac{2 \, {\left(g x + f\right)}^{n} a^{2} d n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, {\left(g x + f\right)}^{n} a^{2} d n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + {\left(g x + f\right)}^{n} a b d n \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left({\left(g x + f\right)}^{n} a b d n \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left(a b n - a b\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right)\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a b n - a b\right)} \cos\left({\left(g x + f\right)}^{n} d + c\right) + {\left({\left(g x + f\right)}^{n} a b d n \cos\left({\left(g x + f\right)}^{n} d + c\right) + b^{2} n - b^{2} + {\left(a b n - a b\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}\,{d x} + 2 \, {\left(b^{2} g x + b^{2} f + {\left(a b g x + a b f\right)} \sin\left({\left(g x + f\right)}^{n} d + c\right)\right)} \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \cos\left({\left(g x + f\right)}^{n} d + c\right) \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n \sin\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} {\left(g x + f\right)}^{n} d g n \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} {\left(g x + f\right)}^{n} d g n\right)} \cos\left(2 \, {\left(g x + f\right)}^{n} d + 2 \, c\right)}"," ",0,"(2*(a*b*g*x + a*b*f)*cos(2*(g*x + f)^n*d + 2*c)*cos((g*x + f)^n*d + c) + 2*(a*b*g*x + a*b*f)*cos((g*x + f)^n*d + c) - ((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))*integrate(-2*(2*(g*x + f)^n*a^2*d*n*cos((g*x + f)^n*d + c)^2 + 2*(g*x + f)^n*a^2*d*n*sin((g*x + f)^n*d + c)^2 + (g*x + f)^n*a*b*d*n*sin((g*x + f)^n*d + c) - ((g*x + f)^n*a*b*d*n*sin((g*x + f)^n*d + c) - (a*b*n - a*b)*cos((g*x + f)^n*d + c))*cos(2*(g*x + f)^n*d + 2*c) + (a*b*n - a*b)*cos((g*x + f)^n*d + c) + ((g*x + f)^n*a*b*d*n*cos((g*x + f)^n*d + c) + b^2*n - b^2 + (a*b*n - a*b)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*n)*cos(2*(g*x + f)^n*d + 2*c)), x) + 2*(b^2*g*x + b^2*f + (a*b*g*x + a*b*f)*sin((g*x + f)^n*d + c))*sin(2*(g*x + f)^n*d + 2*c))/((a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*cos(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*cos((g*x + f)^n*d + c)*sin(2*(g*x + f)^n*d + 2*c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n*sin(2*(g*x + f)^n*d + 2*c)^2 + 4*(a^4 - a^2*b^2)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c)^2 + 4*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n - 2*(2*(a^3*b - a*b^3)*(g*x + f)^n*d*g*n*sin((g*x + f)^n*d + c) + (a^2*b^2 - b^4)*(g*x + f)^n*d*g*n)*cos(2*(g*x + f)^n*d + 2*c))","F",0
285,-1,0,0,0.000000," ","integrate(1/x/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sin(c+d*(g*x+f)^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sin((g*x + f)^n*d + c) + a)^p, x)","F",0
288,1,258,0,0.550590," ","integrate((f*x+e)^2*(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} - \frac{1}{2} \, {\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d - 2 \, x \sin\left(\frac{c x + d}{x}\right)\right)} b e^{2} + \frac{1}{2} \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) + {\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d^{2} + 2 \, d x \cos\left(\frac{c x + d}{x}\right) + 2 \, x^{2} \sin\left(\frac{c x + d}{x}\right)\right)} b e f + \frac{1}{12} \, {\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) + {\left(i \, {\rm Ei}\left(\frac{i \, d}{x}\right) - i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d^{3} + 2 \, d x^{2} \cos\left(\frac{c x + d}{x}\right) - 2 \, {\left(d^{2} x - 2 \, x^{3}\right)} \sin\left(\frac{c x + d}{x}\right)\right)} b f^{2} + a e^{2} x"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 - 1/2*(((Ei(I*d/x) + Ei(-I*d/x))*cos(c) - (-I*Ei(I*d/x) + I*Ei(-I*d/x))*sin(c))*d - 2*x*sin((c*x + d)/x))*b*e^2 + 1/2*(((-I*Ei(I*d/x) + I*Ei(-I*d/x))*cos(c) + (Ei(I*d/x) + Ei(-I*d/x))*sin(c))*d^2 + 2*d*x*cos((c*x + d)/x) + 2*x^2*sin((c*x + d)/x))*b*e*f + 1/12*(((Ei(I*d/x) + Ei(-I*d/x))*cos(c) + (I*Ei(I*d/x) - I*Ei(-I*d/x))*sin(c))*d^3 + 2*d*x^2*cos((c*x + d)/x) - 2*(d^2*x - 2*x^3)*sin((c*x + d)/x))*b*f^2 + a*e^2*x","C",0
289,1,153,0,0.427873," ","integrate((f*x+e)*(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\frac{1}{2} \, a f x^{2} - \frac{1}{2} \, {\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d - 2 \, x \sin\left(\frac{c x + d}{x}\right)\right)} b e + \frac{1}{4} \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) + {\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d^{2} + 2 \, d x \cos\left(\frac{c x + d}{x}\right) + 2 \, x^{2} \sin\left(\frac{c x + d}{x}\right)\right)} b f + a e x"," ",0,"1/2*a*f*x^2 - 1/2*(((Ei(I*d/x) + Ei(-I*d/x))*cos(c) - (-I*Ei(I*d/x) + I*Ei(-I*d/x))*sin(c))*d - 2*x*sin((c*x + d)/x))*b*e + 1/4*(((-I*Ei(I*d/x) + I*Ei(-I*d/x))*cos(c) + (Ei(I*d/x) + Ei(-I*d/x))*sin(c))*d^2 + 2*d*x*cos((c*x + d)/x) + 2*x^2*sin((c*x + d)/x))*b*f + a*e*x","C",0
290,1,65,0,0.364462," ","integrate(a+b*sin(c+d/x),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d - 2 \, x \sin\left(\frac{c x + d}{x}\right)\right)} b + a x"," ",0,"-1/2*(((Ei(I*d/x) + Ei(-I*d/x))*cos(c) - (-I*Ei(I*d/x) + I*Ei(-I*d/x))*sin(c))*d - 2*x*sin((c*x + d)/x))*b + a*x","C",0
291,0,0,0,0.000000," ","integrate((a+b*sin(c+d/x))/(f*x+e),x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left({\left(f x + e\right)} \cos\left(\frac{c x + d}{x}\right)^{2} + {\left(f x + e\right)} \sin\left(\frac{c x + d}{x}\right)^{2}\right)}}\,{d x} + \int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left(f x + e\right)}}\,{d x}\right)} + \frac{a \log\left(f x + e\right)}{f}"," ",0,"b*(integrate(1/2*sin((c*x + d)/x)/((f*x + e)*cos((c*x + d)/x)^2 + (f*x + e)*sin((c*x + d)/x)^2), x) + integrate(1/2*sin((c*x + d)/x)/(f*x + e), x)) + a*log(f*x + e)/f","F",0
292,0,0,0,0.000000," ","integrate((a+b*sin(c+d/x))/(f*x+e)^2,x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)}}\,{d x} + \int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} \cos\left(\frac{c x + d}{x}\right)^{2} + {\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} \sin\left(\frac{c x + d}{x}\right)^{2}\right)}}\,{d x}\right)} - \frac{a}{f^{2} x + e f}"," ",0,"b*(integrate(1/2*sin((c*x + d)/x)/(f^2*x^2 + 2*e*f*x + e^2), x) + integrate(1/2*sin((c*x + d)/x)/((f^2*x^2 + 2*e*f*x + e^2)*cos((c*x + d)/x)^2 + (f^2*x^2 + 2*e*f*x + e^2)*sin((c*x + d)/x)^2), x)) - a/(f^2*x + e*f)","F",0
293,0,0,0,0.000000," ","integrate((a+b*sin(c+d/x))/(f*x+e)^3,x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)}}\,{d x} + \int \frac{\sin\left(\frac{c x + d}{x}\right)}{2 \, {\left({\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} \cos\left(\frac{c x + d}{x}\right)^{2} + {\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} \sin\left(\frac{c x + d}{x}\right)^{2}\right)}}\,{d x}\right)} - \frac{a}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"b*(integrate(1/2*sin((c*x + d)/x)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x) + integrate(1/2*sin((c*x + d)/x)/((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*cos((c*x + d)/x)^2 + (f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*sin((c*x + d)/x)^2), x)) - 1/2*a/(f^3*x^2 + 2*e*f^2*x + e^2*f)","F",0
294,1,322,0,0.561423," ","integrate((f*x+e)*(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} f x^{2} - {\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d - 2 \, x \sin\left(\frac{c x + d}{x}\right)\right)} a b e - \frac{1}{2} \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{2 i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \cos\left(2 \, c\right) + {\left({\rm Ei}\left(\frac{2 i \, d}{x}\right) + {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \sin\left(2 \, c\right)\right)} d + x \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) - x\right)} b^{2} e + \frac{1}{2} \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) + {\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d^{2} + 2 \, d x \cos\left(\frac{c x + d}{x}\right) + 2 \, x^{2} \sin\left(\frac{c x + d}{x}\right)\right)} a b f - \frac{1}{4} \, {\left({\left(2 \, {\left({\rm Ei}\left(\frac{2 i \, d}{x}\right) + {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \cos\left(2 \, c\right) - {\left(-2 i \, {\rm Ei}\left(\frac{2 i \, d}{x}\right) + 2 i \, {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \sin\left(2 \, c\right)\right)} d^{2} + x^{2} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) - 2 \, d x \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) - x^{2}\right)} b^{2} f + a^{2} e x"," ",0,"1/2*a^2*f*x^2 - (((Ei(I*d/x) + Ei(-I*d/x))*cos(c) - (-I*Ei(I*d/x) + I*Ei(-I*d/x))*sin(c))*d - 2*x*sin((c*x + d)/x))*a*b*e - 1/2*(((-I*Ei(2*I*d/x) + I*Ei(-2*I*d/x))*cos(2*c) + (Ei(2*I*d/x) + Ei(-2*I*d/x))*sin(2*c))*d + x*cos(2*(c*x + d)/x) - x)*b^2*e + 1/2*(((-I*Ei(I*d/x) + I*Ei(-I*d/x))*cos(c) + (Ei(I*d/x) + Ei(-I*d/x))*sin(c))*d^2 + 2*d*x*cos((c*x + d)/x) + 2*x^2*sin((c*x + d)/x))*a*b*f - 1/4*((2*(Ei(2*I*d/x) + Ei(-2*I*d/x))*cos(2*c) - (-2*I*Ei(2*I*d/x) + 2*I*Ei(-2*I*d/x))*sin(2*c))*d^2 + x^2*cos(2*(c*x + d)/x) - 2*d*x*sin(2*(c*x + d)/x) - x^2)*b^2*f + a^2*e*x","C",0
295,1,137,0,0.432442," ","integrate((a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","-{\left({\left({\left({\rm Ei}\left(\frac{i \, d}{x}\right) + {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \cos\left(c\right) - {\left(-i \, {\rm Ei}\left(\frac{i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{i \, d}{x}\right)\right)} \sin\left(c\right)\right)} d - 2 \, x \sin\left(\frac{c x + d}{x}\right)\right)} a b - \frac{1}{2} \, {\left({\left({\left(-i \, {\rm Ei}\left(\frac{2 i \, d}{x}\right) + i \, {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \cos\left(2 \, c\right) + {\left({\rm Ei}\left(\frac{2 i \, d}{x}\right) + {\rm Ei}\left(-\frac{2 i \, d}{x}\right)\right)} \sin\left(2 \, c\right)\right)} d + x \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) - x\right)} b^{2} + a^{2} x"," ",0,"-(((Ei(I*d/x) + Ei(-I*d/x))*cos(c) - (-I*Ei(I*d/x) + I*Ei(-I*d/x))*sin(c))*d - 2*x*sin((c*x + d)/x))*a*b - 1/2*(((-I*Ei(2*I*d/x) + I*Ei(-2*I*d/x))*cos(2*c) + (Ei(2*I*d/x) + Ei(-2*I*d/x))*sin(2*c))*d + x*cos(2*(c*x + d)/x) - x)*b^2 + a^2*x","C",0
296,0,0,0,0.000000," ","integrate((a+b*sin(c+d/x))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} - \frac{\frac{1}{2} \, b^{2} f \int \frac{\cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{{\left(f x + e\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + {\left(f x + e\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2}}\,{d x} + \frac{1}{2} \, b^{2} f \int \frac{\cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{f x + e}\,{d x} - 2 \, a b f \int \frac{\sin\left(c + \frac{d}{x}\right)}{{\left(f x + e\right)} {\left(\cos\left(c + \frac{d}{x}\right)^{2} + \sin\left(c + \frac{d}{x}\right)^{2}\right)}}\,{d x} - b^{2} \log\left(f x + e\right) - \frac{2 \, {\left(d \operatorname{Ci}\left({\left(d f - c e + \frac{{\left(c x + d\right)} e}{x}\right)} e^{\left(-1\right)}\right) \sin\left(-{\left(d f - c e\right)} e^{\left(-1\right)}\right) - d \operatorname{Ci}\left(-c + \frac{c x + d}{x}\right) \sin\left(c\right) - d \cos\left(-{\left(d f - c e\right)} e^{\left(-1\right)}\right) \operatorname{Si}\left(-{\left(d f - c e + \frac{{\left(c x + d\right)} e}{x}\right)} e^{\left(-1\right)}\right) + d \cos\left(c\right) \operatorname{Si}\left(c - \frac{c x + d}{x}\right)\right)} a b}{d}}{2 \, f}"," ",0,"a^2*log(f*x + e)/f - 1/2*(2*b^2*f*integrate(1/4*cos(2*(c*x + d)/x)/((f*x + e)*cos(2*(c*x + d)/x)^2 + (f*x + e)*sin(2*(c*x + d)/x)^2), x) + 2*b^2*f*integrate(1/4*cos(2*(c*x + d)/x)/(f*x + e), x) - 2*a*b*f*integrate(sin((c*x + d)/x)/((f*x + e)*cos((c*x + d)/x)^2 + (f*x + e)*sin((c*x + d)/x)^2), x) - 2*a*b*f*integrate(sin((c*x + d)/x)/(f*x + e), x) - b^2*log(f*x + e))/f","F",0
297,-1,0,0,0.000000," ","integrate((a+b*sin(c+d/x))^2/(f*x+e)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((a+b*sin(c+d/x))^2/(f*x+e)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,0,0,0,0.000000," ","integrate((f*x+e)^2/(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{2}}{b \sin\left(c + \frac{d}{x}\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^2/(b*sin(c + d/x) + a), x)","F",0
300,0,0,0,0.000000," ","integrate((f*x+e)/(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\int \frac{f x + e}{b \sin\left(c + \frac{d}{x}\right) + a}\,{d x}"," ",0,"integrate((f*x + e)/(b*sin(c + d/x) + a), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(c + \frac{d}{x}\right) + a}\,{d x}"," ",0,"integrate(1/(b*sin(c + d/x) + a), x)","F",0
302,0,0,0,0.000000," ","integrate((f*x+e)/(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\int \frac{f x + e}{b \sin\left(c + \frac{d}{x}\right) + a}\,{d x}"," ",0,"integrate((f*x + e)/(b*sin(c + d/x) + a), x)","F",0
303,0,0,0,0.000000," ","integrate((f*x+e)^2/(a+b*sin(c+d/x)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{2}}{b \sin\left(c + \frac{d}{x}\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^2/(b*sin(c + d/x) + a), x)","F",0
304,-1,0,0,0.000000," ","integrate((f*x+e)^2/(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,0,0,0,0.000000," ","integrate((f*x+e)/(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a b f x^{3} + a b e x^{2}\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) \cos\left(\frac{c x + d}{x}\right) + 2 \, {\left(a b f x^{3} + a b e x^{2}\right)} \cos\left(\frac{c x + d}{x}\right) - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)\right)} \int \frac{2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(\frac{c x + d}{x}\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \sin\left(\frac{c x + d}{x}\right)^{2} + {\left({\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \cos\left(\frac{c x + d}{x}\right) - {\left(a b d f x + a b d e\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \cos\left(\frac{c x + d}{x}\right) + {\left(3 \, b^{2} f x^{2} + 2 \, b^{2} e x + {\left(a b d f x + a b d e\right)} \cos\left(\frac{c x + d}{x}\right) + {\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a b d f x + a b d e\right)} \sin\left(\frac{c x + d}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}\,{d x} + 2 \, {\left(b^{2} f x^{3} + b^{2} e x^{2} + {\left(a b f x^{3} + a b e x^{2}\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}"," ",0,"-(2*(a*b*f*x^3 + a*b*e*x^2)*cos(2*(c*x + d)/x)*cos((c*x + d)/x) + 2*(a*b*f*x^3 + a*b*e*x^2)*cos((c*x + d)/x) + ((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))*integrate(-2*(2*(a^2*d*f*x + a^2*d*e)*cos((c*x + d)/x)^2 + 2*(a^2*d*f*x + a^2*d*e)*sin((c*x + d)/x)^2 + ((3*a*b*f*x^2 + 2*a*b*e*x)*cos((c*x + d)/x) - (a*b*d*f*x + a*b*d*e)*sin((c*x + d)/x))*cos(2*(c*x + d)/x) + (3*a*b*f*x^2 + 2*a*b*e*x)*cos((c*x + d)/x) + (3*b^2*f*x^2 + 2*b^2*e*x + (a*b*d*f*x + a*b*d*e)*cos((c*x + d)/x) + (3*a*b*f*x^2 + 2*a*b*e*x)*sin((c*x + d)/x))*sin(2*(c*x + d)/x) + (a*b*d*f*x + a*b*d*e)*sin((c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x)), x) + 2*(b^2*f*x^3 + b^2*e*x^2 + (a*b*f*x^3 + a*b*e*x^2)*sin((c*x + d)/x))*sin(2*(c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))","F",0
306,0,0,0,0.000000," ","integrate(1/(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","-\frac{2 \, a b x^{2} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) \cos\left(\frac{c x + d}{x}\right) + 2 \, a b x^{2} \cos\left(\frac{c x + d}{x}\right) - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)\right)} \int \frac{2 \, a^{2} d \cos\left(\frac{c x + d}{x}\right)^{2} + 2 \, a^{2} d \sin\left(\frac{c x + d}{x}\right)^{2} + 2 \, a b x \cos\left(\frac{c x + d}{x}\right) + a b d \sin\left(\frac{c x + d}{x}\right) + {\left(2 \, a b x \cos\left(\frac{c x + d}{x}\right) - a b d \sin\left(\frac{c x + d}{x}\right)\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a b d \cos\left(\frac{c x + d}{x}\right) + 2 \, a b x \sin\left(\frac{c x + d}{x}\right) + 2 \, b^{2} x\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}\,{d x} + 2 \, {\left(a b x^{2} \sin\left(\frac{c x + d}{x}\right) + b^{2} x^{2}\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}"," ",0,"-(2*a*b*x^2*cos(2*(c*x + d)/x)*cos((c*x + d)/x) + 2*a*b*x^2*cos((c*x + d)/x) + ((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))*integrate(-2*(2*a^2*d*cos((c*x + d)/x)^2 + 2*a^2*d*sin((c*x + d)/x)^2 + 2*a*b*x*cos((c*x + d)/x) + a*b*d*sin((c*x + d)/x) + (2*a*b*x*cos((c*x + d)/x) - a*b*d*sin((c*x + d)/x))*cos(2*(c*x + d)/x) + (a*b*d*cos((c*x + d)/x) + 2*a*b*x*sin((c*x + d)/x) + 2*b^2*x)*sin(2*(c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x)), x) + 2*(a*b*x^2*sin((c*x + d)/x) + b^2*x^2)*sin(2*(c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))","F",0
307,0,0,0,0.000000," ","integrate((f*x+e)/(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a b f x^{3} + a b e x^{2}\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) \cos\left(\frac{c x + d}{x}\right) + 2 \, {\left(a b f x^{3} + a b e x^{2}\right)} \cos\left(\frac{c x + d}{x}\right) - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)\right)} \int \frac{2 \, {\left(a^{2} d f x + a^{2} d e\right)} \cos\left(\frac{c x + d}{x}\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} d e\right)} \sin\left(\frac{c x + d}{x}\right)^{2} + {\left({\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \cos\left(\frac{c x + d}{x}\right) - {\left(a b d f x + a b d e\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \cos\left(\frac{c x + d}{x}\right) + {\left(3 \, b^{2} f x^{2} + 2 \, b^{2} e x + {\left(a b d f x + a b d e\right)} \cos\left(\frac{c x + d}{x}\right) + {\left(3 \, a b f x^{2} + 2 \, a b e x\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a b d f x + a b d e\right)} \sin\left(\frac{c x + d}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}\,{d x} + 2 \, {\left(b^{2} f x^{3} + b^{2} e x^{2} + {\left(a b f x^{3} + a b e x^{2}\right)} \sin\left(\frac{c x + d}{x}\right)\right)} \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \cos\left(\frac{c x + d}{x}\right) \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d \sin\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(\frac{c x + d}{x}\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d - 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} b^{2} - b^{4}\right)} d\right)} \cos\left(\frac{2 \, {\left(c x + d\right)}}{x}\right)}"," ",0,"-(2*(a*b*f*x^3 + a*b*e*x^2)*cos(2*(c*x + d)/x)*cos((c*x + d)/x) + 2*(a*b*f*x^3 + a*b*e*x^2)*cos((c*x + d)/x) + ((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))*integrate(-2*(2*(a^2*d*f*x + a^2*d*e)*cos((c*x + d)/x)^2 + 2*(a^2*d*f*x + a^2*d*e)*sin((c*x + d)/x)^2 + ((3*a*b*f*x^2 + 2*a*b*e*x)*cos((c*x + d)/x) - (a*b*d*f*x + a*b*d*e)*sin((c*x + d)/x))*cos(2*(c*x + d)/x) + (3*a*b*f*x^2 + 2*a*b*e*x)*cos((c*x + d)/x) + (3*b^2*f*x^2 + 2*b^2*e*x + (a*b*d*f*x + a*b*d*e)*cos((c*x + d)/x) + (3*a*b*f*x^2 + 2*a*b*e*x)*sin((c*x + d)/x))*sin(2*(c*x + d)/x) + (a*b*d*f*x + a*b*d*e)*sin((c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x)), x) + 2*(b^2*f*x^3 + b^2*e*x^2 + (a*b*f*x^3 + a*b*e*x^2)*sin((c*x + d)/x))*sin(2*(c*x + d)/x))/((a^2*b^2 - b^4)*d*cos(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*cos((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*cos((c*x + d)/x)*sin(2*(c*x + d)/x) + (a^2*b^2 - b^4)*d*sin(2*(c*x + d)/x)^2 + 4*(a^4 - a^2*b^2)*d*sin((c*x + d)/x)^2 + 4*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d - 2*(2*(a^3*b - a*b^3)*d*sin((c*x + d)/x) + (a^2*b^2 - b^4)*d)*cos(2*(c*x + d)/x))","F",0
308,-1,0,0,0.000000," ","integrate((f*x+e)^2/(a+b*sin(c+d/x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*sin(c+d/x))^p,x, algorithm=""maxima"")","\int {\left(f x + e\right)}^{m} {\left(b \sin\left(c + \frac{d}{x}\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((f*x + e)^m*(b*sin(c + d/x) + a)^p, x)","F",0
310,0,0,0,0.000000," ","integrate(x^m*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{3}\right)^{\frac{1}{3}} x^{m}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^3)^(1/3)*x^m, x)","F",0
311,1,146,0,1.147952," ","integrate(x^3*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{3 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a^{2} c^{\frac{1}{3}} - 3 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a c^{\frac{1}{3}} + \frac{4 \, a^{3} c^{\frac{1}{3}}}{\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1} + {\left({\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c^{\frac{1}{3}}}{2 \, b^{4}}"," ",0,"1/2*(3*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a^2*c^(1/3) - 3*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*a*c^(1/3) + 4*a^3*c^(1/3)/(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1) + (((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 3*((b*x + a)^2 - 2)*sin(b*x + a))*c^(1/3))/b^4","A",0
312,1,99,0,1.370556," ","integrate(x^2*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a c^{\frac{1}{3}} - {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c^{\frac{1}{3}} + \frac{4 \, a^{2} c^{\frac{1}{3}}}{\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1}}{2 \, b^{3}}"," ",0,"-1/2*(2*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a*c^(1/3) - (((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*c^(1/3) + 4*a^2*c^(1/3)/(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))/b^3","A",0
313,1,60,0,0.940727," ","integrate(x*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{{\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} c^{\frac{1}{3}} + \frac{4 \, a c^{\frac{1}{3}}}{\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1}}{2 \, b^{2}}"," ",0,"1/2*(((b*x + a)*cos(b*x + a) - sin(b*x + a))*c^(1/3) + 4*a*c^(1/3)/(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))/b^2","A",0
314,1,31,0,1.221488," ","integrate((c*sin(b*x+a)^3)^(1/3),x, algorithm=""maxima"")","-\frac{2 \, c^{\frac{1}{3}}}{b {\left(\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1\right)}}"," ",0,"-2*c^(1/3)/(b*(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))","A",0
315,1,42,0,1.213802," ","integrate((c*sin(b*x+a)^3)^(1/3)/x,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(i \, E_{1}\left(i \, b x\right) - i \, E_{1}\left(-i \, b x\right)\right)} \cos\left(a\right) + {\left(E_{1}\left(i \, b x\right) + E_{1}\left(-i \, b x\right)\right)} \sin\left(a\right)\right)} c^{\frac{1}{3}}"," ",0,"1/4*((I*exp_integral_e(1, I*b*x) - I*exp_integral_e(1, -I*b*x))*cos(a) + (exp_integral_e(1, I*b*x) + exp_integral_e(1, -I*b*x))*sin(a))*c^(1/3)","C",0
316,1,243,0,1.026583," ","integrate((c*sin(b*x+a)^3)^(1/3)/x^2,x, algorithm=""maxima"")","\frac{{\left({\left({\left(8 \, \sqrt{3} - 8 i\right)} E_{2}\left(i \, b x\right) + {\left(8 \, \sqrt{3} + 8 i\right)} E_{2}\left(-i \, b x\right)\right)} \cos\left(a\right)^{3} + {\left({\left(8 \, \sqrt{3} - 8 i\right)} E_{2}\left(i \, b x\right) + {\left(8 \, \sqrt{3} + 8 i\right)} E_{2}\left(-i \, b x\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 8 \, {\left({\left(-i \, \sqrt{3} - 1\right)} E_{2}\left(i \, b x\right) + {\left(i \, \sqrt{3} - 1\right)} E_{2}\left(-i \, b x\right)\right)} \sin\left(a\right)^{3} - {\left({\left(8 \, \sqrt{3} + 8 i\right)} E_{2}\left(i \, b x\right) + {\left(8 \, \sqrt{3} - 8 i\right)} E_{2}\left(-i \, b x\right)\right)} \cos\left(a\right) + 8 \, {\left({\left({\left(-i \, \sqrt{3} - 1\right)} E_{2}\left(i \, b x\right) + {\left(i \, \sqrt{3} - 1\right)} E_{2}\left(-i \, b x\right)\right)} \cos\left(a\right)^{2} + {\left(i \, \sqrt{3} - 1\right)} E_{2}\left(i \, b x\right) + {\left(-i \, \sqrt{3} - 1\right)} E_{2}\left(-i \, b x\right)\right)} \sin\left(a\right)\right)} b c^{\frac{1}{3}}}{64 \, {\left(a \cos\left(a\right)^{2} + a \sin\left(a\right)^{2} - {\left(b x + a\right)} {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)}\right)}}"," ",0,"1/64*(((8*sqrt(3) - 8*I)*exp_integral_e(2, I*b*x) + (8*sqrt(3) + 8*I)*exp_integral_e(2, -I*b*x))*cos(a)^3 + ((8*sqrt(3) - 8*I)*exp_integral_e(2, I*b*x) + (8*sqrt(3) + 8*I)*exp_integral_e(2, -I*b*x))*cos(a)*sin(a)^2 + 8*((-I*sqrt(3) - 1)*exp_integral_e(2, I*b*x) + (I*sqrt(3) - 1)*exp_integral_e(2, -I*b*x))*sin(a)^3 - ((8*sqrt(3) + 8*I)*exp_integral_e(2, I*b*x) + (8*sqrt(3) - 8*I)*exp_integral_e(2, -I*b*x))*cos(a) + 8*(((-I*sqrt(3) - 1)*exp_integral_e(2, I*b*x) + (I*sqrt(3) - 1)*exp_integral_e(2, -I*b*x))*cos(a)^2 + (I*sqrt(3) - 1)*exp_integral_e(2, I*b*x) + (-I*sqrt(3) - 1)*exp_integral_e(2, -I*b*x))*sin(a))*b*c^(1/3)/(a*cos(a)^2 + a*sin(a)^2 - (b*x + a)*(cos(a)^2 + sin(a)^2))","C",0
317,1,270,0,1.007240," ","integrate((c*sin(b*x+a)^3)^(1/3)/x^3,x, algorithm=""maxima"")","-\frac{{\left({\left({\left(8 \, \sqrt{3} - 8 i\right)} E_{3}\left(i \, b x\right) + {\left(8 \, \sqrt{3} + 8 i\right)} E_{3}\left(-i \, b x\right)\right)} \cos\left(a\right)^{3} + {\left({\left(8 \, \sqrt{3} - 8 i\right)} E_{3}\left(i \, b x\right) + {\left(8 \, \sqrt{3} + 8 i\right)} E_{3}\left(-i \, b x\right)\right)} \cos\left(a\right) \sin\left(a\right)^{2} + 8 \, {\left({\left(-i \, \sqrt{3} - 1\right)} E_{3}\left(i \, b x\right) + {\left(i \, \sqrt{3} - 1\right)} E_{3}\left(-i \, b x\right)\right)} \sin\left(a\right)^{3} - {\left({\left(8 \, \sqrt{3} + 8 i\right)} E_{3}\left(i \, b x\right) + {\left(8 \, \sqrt{3} - 8 i\right)} E_{3}\left(-i \, b x\right)\right)} \cos\left(a\right) + 8 \, {\left({\left({\left(-i \, \sqrt{3} - 1\right)} E_{3}\left(i \, b x\right) + {\left(i \, \sqrt{3} - 1\right)} E_{3}\left(-i \, b x\right)\right)} \cos\left(a\right)^{2} + {\left(i \, \sqrt{3} - 1\right)} E_{3}\left(i \, b x\right) + {\left(-i \, \sqrt{3} - 1\right)} E_{3}\left(-i \, b x\right)\right)} \sin\left(a\right)\right)} b^{2} c^{\frac{1}{3}}}{64 \, {\left(a^{2} \cos\left(a\right)^{2} + a^{2} \sin\left(a\right)^{2} + {\left(b x + a\right)}^{2} {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} - 2 \, {\left(a \cos\left(a\right)^{2} + a \sin\left(a\right)^{2}\right)} {\left(b x + a\right)}\right)}}"," ",0,"-1/64*(((8*sqrt(3) - 8*I)*exp_integral_e(3, I*b*x) + (8*sqrt(3) + 8*I)*exp_integral_e(3, -I*b*x))*cos(a)^3 + ((8*sqrt(3) - 8*I)*exp_integral_e(3, I*b*x) + (8*sqrt(3) + 8*I)*exp_integral_e(3, -I*b*x))*cos(a)*sin(a)^2 + 8*((-I*sqrt(3) - 1)*exp_integral_e(3, I*b*x) + (I*sqrt(3) - 1)*exp_integral_e(3, -I*b*x))*sin(a)^3 - ((8*sqrt(3) + 8*I)*exp_integral_e(3, I*b*x) + (8*sqrt(3) - 8*I)*exp_integral_e(3, -I*b*x))*cos(a) + 8*(((-I*sqrt(3) - 1)*exp_integral_e(3, I*b*x) + (I*sqrt(3) - 1)*exp_integral_e(3, -I*b*x))*cos(a)^2 + (I*sqrt(3) - 1)*exp_integral_e(3, I*b*x) + (-I*sqrt(3) - 1)*exp_integral_e(3, -I*b*x))*sin(a))*b^2*c^(1/3)/(a^2*cos(a)^2 + a^2*sin(a)^2 + (b*x + a)^2*(cos(a)^2 + sin(a)^2) - 2*(a*cos(a)^2 + a*sin(a)^2)*(b*x + a))","C",0
318,0,0,0,0.000000," ","integrate(x^m*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{2} + a\right)^{3}\right)^{\frac{1}{3}} x^{m}\,{d x}"," ",0,"integrate((c*sin(b*x^2 + a)^3)^(1/3)*x^m, x)","F",0
319,1,32,0,1.004378," ","integrate(x^3*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{{\left(b x^{2} \cos\left(b x^{2} + a\right) - \sin\left(b x^{2} + a\right)\right)} c^{\frac{1}{3}}}{4 \, b^{2}}"," ",0,"1/4*(b*x^2*cos(b*x^2 + a) - sin(b*x^2 + a))*c^(1/3)/b^2","A",0
320,1,73,0,0.960626," ","integrate(x^2*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{8 \, b^{2} c^{\frac{1}{3}} x \cos\left(b x^{2} + a\right) + \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(a\right) + \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{i \, b} x\right) + {\left(-\left(i + 1\right) \, \cos\left(a\right) - \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{-i \, b} x\right)\right)} b^{\frac{3}{2}} c^{\frac{1}{3}}}{32 \, b^{3}}"," ",0,"1/32*(8*b^2*c^(1/3)*x*cos(b*x^2 + a) + sqrt(2)*sqrt(pi)*(((I - 1)*cos(a) + (I + 1)*sin(a))*erf(sqrt(I*b)*x) + (-(I + 1)*cos(a) - (I - 1)*sin(a))*erf(sqrt(-I*b)*x))*b^(3/2)*c^(1/3))/b^3","C",0
321,1,16,0,0.955248," ","integrate(x*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{c^{\frac{1}{3}} \cos\left(b x^{2} + a\right)}{4 \, b}"," ",0,"1/4*c^(1/3)*cos(b*x^2 + a)/b","A",0
322,1,51,0,1.926386," ","integrate((c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} {\left({\left(-\left(i + 1\right) \, \cos\left(a\right) + \left(i - 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{i \, b} x\right) + {\left(\left(i - 1\right) \, \cos\left(a\right) - \left(i + 1\right) \, \sin\left(a\right)\right)} \operatorname{erf}\left(\sqrt{-i \, b} x\right)\right)} c^{\frac{1}{3}}}{16 \, \sqrt{b}}"," ",0,"1/16*sqrt(2)*sqrt(pi)*((-(I + 1)*cos(a) + (I - 1)*sin(a))*erf(sqrt(I*b)*x) + ((I - 1)*cos(a) - (I + 1)*sin(a))*erf(sqrt(-I*b)*x))*c^(1/3)/sqrt(b)","C",0
323,1,47,0,2.928206," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(i \, {\rm Ei}\left(i \, b x^{2}\right) - i \, {\rm Ei}\left(-i \, b x^{2}\right)\right)} \cos\left(a\right) - {\left({\rm Ei}\left(i \, b x^{2}\right) + {\rm Ei}\left(-i \, b x^{2}\right)\right)} \sin\left(a\right)\right)} c^{\frac{1}{3}}"," ",0,"1/8*((I*Ei(I*b*x^2) - I*Ei(-I*b*x^2))*cos(a) - (Ei(I*b*x^2) + Ei(-I*b*x^2))*sin(a))*c^(1/3)","C",0
324,1,76,0,2.449517," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x^2,x, algorithm=""maxima"")","\frac{\sqrt{b x^{2}} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, b x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, b x^{2}\right)\right)} \cos\left(a\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, b x^{2}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, b x^{2}\right)\right)} \sin\left(a\right)\right)} c^{\frac{1}{3}}}{16 \, x}"," ",0,"1/16*sqrt(b*x^2)*(((I - 1)*sqrt(2)*gamma(-1/2, I*b*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -I*b*x^2))*cos(a) + ((I + 1)*sqrt(2)*gamma(-1/2, I*b*x^2) - (I - 1)*sqrt(2)*gamma(-1/2, -I*b*x^2))*sin(a))*c^(1/3)/x","C",0
325,1,52,0,2.728143," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left({\left(\Gamma\left(-1, i \, b x^{2}\right) + \Gamma\left(-1, -i \, b x^{2}\right)\right)} \cos\left(a\right) - {\left(i \, \Gamma\left(-1, i \, b x^{2}\right) - i \, \Gamma\left(-1, -i \, b x^{2}\right)\right)} \sin\left(a\right)\right)} b c^{\frac{1}{3}}"," ",0,"-1/8*((gamma(-1, I*b*x^2) + gamma(-1, -I*b*x^2))*cos(a) - (I*gamma(-1, I*b*x^2) - I*gamma(-1, -I*b*x^2))*sin(a))*b*c^(1/3)","C",0
326,0,0,0,0.000000," ","integrate(x^m*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}} x^{m}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)*x^m, x)","F",0
327,0,0,0,0.000000," ","integrate(x^3*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}} x^{3}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)*x^3, x)","F",0
328,0,0,0,0.000000," ","integrate(x^2*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}} x^{2}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)*x^2, x)","F",0
329,0,0,0,0.000000," ","integrate(x*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}} x\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)*x, x)","F",0
330,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""maxima"")","\int \left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3), x)","F",0
331,1,144,0,2.330925," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x,x, algorithm=""maxima"")","\frac{{\left({\left({\left(\sqrt{3} + i\right)} {\rm Ei}\left(i \, b x^{n}\right) - {\left(\sqrt{3} + i\right)} {\rm Ei}\left(-i \, b x^{n}\right) - {\left(\sqrt{3} - i\right)} {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\left(\sqrt{3} - i\right)} {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(a\right) - {\left({\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(i \, b x^{n}\right) + {\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-i \, b x^{n}\right) + {\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(a\right)\right)} c^{\frac{1}{3}}}{8 \, n}"," ",0,"1/8*(((sqrt(3) + I)*Ei(I*b*x^n) - (sqrt(3) + I)*Ei(-I*b*x^n) - (sqrt(3) - I)*Ei(I*b*e^(n*conjugate(log(x)))) + (sqrt(3) - I)*Ei(-I*b*e^(n*conjugate(log(x)))))*cos(a) - ((-I*sqrt(3) + 1)*Ei(I*b*x^n) + (-I*sqrt(3) + 1)*Ei(-I*b*x^n) + (I*sqrt(3) + 1)*Ei(I*b*e^(n*conjugate(log(x)))) + (I*sqrt(3) + 1)*Ei(-I*b*e^(n*conjugate(log(x)))))*sin(a))*c^(1/3)/n","C",0
332,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)/x^2, x)","F",0
333,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x^3,x, algorithm=""maxima"")","\int \frac{\left(c \sin\left(b x^{n} + a\right)^{3}\right)^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((c*sin(b*x^n + a)^3)^(1/3)/x^3, x)","F",0
334,0,0,0,0.000000," ","integrate(x^m*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""maxima"")","\frac{{\left({\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(x\right) + \log\left(x\right)\right)}\right)} c^{\frac{2}{3}}}{4 \, {\left(m + 1\right)}}"," ",0,"1/4*((m + 1)*integrate(x^m*cos(2*b*x + 2*a), x) - e^(m*log(x) + log(x)))*c^(2/3)/(m + 1)","F",0
335,1,286,0,1.237233," ","integrate(x^3*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{32 \, {\left(c^{\frac{2}{3}} \arctan\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1}\right) - \frac{\frac{c^{\frac{2}{3}} \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} - \frac{c^{\frac{2}{3}} \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}}}{\frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1}\right)} a^{3} + 6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} c^{\frac{2}{3}} - 2 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{\frac{2}{3}} + {\left(2 \, {\left(b x + a\right)}^{4} - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{\frac{2}{3}}}{32 \, b^{4}}"," ",0,"-1/32*(32*(c^(2/3)*arctan(sin(b*x + a)/(cos(b*x + a) + 1)) - (c^(2/3)*sin(b*x + a)/(cos(b*x + a) + 1) - c^(2/3)*sin(b*x + a)^3/(cos(b*x + a) + 1)^3)/(2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1))*a^3 + 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a^2*c^(2/3) - 2*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*c^(2/3) + (2*(b*x + a)^4 - 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*c^(2/3))/b^4","B",0
336,1,219,0,0.599046," ","integrate(x^2*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""maxima"")","\frac{48 \, {\left(c^{\frac{2}{3}} \arctan\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1}\right) - \frac{\frac{c^{\frac{2}{3}} \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} - \frac{c^{\frac{2}{3}} \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}}}{\frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1}\right)} a^{2} + 6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a c^{\frac{2}{3}} - {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{\frac{2}{3}}}{48 \, b^{3}}"," ",0,"1/48*(48*(c^(2/3)*arctan(sin(b*x + a)/(cos(b*x + a) + 1)) - (c^(2/3)*sin(b*x + a)/(cos(b*x + a) + 1) - c^(2/3)*sin(b*x + a)^3/(cos(b*x + a) + 1)^3)/(2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1))*a^2 + 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a*c^(2/3) - (4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c^(2/3))/b^3","A",0
337,1,162,0,0.487841," ","integrate(x*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{16 \, {\left(c^{\frac{2}{3}} \arctan\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1}\right) - \frac{\frac{c^{\frac{2}{3}} \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} - \frac{c^{\frac{2}{3}} \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}}}{\frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1}\right)} a + {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} c^{\frac{2}{3}}}{16 \, b^{2}}"," ",0,"-1/16*(16*(c^(2/3)*arctan(sin(b*x + a)/(cos(b*x + a) + 1)) - (c^(2/3)*sin(b*x + a)/(cos(b*x + a) + 1) - c^(2/3)*sin(b*x + a)^3/(cos(b*x + a) + 1)^3)/(2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1))*a + (2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*c^(2/3))/b^2","B",0
338,1,116,0,0.524299," ","integrate((c*sin(b*x+a)^3)^(2/3),x, algorithm=""maxima"")","\frac{c^{\frac{2}{3}} \arctan\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1}\right) - \frac{\frac{c^{\frac{2}{3}} \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} - \frac{c^{\frac{2}{3}} \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}}}{\frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1}}{b}"," ",0,"(c^(2/3)*arctan(sin(b*x + a)/(cos(b*x + a) + 1)) - (c^(2/3)*sin(b*x + a)/(cos(b*x + a) + 1) - c^(2/3)*sin(b*x + a)^3/(cos(b*x + a) + 1)^3)/(2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1))/b","B",0
339,1,52,0,1.110668," ","integrate((c*sin(b*x+a)^3)^(2/3)/x,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left({\left(E_{1}\left(2 i \, b x\right) + E_{1}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + {\left(-i \, E_{1}\left(2 i \, b x\right) + i \, E_{1}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right) + 2 \, \log\left(b x\right)\right)} c^{\frac{2}{3}}"," ",0,"-1/8*((exp_integral_e(1, 2*I*b*x) + exp_integral_e(1, -2*I*b*x))*cos(2*a) + (-I*exp_integral_e(1, 2*I*b*x) + I*exp_integral_e(1, -2*I*b*x))*sin(2*a) + 2*log(b*x))*c^(2/3)","C",0
340,1,280,0,1.048553," ","integrate((c*sin(b*x+a)^3)^(2/3)/x^2,x, algorithm=""maxima"")","\frac{{\left(64 \, {\left({\left(-i \, \sqrt{3} + 1\right)} E_{2}\left(2 i \, b x\right) + {\left(i \, \sqrt{3} + 1\right)} E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left({\left(64 \, \sqrt{3} + 64 i\right)} E_{2}\left(2 i \, b x\right) + {\left(64 \, \sqrt{3} - 64 i\right)} E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 64 \, {\left({\left({\left(-i \, \sqrt{3} + 1\right)} E_{2}\left(2 i \, b x\right) + {\left(i \, \sqrt{3} + 1\right)} E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) - 4\right)} \sin\left(2 \, a\right)^{2} + 64 \, {\left({\left(i \, \sqrt{3} + 1\right)} E_{2}\left(2 i \, b x\right) + {\left(-i \, \sqrt{3} + 1\right)} E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) - 256 \, \cos\left(2 \, a\right)^{2} - {\left({\left({\left(64 \, \sqrt{3} + 64 i\right)} E_{2}\left(2 i \, b x\right) + {\left(64 \, \sqrt{3} - 64 i\right)} E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} - {\left(64 \, \sqrt{3} - 64 i\right)} E_{2}\left(2 i \, b x\right) - {\left(64 \, \sqrt{3} + 64 i\right)} E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} b c^{\frac{2}{3}}}{1024 \, {\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2} - {\left(b x + a\right)} {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)}\right)}}"," ",0,"1/1024*(64*((-I*sqrt(3) + 1)*exp_integral_e(2, 2*I*b*x) + (I*sqrt(3) + 1)*exp_integral_e(2, -2*I*b*x))*cos(2*a)^3 - ((64*sqrt(3) + 64*I)*exp_integral_e(2, 2*I*b*x) + (64*sqrt(3) - 64*I)*exp_integral_e(2, -2*I*b*x))*sin(2*a)^3 + 64*(((-I*sqrt(3) + 1)*exp_integral_e(2, 2*I*b*x) + (I*sqrt(3) + 1)*exp_integral_e(2, -2*I*b*x))*cos(2*a) - 4)*sin(2*a)^2 + 64*((I*sqrt(3) + 1)*exp_integral_e(2, 2*I*b*x) + (-I*sqrt(3) + 1)*exp_integral_e(2, -2*I*b*x))*cos(2*a) - 256*cos(2*a)^2 - (((64*sqrt(3) + 64*I)*exp_integral_e(2, 2*I*b*x) + (64*sqrt(3) - 64*I)*exp_integral_e(2, -2*I*b*x))*cos(2*a)^2 - (64*sqrt(3) - 64*I)*exp_integral_e(2, 2*I*b*x) - (64*sqrt(3) + 64*I)*exp_integral_e(2, -2*I*b*x))*sin(2*a))*b*c^(2/3)/(a*cos(2*a)^2 + a*sin(2*a)^2 - (b*x + a)*(cos(2*a)^2 + sin(2*a)^2))","C",0
341,1,311,0,1.677203," ","integrate((c*sin(b*x+a)^3)^(2/3)/x^3,x, algorithm=""maxima"")","-\frac{{\left(128 \, {\left({\left(-i \, \sqrt{3} + 1\right)} E_{3}\left(2 i \, b x\right) + {\left(i \, \sqrt{3} + 1\right)} E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left({\left(128 \, \sqrt{3} + 128 i\right)} E_{3}\left(2 i \, b x\right) + {\left(128 \, \sqrt{3} - 128 i\right)} E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 128 \, {\left({\left({\left(-i \, \sqrt{3} + 1\right)} E_{3}\left(2 i \, b x\right) + {\left(i \, \sqrt{3} + 1\right)} E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) - 2\right)} \sin\left(2 \, a\right)^{2} + 128 \, {\left({\left(i \, \sqrt{3} + 1\right)} E_{3}\left(2 i \, b x\right) + {\left(-i \, \sqrt{3} + 1\right)} E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) - 256 \, \cos\left(2 \, a\right)^{2} - {\left({\left({\left(128 \, \sqrt{3} + 128 i\right)} E_{3}\left(2 i \, b x\right) + {\left(128 \, \sqrt{3} - 128 i\right)} E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} - {\left(128 \, \sqrt{3} - 128 i\right)} E_{3}\left(2 i \, b x\right) - {\left(128 \, \sqrt{3} + 128 i\right)} E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} b^{2} c^{\frac{2}{3}}}{2048 \, {\left(a^{2} \cos\left(2 \, a\right)^{2} + a^{2} \sin\left(2 \, a\right)^{2} + {\left(b x + a\right)}^{2} {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} - 2 \, {\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2}\right)} {\left(b x + a\right)}\right)}}"," ",0,"-1/2048*(128*((-I*sqrt(3) + 1)*exp_integral_e(3, 2*I*b*x) + (I*sqrt(3) + 1)*exp_integral_e(3, -2*I*b*x))*cos(2*a)^3 - ((128*sqrt(3) + 128*I)*exp_integral_e(3, 2*I*b*x) + (128*sqrt(3) - 128*I)*exp_integral_e(3, -2*I*b*x))*sin(2*a)^3 + 128*(((-I*sqrt(3) + 1)*exp_integral_e(3, 2*I*b*x) + (I*sqrt(3) + 1)*exp_integral_e(3, -2*I*b*x))*cos(2*a) - 2)*sin(2*a)^2 + 128*((I*sqrt(3) + 1)*exp_integral_e(3, 2*I*b*x) + (-I*sqrt(3) + 1)*exp_integral_e(3, -2*I*b*x))*cos(2*a) - 256*cos(2*a)^2 - (((128*sqrt(3) + 128*I)*exp_integral_e(3, 2*I*b*x) + (128*sqrt(3) - 128*I)*exp_integral_e(3, -2*I*b*x))*cos(2*a)^2 - (128*sqrt(3) - 128*I)*exp_integral_e(3, 2*I*b*x) - (128*sqrt(3) + 128*I)*exp_integral_e(3, -2*I*b*x))*sin(2*a))*b^2*c^(2/3)/(a^2*cos(2*a)^2 + a^2*sin(2*a)^2 + (b*x + a)^2*(cos(2*a)^2 + sin(2*a)^2) - 2*(a*cos(2*a)^2 + a*sin(2*a)^2)*(b*x + a))","C",0
342,0,0,0,0.000000," ","integrate(x^m*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(x x^{m} - {\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x^{2} + 2 \, a\right)\,{d x}\right)} c^{\frac{2}{3}}}{4 \, {\left(m + 1\right)}}"," ",0,"-1/4*(x*x^m - (m + 1)*integrate(x^m*cos(2*b*x^2 + 2*a), x))*c^(2/3)/(m + 1)","F",0
343,1,47,0,0.627004," ","integrate(x^3*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(2 \, b^{2} x^{4} - 2 \, b x^{2} \sin\left(2 \, b x^{2} + 2 \, a\right) - \cos\left(2 \, b x^{2} + 2 \, a\right)\right)} c^{\frac{2}{3}}}{32 \, b^{2}}"," ",0,"-1/32*(2*b^2*x^4 - 2*b*x^2*sin(2*b*x^2 + 2*a) - cos(2*b*x^2 + 2*a))*c^(2/3)/b^2","A",0
344,1,98,0,0.656724," ","integrate(x^2*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""maxima"")","\frac{4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(-\left(3 i + 3\right) \, \cos\left(2 \, a\right) + \left(3 i - 3\right) \, \sin\left(2 \, a\right)\right)} \operatorname{erf}\left(\sqrt{2 i \, b} x\right) + {\left(\left(3 i - 3\right) \, \cos\left(2 \, a\right) - \left(3 i + 3\right) \, \sin\left(2 \, a\right)\right)} \operatorname{erf}\left(\sqrt{-2 i \, b} x\right)\right)} b^{\frac{3}{2}} c^{\frac{2}{3}} - 16 \, {\left(4 \, b^{3} x^{3} - 3 \, b^{2} x \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} c^{\frac{2}{3}}}{768 \, b^{3}}"," ",0,"1/768*(4^(1/4)*sqrt(2)*sqrt(pi)*((-(3*I + 3)*cos(2*a) + (3*I - 3)*sin(2*a))*erf(sqrt(2*I*b)*x) + ((3*I - 3)*cos(2*a) - (3*I + 3)*sin(2*a))*erf(sqrt(-2*I*b)*x))*b^(3/2)*c^(2/3) - 16*(4*b^3*x^3 - 3*b^2*x*sin(2*b*x^2 + 2*a))*c^(2/3))/b^3","C",0
345,1,28,0,0.971025," ","integrate(x*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(2 \, b x^{2} - \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} c^{\frac{2}{3}}}{16 \, b}"," ",0,"-1/16*(2*b*x^2 - sin(2*b*x^2 + 2*a))*c^(2/3)/b","A",0
346,1,76,0,0.752504," ","integrate((c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""maxima"")","-\frac{4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} {\left({\left(\left(i - 1\right) \, \cos\left(2 \, a\right) + \left(i + 1\right) \, \sin\left(2 \, a\right)\right)} \operatorname{erf}\left(\sqrt{2 i \, b} x\right) + {\left(-\left(i + 1\right) \, \cos\left(2 \, a\right) - \left(i - 1\right) \, \sin\left(2 \, a\right)\right)} \operatorname{erf}\left(\sqrt{-2 i \, b} x\right)\right)} b^{\frac{3}{2}} c^{\frac{2}{3}} + 16 \, b^{2} c^{\frac{2}{3}} x}{64 \, b^{2}}"," ",0,"-1/64*(4^(1/4)*sqrt(2)*sqrt(pi)*(((I - 1)*cos(2*a) + (I + 1)*sin(2*a))*erf(sqrt(2*I*b)*x) + (-(I + 1)*cos(2*a) - (I - 1)*sin(2*a))*erf(sqrt(-2*I*b)*x))*b^(3/2)*c^(2/3) + 16*b^2*c^(2/3)*x)/b^2","C",0
347,1,55,0,1.260370," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x,x, algorithm=""maxima"")","\frac{1}{16} \, {\left({\left({\rm Ei}\left(2 i \, b x^{2}\right) + {\rm Ei}\left(-2 i \, b x^{2}\right)\right)} \cos\left(2 \, a\right) - {\left(-i \, {\rm Ei}\left(2 i \, b x^{2}\right) + i \, {\rm Ei}\left(-2 i \, b x^{2}\right)\right)} \sin\left(2 \, a\right) - 4 \, \log\left(x\right)\right)} c^{\frac{2}{3}}"," ",0,"1/16*((Ei(2*I*b*x^2) + Ei(-2*I*b*x^2))*cos(2*a) - (-I*Ei(2*I*b*x^2) + I*Ei(-2*I*b*x^2))*sin(2*a) - 4*log(x))*c^(2/3)","C",0
348,1,90,0,1.069960," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x^2,x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{b x^{2}} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 2 i \, b x^{2}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -2 i \, b x^{2}\right)\right)} \cos\left(2 \, a\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, 2 i \, b x^{2}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -2 i \, b x^{2}\right)\right)} \sin\left(2 \, a\right)\right)} c^{\frac{2}{3}} + 8 \, c^{\frac{2}{3}}}{32 \, x}"," ",0,"1/32*(sqrt(2)*sqrt(b*x^2)*((-(I + 1)*sqrt(2)*gamma(-1/2, 2*I*b*x^2) + (I - 1)*sqrt(2)*gamma(-1/2, -2*I*b*x^2))*cos(2*a) + ((I - 1)*sqrt(2)*gamma(-1/2, 2*I*b*x^2) - (I + 1)*sqrt(2)*gamma(-1/2, -2*I*b*x^2))*sin(2*a))*c^(2/3) + 8*c^(2/3))/x","C",0
349,1,64,0,1.119019," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x^3,x, algorithm=""maxima"")","-\frac{{\left({\left({\left(i \, \Gamma\left(-1, 2 i \, b x^{2}\right) - i \, \Gamma\left(-1, -2 i \, b x^{2}\right)\right)} \cos\left(2 \, a\right) + {\left(\Gamma\left(-1, 2 i \, b x^{2}\right) + \Gamma\left(-1, -2 i \, b x^{2}\right)\right)} \sin\left(2 \, a\right)\right)} b x^{2} - 1\right)} c^{\frac{2}{3}}}{8 \, x^{2}}"," ",0,"-1/8*(((I*gamma(-1, 2*I*b*x^2) - I*gamma(-1, -2*I*b*x^2))*cos(2*a) + (gamma(-1, 2*I*b*x^2) + gamma(-1, -2*I*b*x^2))*sin(2*a))*b*x^2 - 1)*c^(2/3)/x^2","C",0
350,0,0,0,0.000000," ","integrate(x^m*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(x x^{m} - {\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}\right)} c^{\frac{2}{3}}}{4 \, {\left(m + 1\right)}}"," ",0,"-1/4*(x*x^m - (m + 1)*integrate(x^m*cos(2*b*x^n + 2*a), x))*c^(2/3)/(m + 1)","F",0
351,0,0,0,0.000000," ","integrate(x^3*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(x^{4} - 4 \, \int x^{3} \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}\right)} c^{\frac{2}{3}}"," ",0,"-1/16*(x^4 - 4*integrate(x^3*cos(2*b*x^n + 2*a), x))*c^(2/3)","F",0
352,0,0,0,0.000000," ","integrate(x^2*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(x^{3} - 3 \, \int x^{2} \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}\right)} c^{\frac{2}{3}}"," ",0,"-1/12*(x^3 - 3*integrate(x^2*cos(2*b*x^n + 2*a), x))*c^(2/3)","F",0
353,0,0,0,0.000000," ","integrate(x*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(x^{2} - 2 \, \int x \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}\right)} c^{\frac{2}{3}}"," ",0,"-1/8*(x^2 - 2*integrate(x*cos(2*b*x^n + 2*a), x))*c^(2/3)","F",0
354,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""maxima"")","-\frac{1}{4} \, c^{\frac{2}{3}} {\left(x - \int \cos\left(2 \, b x^{n} + 2 \, a\right)\,{d x}\right)}"," ",0,"-1/4*c^(2/3)*(x - integrate(cos(2*b*x^n + 2*a), x))","F",0
355,1,153,0,1.025459," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x,x, algorithm=""maxima"")","\frac{{\left({\left({\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(2 i \, b x^{n}\right) + {\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-2 i \, b x^{n}\right) + {\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \cos\left(2 \, a\right) - 4 \, n \log\left(x\right) - {\left({\left(\sqrt{3} - i\right)} {\rm Ei}\left(2 i \, b x^{n}\right) - {\left(\sqrt{3} - i\right)} {\rm Ei}\left(-2 i \, b x^{n}\right) - {\left(\sqrt{3} + i\right)} {\rm Ei}\left(2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right) + {\left(\sqrt{3} + i\right)} {\rm Ei}\left(-2 i \, b e^{\left(n \overline{\log\left(x\right)}\right)}\right)\right)} \sin\left(2 \, a\right)\right)} c^{\frac{2}{3}}}{16 \, n}"," ",0,"1/16*(((I*sqrt(3) + 1)*Ei(2*I*b*x^n) + (I*sqrt(3) + 1)*Ei(-2*I*b*x^n) + (-I*sqrt(3) + 1)*Ei(2*I*b*e^(n*conjugate(log(x)))) + (-I*sqrt(3) + 1)*Ei(-2*I*b*e^(n*conjugate(log(x)))))*cos(2*a) - 4*n*log(x) - ((sqrt(3) - I)*Ei(2*I*b*x^n) - (sqrt(3) - I)*Ei(-2*I*b*x^n) - (sqrt(3) + I)*Ei(2*I*b*e^(n*conjugate(log(x)))) + (sqrt(3) + I)*Ei(-2*I*b*e^(n*conjugate(log(x)))))*sin(2*a))*c^(2/3)/n","C",0
356,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x^2,x, algorithm=""maxima"")","\frac{{\left(x \int \frac{\cos\left(2 \, b x^{n} + 2 \, a\right)}{x^{2}}\,{d x} + 1\right)} c^{\frac{2}{3}}}{4 \, x}"," ",0,"1/4*(x*integrate(cos(2*b*x^n + 2*a)/x^2, x) + 1)*c^(2/3)/x","F",0
357,0,0,0,0.000000," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x^3,x, algorithm=""maxima"")","\frac{{\left(2 \, x^{2} \int \frac{\cos\left(2 \, b x^{n} + 2 \, a\right)}{x^{3}}\,{d x} + 1\right)} c^{\frac{2}{3}}}{8 \, x^{2}}"," ",0,"1/8*(2*x^2*integrate(cos(2*b*x^n + 2*a)/x^3, x) + 1)*c^(2/3)/x^2","F",0
