1,0,0,0,0.000000," ","integrate(x^5*(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + b {\left(\int \frac{x^{5} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x} + \int \frac{x^{5} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x}\right)}"," ",0,"1/6*a*x^6 + b*(integrate(x^5*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1), x) + integrate(x^5*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1), x))","F",0
2,0,0,0,0.000000," ","integrate(x^4*(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + b {\left(\int \frac{x^{4} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x} + \int \frac{x^{4} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x}\right)}"," ",0,"1/5*a*x^5 + b*(integrate(x^4*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1), x) + integrate(x^4*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1), x))","F",0
3,0,0,0,0.000000," ","integrate(x^3*(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + b {\left(\int \frac{x^{3} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x} + \int \frac{x^{3} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x}\right)}"," ",0,"1/4*a*x^4 + b*(integrate(x^3*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1), x) + integrate(x^3*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1), x))","F",0
4,0,0,0,0.000000," ","integrate(x^2*(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + b {\left(\int \frac{x^{2} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x} + \int \frac{x^{2} \sin\left(d x^{2} + c\right)}{\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1}\,{d x}\right)}"," ",0,"1/3*a*x^3 + b*(integrate(x^2*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1), x) + integrate(x^2*sin(d*x^2 + c)/(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1), x))","F",0
5,1,31,0,0.324665," ","integrate(x*(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} - \frac{b \log\left(\cot\left(d x^{2} + c\right) + \csc\left(d x^{2} + c\right)\right)}{2 \, d}"," ",0,"1/2*a*x^2 - 1/2*b*log(cot(d*x^2 + c) + csc(d*x^2 + c))/d","A",0
6,0,0,0,0.000000," ","integrate((a+b*csc(d*x^2+c))/x,x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(d x^{2} + c\right)}{x \cos\left(d x^{2} + c\right)^{2} + x \sin\left(d x^{2} + c\right)^{2} + 2 \, x \cos\left(d x^{2} + c\right) + x}\,{d x} + \int \frac{\sin\left(d x^{2} + c\right)}{x \cos\left(d x^{2} + c\right)^{2} + x \sin\left(d x^{2} + c\right)^{2} - 2 \, x \cos\left(d x^{2} + c\right) + x}\,{d x}\right)} + a \log\left(x\right)"," ",0,"b*(integrate(sin(d*x^2 + c)/(x*cos(d*x^2 + c)^2 + x*sin(d*x^2 + c)^2 + 2*x*cos(d*x^2 + c) + x), x) + integrate(sin(d*x^2 + c)/(x*cos(d*x^2 + c)^2 + x*sin(d*x^2 + c)^2 - 2*x*cos(d*x^2 + c) + x), x)) + a*log(x)","F",0
7,0,0,0,0.000000," ","integrate((a+b*csc(d*x^2+c))/x^2,x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(d x^{2} + c\right)}{x^{2} \cos\left(d x^{2} + c\right)^{2} + x^{2} \sin\left(d x^{2} + c\right)^{2} + 2 \, x^{2} \cos\left(d x^{2} + c\right) + x^{2}}\,{d x} + \int \frac{\sin\left(d x^{2} + c\right)}{x^{2} \cos\left(d x^{2} + c\right)^{2} + x^{2} \sin\left(d x^{2} + c\right)^{2} - 2 \, x^{2} \cos\left(d x^{2} + c\right) + x^{2}}\,{d x}\right)} - \frac{a}{x}"," ",0,"b*(integrate(sin(d*x^2 + c)/(x^2*cos(d*x^2 + c)^2 + x^2*sin(d*x^2 + c)^2 + 2*x^2*cos(d*x^2 + c) + x^2), x) + integrate(sin(d*x^2 + c)/(x^2*cos(d*x^2 + c)^2 + x^2*sin(d*x^2 + c)^2 - 2*x^2*cos(d*x^2 + c) + x^2), x)) - a/x","F",0
8,1,805,0,0.827554," ","integrate(x^5*(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} - \frac{2 \, b^{2} d^{2} x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 i \, b^{2} d^{2} x^{4} \sin\left(2 \, d x^{2} + 2 \, c\right) - {\left(2 \, a b d^{2} x^{4} - 2 \, b^{2} d x^{2} - 2 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(2 i \, a b d^{2} x^{4} - 2 i \, b^{2} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \arctan\left(\sin\left(d x^{2} + c\right), \cos\left(d x^{2} + c\right) + 1\right) - {\left(2 \, a b d^{2} x^{4} + 2 \, b^{2} d x^{2} - 2 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(2 i \, a b d^{2} x^{4} + 2 i \, b^{2} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \arctan\left(\sin\left(d x^{2} + c\right), -\cos\left(d x^{2} + c\right) + 1\right) + {\left(4 \, a b d x^{2} - 2 \, b^{2} - 2 \, {\left(2 \, a b d x^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(-4 i \, a b d x^{2} + 2 i \, b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x^{2} + i \, c\right)}\right) - {\left(4 \, a b d x^{2} + 2 \, b^{2} - 2 \, {\left(2 \, a b d x^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(4 i \, a b d x^{2} + 2 i \, b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x^{2} + i \, c\right)}\right) + {\left(i \, a b d^{2} x^{4} - i \, b^{2} d x^{2} + {\left(-i \, a b d^{2} x^{4} + i \, b^{2} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1\right) + {\left(-i \, a b d^{2} x^{4} - i \, b^{2} d x^{2} + {\left(i \, a b d^{2} x^{4} + i \, b^{2} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(a b d^{2} x^{4} + b^{2} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1\right) + {\left(-4 i \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + 4 i \, a b\right)} {\rm Li}_{3}(-e^{\left(i \, d x^{2} + i \, c\right)}) + {\left(4 i \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) - 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) - 4 i \, a b\right)} {\rm Li}_{3}(e^{\left(i \, d x^{2} + i \, c\right)})}{-2 i \, d^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 \, d^{3} \sin\left(2 \, d x^{2} + 2 \, c\right) + 2 i \, d^{3}}"," ",0,"1/6*a^2*x^6 - (2*b^2*d^2*x^4*cos(2*d*x^2 + 2*c) + 2*I*b^2*d^2*x^4*sin(2*d*x^2 + 2*c) - (2*a*b*d^2*x^4 - 2*b^2*d*x^2 - 2*(a*b*d^2*x^4 - b^2*d*x^2)*cos(2*d*x^2 + 2*c) - (2*I*a*b*d^2*x^4 - 2*I*b^2*d*x^2)*sin(2*d*x^2 + 2*c))*arctan2(sin(d*x^2 + c), cos(d*x^2 + c) + 1) - (2*a*b*d^2*x^4 + 2*b^2*d*x^2 - 2*(a*b*d^2*x^4 + b^2*d*x^2)*cos(2*d*x^2 + 2*c) - (2*I*a*b*d^2*x^4 + 2*I*b^2*d*x^2)*sin(2*d*x^2 + 2*c))*arctan2(sin(d*x^2 + c), -cos(d*x^2 + c) + 1) + (4*a*b*d*x^2 - 2*b^2 - 2*(2*a*b*d*x^2 - b^2)*cos(2*d*x^2 + 2*c) + (-4*I*a*b*d*x^2 + 2*I*b^2)*sin(2*d*x^2 + 2*c))*dilog(-e^(I*d*x^2 + I*c)) - (4*a*b*d*x^2 + 2*b^2 - 2*(2*a*b*d*x^2 + b^2)*cos(2*d*x^2 + 2*c) - (4*I*a*b*d*x^2 + 2*I*b^2)*sin(2*d*x^2 + 2*c))*dilog(e^(I*d*x^2 + I*c)) + (I*a*b*d^2*x^4 - I*b^2*d*x^2 + (-I*a*b*d^2*x^4 + I*b^2*d*x^2)*cos(2*d*x^2 + 2*c) + (a*b*d^2*x^4 - b^2*d*x^2)*sin(2*d*x^2 + 2*c))*log(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1) + (-I*a*b*d^2*x^4 - I*b^2*d*x^2 + (I*a*b*d^2*x^4 + I*b^2*d*x^2)*cos(2*d*x^2 + 2*c) - (a*b*d^2*x^4 + b^2*d*x^2)*sin(2*d*x^2 + 2*c))*log(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1) + (-4*I*a*b*cos(2*d*x^2 + 2*c) + 4*a*b*sin(2*d*x^2 + 2*c) + 4*I*a*b)*polylog(3, -e^(I*d*x^2 + I*c)) + (4*I*a*b*cos(2*d*x^2 + 2*c) - 4*a*b*sin(2*d*x^2 + 2*c) - 4*I*a*b)*polylog(3, e^(I*d*x^2 + I*c)))/(-2*I*d^3*cos(2*d*x^2 + 2*c) + 2*d^3*sin(2*d*x^2 + 2*c) + 2*I*d^3)","B",0
9,0,0,0,0.000000," ","integrate(x^4*(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} - \frac{b^{2} x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{1}{2} \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} \int \frac{{\left(4 \, a b d x^{4} - 3 \, b^{2} x^{2}\right)} \sin\left(d x^{2} + c\right)}{d \cos\left(d x^{2} + c\right)^{2} + d \sin\left(d x^{2} + c\right)^{2} + 2 \, d \cos\left(d x^{2} + c\right) + d}\,{d x} - \frac{1}{2} \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} \int \frac{{\left(4 \, a b d x^{4} + 3 \, b^{2} x^{2}\right)} \sin\left(d x^{2} + c\right)}{d \cos\left(d x^{2} + c\right)^{2} + d \sin\left(d x^{2} + c\right)^{2} - 2 \, d \cos\left(d x^{2} + c\right) + d}\,{d x}}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}"," ",0,"1/5*a^2*x^5 - (b^2*x^3*sin(2*d*x^2 + 2*c) - (d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)*integrate(1/2*(4*a*b*d*x^4 - 3*b^2*x^2)*sin(d*x^2 + c)/(d*cos(d*x^2 + c)^2 + d*sin(d*x^2 + c)^2 + 2*d*cos(d*x^2 + c) + d), x) - (d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)*integrate(1/2*(4*a*b*d*x^4 + 3*b^2*x^2)*sin(d*x^2 + c)/(d*cos(d*x^2 + c)^2 + d*sin(d*x^2 + c)^2 - 2*d*cos(d*x^2 + c) + d), x))/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)","F",0
10,1,607,0,0.652802," ","integrate(x^3*(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} x^{4} - \frac{4 \, b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 i \, b^{2} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - {\left(4 \, a b d x^{2} - 2 \, b^{2} - 2 \, {\left(2 \, a b d x^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(4 i \, a b d x^{2} - 2 i \, b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \arctan\left(\sin\left(d x^{2} + c\right), \cos\left(d x^{2} + c\right) + 1\right) - {\left(2 \, b^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 i \, b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - 2 \, b^{2}\right)} \arctan\left(\sin\left(d x^{2} + c\right), \cos\left(d x^{2} + c\right) - 1\right) + 4 \, {\left(a b d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + i \, a b d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - a b d x^{2}\right)} \arctan\left(\sin\left(d x^{2} + c\right), -\cos\left(d x^{2} + c\right) + 1\right) - {\left(4 \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 i \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) - 4 \, a b\right)} {\rm Li}_2\left(-e^{\left(i \, d x^{2} + i \, c\right)}\right) + {\left(4 \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 i \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) - 4 \, a b\right)} {\rm Li}_2\left(e^{\left(i \, d x^{2} + i \, c\right)}\right) + {\left(2 i \, a b d x^{2} - i \, b^{2} + {\left(-2 i \, a b d x^{2} + i \, b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(2 \, a b d x^{2} - b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} + 2 \, \cos\left(d x^{2} + c\right) + 1\right) + {\left(-2 i \, a b d x^{2} - i \, b^{2} + {\left(2 i \, a b d x^{2} + i \, b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(2 \, a b d x^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\cos\left(d x^{2} + c\right)^{2} + \sin\left(d x^{2} + c\right)^{2} - 2 \, \cos\left(d x^{2} + c\right) + 1\right)}{-4 i \, d^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, d^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + 4 i \, d^{2}}"," ",0,"1/4*a^2*x^4 - (4*b^2*d*x^2*cos(2*d*x^2 + 2*c) + 4*I*b^2*d*x^2*sin(2*d*x^2 + 2*c) - (4*a*b*d*x^2 - 2*b^2 - 2*(2*a*b*d*x^2 - b^2)*cos(2*d*x^2 + 2*c) - (4*I*a*b*d*x^2 - 2*I*b^2)*sin(2*d*x^2 + 2*c))*arctan2(sin(d*x^2 + c), cos(d*x^2 + c) + 1) - (2*b^2*cos(2*d*x^2 + 2*c) + 2*I*b^2*sin(2*d*x^2 + 2*c) - 2*b^2)*arctan2(sin(d*x^2 + c), cos(d*x^2 + c) - 1) + 4*(a*b*d*x^2*cos(2*d*x^2 + 2*c) + I*a*b*d*x^2*sin(2*d*x^2 + 2*c) - a*b*d*x^2)*arctan2(sin(d*x^2 + c), -cos(d*x^2 + c) + 1) - (4*a*b*cos(2*d*x^2 + 2*c) + 4*I*a*b*sin(2*d*x^2 + 2*c) - 4*a*b)*dilog(-e^(I*d*x^2 + I*c)) + (4*a*b*cos(2*d*x^2 + 2*c) + 4*I*a*b*sin(2*d*x^2 + 2*c) - 4*a*b)*dilog(e^(I*d*x^2 + I*c)) + (2*I*a*b*d*x^2 - I*b^2 + (-2*I*a*b*d*x^2 + I*b^2)*cos(2*d*x^2 + 2*c) + (2*a*b*d*x^2 - b^2)*sin(2*d*x^2 + 2*c))*log(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 + 2*cos(d*x^2 + c) + 1) + (-2*I*a*b*d*x^2 - I*b^2 + (2*I*a*b*d*x^2 + I*b^2)*cos(2*d*x^2 + 2*c) - (2*a*b*d*x^2 + b^2)*sin(2*d*x^2 + 2*c))*log(cos(d*x^2 + c)^2 + sin(d*x^2 + c)^2 - 2*cos(d*x^2 + c) + 1))/(-4*I*d^2*cos(2*d*x^2 + 2*c) + 4*d^2*sin(2*d*x^2 + 2*c) + 4*I*d^2)","B",0
11,0,0,0,0.000000," ","integrate(x^2*(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} - \frac{b^{2} x \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{1}{2} \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} \int \frac{{\left(4 \, a b d x^{2} - b^{2}\right)} \sin\left(d x^{2} + c\right)}{d \cos\left(d x^{2} + c\right)^{2} + d \sin\left(d x^{2} + c\right)^{2} + 2 \, d \cos\left(d x^{2} + c\right) + d}\,{d x} - \frac{1}{2} \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} \int \frac{{\left(4 \, a b d x^{2} + b^{2}\right)} \sin\left(d x^{2} + c\right)}{d \cos\left(d x^{2} + c\right)^{2} + d \sin\left(d x^{2} + c\right)^{2} - 2 \, d \cos\left(d x^{2} + c\right) + d}\,{d x}}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}"," ",0,"1/3*a^2*x^3 - (b^2*x*sin(2*d*x^2 + 2*c) - (d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)*integrate(1/2*(4*a*b*d*x^2 - b^2)*sin(d*x^2 + c)/(d*cos(d*x^2 + c)^2 + d*sin(d*x^2 + c)^2 + 2*d*cos(d*x^2 + c) + d), x) - (d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)*integrate(1/2*(4*a*b*d*x^2 + b^2)*sin(d*x^2 + c)/(d*cos(d*x^2 + c)^2 + d*sin(d*x^2 + c)^2 - 2*d*cos(d*x^2 + c) + d), x))/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)","F",0
12,1,98,0,0.494312," ","integrate(x*(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} - \frac{a b \log\left(\cot\left(d x^{2} + c\right) + \csc\left(d x^{2} + c\right)\right)}{d} - \frac{b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}"," ",0,"1/2*a^2*x^2 - a*b*log(cot(d*x^2 + c) + csc(d*x^2 + c))/d - b^2*sin(2*d*x^2 + 2*c)/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 - 2*d*cos(2*d*x^2 + 2*c) + d)","B",0
13,0,0,0,0.000000," ","integrate((a+b*csc(d*x^2+c))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) - \frac{b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{{\left(d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}\right)} {\left(2 \, a d \int \frac{x^{2} \sin\left(d x^{2} + c\right)}{x^{3} \cos\left(d x^{2} + c\right)^{2} + x^{3} \sin\left(d x^{2} + c\right)^{2} + 2 \, x^{3} \cos\left(d x^{2} + c\right) + x^{3}}\,{d x} + b \int \frac{\sin\left(d x^{2} + c\right)}{x^{3} \cos\left(d x^{2} + c\right)^{2} + x^{3} \sin\left(d x^{2} + c\right)^{2} + 2 \, x^{3} \cos\left(d x^{2} + c\right) + x^{3}}\,{d x}\right)} b}{d} - \frac{{\left(d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}\right)} {\left(2 \, a d \int \frac{x^{2} \sin\left(d x^{2} + c\right)}{x^{3} \cos\left(d x^{2} + c\right)^{2} + x^{3} \sin\left(d x^{2} + c\right)^{2} - 2 \, x^{3} \cos\left(d x^{2} + c\right) + x^{3}}\,{d x} - b \int \frac{\sin\left(d x^{2} + c\right)}{x^{3} \cos\left(d x^{2} + c\right)^{2} + x^{3} \sin\left(d x^{2} + c\right)^{2} - 2 \, x^{3} \cos\left(d x^{2} + c\right) + x^{3}}\,{d x}\right)} b}{d}}{d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}}"," ",0,"a^2*log(x) - (b^2*sin(2*d*x^2 + 2*c) - (d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 - 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)*integrate((2*a*b*d*x^2 + b^2)*sin(d*x^2 + c)/(d*x^3*cos(d*x^2 + c)^2 + d*x^3*sin(d*x^2 + c)^2 + 2*d*x^3*cos(d*x^2 + c) + d*x^3), x) - (d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 - 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)*integrate((2*a*b*d*x^2 - b^2)*sin(d*x^2 + c)/(d*x^3*cos(d*x^2 + c)^2 + d*x^3*sin(d*x^2 + c)^2 - 2*d*x^3*cos(d*x^2 + c) + d*x^3), x))/(d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 - 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)","F",0
14,0,0,0,0.000000," ","integrate((a+b*csc(d*x^2+c))^2/x^2,x, algorithm=""maxima"")","-\frac{a^{2}}{x} - \frac{b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{1}{2} \, {\left(d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}\right)} \int \frac{{\left(4 \, a b d x^{2} + 3 \, b^{2}\right)} \sin\left(d x^{2} + c\right)}{d x^{4} \cos\left(d x^{2} + c\right)^{2} + d x^{4} \sin\left(d x^{2} + c\right)^{2} + 2 \, d x^{4} \cos\left(d x^{2} + c\right) + d x^{4}}\,{d x} - \frac{1}{2} \, {\left(d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}\right)} \int \frac{{\left(4 \, a b d x^{2} - 3 \, b^{2}\right)} \sin\left(d x^{2} + c\right)}{d x^{4} \cos\left(d x^{2} + c\right)^{2} + d x^{4} \sin\left(d x^{2} + c\right)^{2} - 2 \, d x^{4} \cos\left(d x^{2} + c\right) + d x^{4}}\,{d x}}{d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}}"," ",0,"-a^2/x - (b^2*sin(2*d*x^2 + 2*c) - (d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 - 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3)*integrate(1/2*(4*a*b*d*x^2 + 3*b^2)*sin(d*x^2 + c)/(d*x^4*cos(d*x^2 + c)^2 + d*x^4*sin(d*x^2 + c)^2 + 2*d*x^4*cos(d*x^2 + c) + d*x^4), x) - (d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 - 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3)*integrate(1/2*(4*a*b*d*x^2 - 3*b^2)*sin(d*x^2 + c)/(d*x^4*cos(d*x^2 + c)^2 + d*x^4*sin(d*x^2 + c)^2 - 2*d*x^4*cos(d*x^2 + c) + d*x^4), x))/(d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 - 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3)","F",0
15,1,3543,0,0.581372," ","integrate(x*csc(b*x^2+a)^7,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \cos\left(11 \, b x^{2} + 11 \, a\right) - 85 \, \cos\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) + 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \cos\left(b x^{2} + a\right)\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) - 60 \, {\left(6 \, \cos\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(11 \, b x^{2} + 11 \, a\right) + 24 \, {\left(85 \, \cos\left(9 \, b x^{2} + 9 \, a\right) - 198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) + 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \cos\left(b x^{2} + a\right)\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) - 340 \, {\left(15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(9 \, b x^{2} + 9 \, a\right) + 60 \, {\left(198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) + 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \cos\left(b x^{2} + a\right)\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) - 792 \, {\left(20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(7 \, b x^{2} + 7 \, a\right) - 80 \, {\left(198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \cos\left(b x^{2} + a\right)\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) + 792 \, {\left(15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(5 \, b x^{2} + 5 \, a\right) - 300 \, {\left(17 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 3 \, \cos\left(b x^{2} + a\right)\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) + 340 \, {\left(6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(3 \, b x^{2} + 3 \, a\right) - 360 \, \cos\left(2 \, b x^{2} + 2 \, a\right) \cos\left(b x^{2} + a\right) + 15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) - \cos\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) - 36 \, \cos\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) - 225 \, \cos\left(8 \, b x^{2} + 8 \, a\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) - 400 \, \cos\left(6 \, b x^{2} + 6 \, a\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) - 225 \, \cos\left(4 \, b x^{2} + 4 \, a\right)^{2} - 36 \, \cos\left(2 \, b x^{2} + 2 \, a\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) - \sin\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) - 36 \, \sin\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) - 225 \, \sin\left(8 \, b x^{2} + 8 \, a\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 2 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) - 400 \, \sin\left(6 \, b x^{2} + 6 \, a\right)^{2} - 225 \, \sin\left(4 \, b x^{2} + 4 \, a\right)^{2} + 180 \, \sin\left(4 \, b x^{2} + 4 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) - 36 \, \sin\left(2 \, b x^{2} + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x^{2}\right)^{2} + 2 \, \cos\left(b x^{2}\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x^{2}\right)^{2} - 2 \, \sin\left(b x^{2}\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) - \cos\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) - 36 \, \cos\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) - 225 \, \cos\left(8 \, b x^{2} + 8 \, a\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) - 400 \, \cos\left(6 \, b x^{2} + 6 \, a\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) - 225 \, \cos\left(4 \, b x^{2} + 4 \, a\right)^{2} - 36 \, \cos\left(2 \, b x^{2} + 2 \, a\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) - \sin\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) - 36 \, \sin\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) - 225 \, \sin\left(8 \, b x^{2} + 8 \, a\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 2 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) - 400 \, \sin\left(6 \, b x^{2} + 6 \, a\right)^{2} - 225 \, \sin\left(4 \, b x^{2} + 4 \, a\right)^{2} + 180 \, \sin\left(4 \, b x^{2} + 4 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) - 36 \, \sin\left(2 \, b x^{2} + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x^{2} + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x^{2}\right)^{2} - 2 \, \cos\left(b x^{2}\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x^{2}\right)^{2} + 2 \, \sin\left(b x^{2}\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(15 \, \sin\left(11 \, b x^{2} + 11 \, a\right) - 85 \, \sin\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) + 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \sin\left(b x^{2} + a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) - 60 \, {\left(6 \, \sin\left(10 \, b x^{2} + 10 \, a\right) - 15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(11 \, b x^{2} + 11 \, a\right) + 24 \, {\left(85 \, \sin\left(9 \, b x^{2} + 9 \, a\right) - 198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) + 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \sin\left(b x^{2} + a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) - 340 \, {\left(15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) - 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(9 \, b x^{2} + 9 \, a\right) + 60 \, {\left(198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) + 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \sin\left(b x^{2} + a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) - 792 \, {\left(20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(7 \, b x^{2} + 7 \, a\right) - 80 \, {\left(198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \sin\left(b x^{2} + a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) + 2376 \, {\left(5 \, \sin\left(4 \, b x^{2} + 4 \, a\right) - 2 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(5 \, b x^{2} + 5 \, a\right) - 300 \, {\left(17 \, \sin\left(3 \, b x^{2} + 3 \, a\right) - 3 \, \sin\left(b x^{2} + a\right)\right)} \sin\left(4 \, b x^{2} + 4 \, a\right) + 2040 \, \sin\left(3 \, b x^{2} + 3 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) - 360 \, \sin\left(2 \, b x^{2} + 2 \, a\right) \sin\left(b x^{2} + a\right) + 60 \, \cos\left(b x^{2} + a\right)}{192 \, {\left(b \cos\left(12 \, b x^{2} + 12 \, a\right)^{2} + 36 \, b \cos\left(10 \, b x^{2} + 10 \, a\right)^{2} + 225 \, b \cos\left(8 \, b x^{2} + 8 \, a\right)^{2} + 400 \, b \cos\left(6 \, b x^{2} + 6 \, a\right)^{2} + 225 \, b \cos\left(4 \, b x^{2} + 4 \, a\right)^{2} + 36 \, b \cos\left(2 \, b x^{2} + 2 \, a\right)^{2} + b \sin\left(12 \, b x^{2} + 12 \, a\right)^{2} + 36 \, b \sin\left(10 \, b x^{2} + 10 \, a\right)^{2} + 225 \, b \sin\left(8 \, b x^{2} + 8 \, a\right)^{2} + 400 \, b \sin\left(6 \, b x^{2} + 6 \, a\right)^{2} + 225 \, b \sin\left(4 \, b x^{2} + 4 \, a\right)^{2} - 180 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) + 36 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)^{2} - 2 \, {\left(6 \, b \cos\left(10 \, b x^{2} + 10 \, a\right) - 15 \, b \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) - b\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) - 12 \, {\left(15 \, b \cos\left(8 \, b x^{2} + 8 \, a\right) - 20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) - 30 \, {\left(20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) - 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) - b\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) - 40 \, {\left(15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) - 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) - 30 \, {\left(6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) - b\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) - 12 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) - 2 \, {\left(6 \, b \sin\left(10 \, b x^{2} + 10 \, a\right) - 15 \, b \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) - 12 \, {\left(15 \, b \sin\left(8 \, b x^{2} + 8 \, a\right) - 20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) - 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) - 30 \, {\left(20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) - 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) - 120 \, {\left(5 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) - 2 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) + b\right)}}"," ",0,"1/192*(4*(15*cos(11*b*x^2 + 11*a) - 85*cos(9*b*x^2 + 9*a) + 198*cos(7*b*x^2 + 7*a) + 198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) + 15*cos(b*x^2 + a))*cos(12*b*x^2 + 12*a) - 60*(6*cos(10*b*x^2 + 10*a) - 15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(11*b*x^2 + 11*a) + 24*(85*cos(9*b*x^2 + 9*a) - 198*cos(7*b*x^2 + 7*a) - 198*cos(5*b*x^2 + 5*a) + 85*cos(3*b*x^2 + 3*a) - 15*cos(b*x^2 + a))*cos(10*b*x^2 + 10*a) - 340*(15*cos(8*b*x^2 + 8*a) - 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(9*b*x^2 + 9*a) + 60*(198*cos(7*b*x^2 + 7*a) + 198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) + 15*cos(b*x^2 + a))*cos(8*b*x^2 + 8*a) - 792*(20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(7*b*x^2 + 7*a) - 80*(198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) + 15*cos(b*x^2 + a))*cos(6*b*x^2 + 6*a) + 792*(15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(5*b*x^2 + 5*a) - 300*(17*cos(3*b*x^2 + 3*a) - 3*cos(b*x^2 + a))*cos(4*b*x^2 + 4*a) + 340*(6*cos(2*b*x^2 + 2*a) - 1)*cos(3*b*x^2 + 3*a) - 360*cos(2*b*x^2 + 2*a)*cos(b*x^2 + a) + 15*(2*(6*cos(10*b*x^2 + 10*a) - 15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(12*b*x^2 + 12*a) - cos(12*b*x^2 + 12*a)^2 + 12*(15*cos(8*b*x^2 + 8*a) - 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(10*b*x^2 + 10*a) - 36*cos(10*b*x^2 + 10*a)^2 + 30*(20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(8*b*x^2 + 8*a) - 225*cos(8*b*x^2 + 8*a)^2 + 40*(15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(6*b*x^2 + 6*a) - 400*cos(6*b*x^2 + 6*a)^2 + 30*(6*cos(2*b*x^2 + 2*a) - 1)*cos(4*b*x^2 + 4*a) - 225*cos(4*b*x^2 + 4*a)^2 - 36*cos(2*b*x^2 + 2*a)^2 + 2*(6*sin(10*b*x^2 + 10*a) - 15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(12*b*x^2 + 12*a) - sin(12*b*x^2 + 12*a)^2 + 12*(15*sin(8*b*x^2 + 8*a) - 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) - 6*sin(2*b*x^2 + 2*a))*sin(10*b*x^2 + 10*a) - 36*sin(10*b*x^2 + 10*a)^2 + 30*(20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(8*b*x^2 + 8*a) - 225*sin(8*b*x^2 + 8*a)^2 + 120*(5*sin(4*b*x^2 + 4*a) - 2*sin(2*b*x^2 + 2*a))*sin(6*b*x^2 + 6*a) - 400*sin(6*b*x^2 + 6*a)^2 - 225*sin(4*b*x^2 + 4*a)^2 + 180*sin(4*b*x^2 + 4*a)*sin(2*b*x^2 + 2*a) - 36*sin(2*b*x^2 + 2*a)^2 + 12*cos(2*b*x^2 + 2*a) - 1)*log(cos(b*x^2)^2 + 2*cos(b*x^2)*cos(a) + cos(a)^2 + sin(b*x^2)^2 - 2*sin(b*x^2)*sin(a) + sin(a)^2) - 15*(2*(6*cos(10*b*x^2 + 10*a) - 15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(12*b*x^2 + 12*a) - cos(12*b*x^2 + 12*a)^2 + 12*(15*cos(8*b*x^2 + 8*a) - 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(10*b*x^2 + 10*a) - 36*cos(10*b*x^2 + 10*a)^2 + 30*(20*cos(6*b*x^2 + 6*a) - 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) - 1)*cos(8*b*x^2 + 8*a) - 225*cos(8*b*x^2 + 8*a)^2 + 40*(15*cos(4*b*x^2 + 4*a) - 6*cos(2*b*x^2 + 2*a) + 1)*cos(6*b*x^2 + 6*a) - 400*cos(6*b*x^2 + 6*a)^2 + 30*(6*cos(2*b*x^2 + 2*a) - 1)*cos(4*b*x^2 + 4*a) - 225*cos(4*b*x^2 + 4*a)^2 - 36*cos(2*b*x^2 + 2*a)^2 + 2*(6*sin(10*b*x^2 + 10*a) - 15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(12*b*x^2 + 12*a) - sin(12*b*x^2 + 12*a)^2 + 12*(15*sin(8*b*x^2 + 8*a) - 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) - 6*sin(2*b*x^2 + 2*a))*sin(10*b*x^2 + 10*a) - 36*sin(10*b*x^2 + 10*a)^2 + 30*(20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(8*b*x^2 + 8*a) - 225*sin(8*b*x^2 + 8*a)^2 + 120*(5*sin(4*b*x^2 + 4*a) - 2*sin(2*b*x^2 + 2*a))*sin(6*b*x^2 + 6*a) - 400*sin(6*b*x^2 + 6*a)^2 - 225*sin(4*b*x^2 + 4*a)^2 + 180*sin(4*b*x^2 + 4*a)*sin(2*b*x^2 + 2*a) - 36*sin(2*b*x^2 + 2*a)^2 + 12*cos(2*b*x^2 + 2*a) - 1)*log(cos(b*x^2)^2 - 2*cos(b*x^2)*cos(a) + cos(a)^2 + sin(b*x^2)^2 + 2*sin(b*x^2)*sin(a) + sin(a)^2) + 4*(15*sin(11*b*x^2 + 11*a) - 85*sin(9*b*x^2 + 9*a) + 198*sin(7*b*x^2 + 7*a) + 198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) + 15*sin(b*x^2 + a))*sin(12*b*x^2 + 12*a) - 60*(6*sin(10*b*x^2 + 10*a) - 15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(11*b*x^2 + 11*a) + 24*(85*sin(9*b*x^2 + 9*a) - 198*sin(7*b*x^2 + 7*a) - 198*sin(5*b*x^2 + 5*a) + 85*sin(3*b*x^2 + 3*a) - 15*sin(b*x^2 + a))*sin(10*b*x^2 + 10*a) - 340*(15*sin(8*b*x^2 + 8*a) - 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) - 6*sin(2*b*x^2 + 2*a))*sin(9*b*x^2 + 9*a) + 60*(198*sin(7*b*x^2 + 7*a) + 198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) + 15*sin(b*x^2 + a))*sin(8*b*x^2 + 8*a) - 792*(20*sin(6*b*x^2 + 6*a) - 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(7*b*x^2 + 7*a) - 80*(198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) + 15*sin(b*x^2 + a))*sin(6*b*x^2 + 6*a) + 2376*(5*sin(4*b*x^2 + 4*a) - 2*sin(2*b*x^2 + 2*a))*sin(5*b*x^2 + 5*a) - 300*(17*sin(3*b*x^2 + 3*a) - 3*sin(b*x^2 + a))*sin(4*b*x^2 + 4*a) + 2040*sin(3*b*x^2 + 3*a)*sin(2*b*x^2 + 2*a) - 360*sin(2*b*x^2 + 2*a)*sin(b*x^2 + a) + 60*cos(b*x^2 + a))/(b*cos(12*b*x^2 + 12*a)^2 + 36*b*cos(10*b*x^2 + 10*a)^2 + 225*b*cos(8*b*x^2 + 8*a)^2 + 400*b*cos(6*b*x^2 + 6*a)^2 + 225*b*cos(4*b*x^2 + 4*a)^2 + 36*b*cos(2*b*x^2 + 2*a)^2 + b*sin(12*b*x^2 + 12*a)^2 + 36*b*sin(10*b*x^2 + 10*a)^2 + 225*b*sin(8*b*x^2 + 8*a)^2 + 400*b*sin(6*b*x^2 + 6*a)^2 + 225*b*sin(4*b*x^2 + 4*a)^2 - 180*b*sin(4*b*x^2 + 4*a)*sin(2*b*x^2 + 2*a) + 36*b*sin(2*b*x^2 + 2*a)^2 - 2*(6*b*cos(10*b*x^2 + 10*a) - 15*b*cos(8*b*x^2 + 8*a) + 20*b*cos(6*b*x^2 + 6*a) - 15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) - b)*cos(12*b*x^2 + 12*a) - 12*(15*b*cos(8*b*x^2 + 8*a) - 20*b*cos(6*b*x^2 + 6*a) + 15*b*cos(4*b*x^2 + 4*a) - 6*b*cos(2*b*x^2 + 2*a) + b)*cos(10*b*x^2 + 10*a) - 30*(20*b*cos(6*b*x^2 + 6*a) - 15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) - b)*cos(8*b*x^2 + 8*a) - 40*(15*b*cos(4*b*x^2 + 4*a) - 6*b*cos(2*b*x^2 + 2*a) + b)*cos(6*b*x^2 + 6*a) - 30*(6*b*cos(2*b*x^2 + 2*a) - b)*cos(4*b*x^2 + 4*a) - 12*b*cos(2*b*x^2 + 2*a) - 2*(6*b*sin(10*b*x^2 + 10*a) - 15*b*sin(8*b*x^2 + 8*a) + 20*b*sin(6*b*x^2 + 6*a) - 15*b*sin(4*b*x^2 + 4*a) + 6*b*sin(2*b*x^2 + 2*a))*sin(12*b*x^2 + 12*a) - 12*(15*b*sin(8*b*x^2 + 8*a) - 20*b*sin(6*b*x^2 + 6*a) + 15*b*sin(4*b*x^2 + 4*a) - 6*b*sin(2*b*x^2 + 2*a))*sin(10*b*x^2 + 10*a) - 30*(20*b*sin(6*b*x^2 + 6*a) - 15*b*sin(4*b*x^2 + 4*a) + 6*b*sin(2*b*x^2 + 2*a))*sin(8*b*x^2 + 8*a) - 120*(5*b*sin(4*b*x^2 + 4*a) - 2*b*sin(2*b*x^2 + 2*a))*sin(6*b*x^2 + 6*a) + b)","B",0
16,-1,0,0,0.000000," ","integrate(x^5/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(x^4/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-2,0,0,0.000000," ","integrate(x^3/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
19,-1,0,0,0.000000," ","integrate(x^2/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate(x/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate(1/x/(a+b*csc(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,0,0,0,0.000000," ","integrate((a+b*csc(d*x^2+c))/x^2,x, algorithm=""maxima"")","b {\left(\int \frac{\sin\left(d x^{2} + c\right)}{x^{2} \cos\left(d x^{2} + c\right)^{2} + x^{2} \sin\left(d x^{2} + c\right)^{2} + 2 \, x^{2} \cos\left(d x^{2} + c\right) + x^{2}}\,{d x} + \int \frac{\sin\left(d x^{2} + c\right)}{x^{2} \cos\left(d x^{2} + c\right)^{2} + x^{2} \sin\left(d x^{2} + c\right)^{2} - 2 \, x^{2} \cos\left(d x^{2} + c\right) + x^{2}}\,{d x}\right)} - \frac{a}{x}"," ",0,"b*(integrate(sin(d*x^2 + c)/(x^2*cos(d*x^2 + c)^2 + x^2*sin(d*x^2 + c)^2 + 2*x^2*cos(d*x^2 + c) + x^2), x) + integrate(sin(d*x^2 + c)/(x^2*cos(d*x^2 + c)^2 + x^2*sin(d*x^2 + c)^2 - 2*x^2*cos(d*x^2 + c) + x^2), x)) - a/x","F",0
23,-2,0,0,0.000000," ","integrate(x^5/(a+b*csc(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
24,-1,0,0,0.000000," ","integrate(x^4/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-2,0,0,0.000000," ","integrate(x^3/(a+b*csc(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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
26,-1,0,0,0.000000," ","integrate(x^2/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate(x/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate(1/x/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate(1/x^3/(a+b*csc(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,1,1498,0,4.118638," ","integrate(x^3*(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{8} a - 8 \, {\left(d \sqrt{x} + c\right)}^{7} a c + 28 \, {\left(d \sqrt{x} + c\right)}^{6} a c^{2} - 56 \, {\left(d \sqrt{x} + c\right)}^{5} a c^{3} + 70 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{4} - 56 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{5} + 28 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{6} - 8 \, {\left(d \sqrt{x} + c\right)} a c^{7} + 8 \, b c^{7} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - 4 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{7} b - 14 i \, {\left(d \sqrt{x} + c\right)}^{6} b c + 42 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 70 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 70 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 42 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 14 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{7} b - 14 i \, {\left(d \sqrt{x} + c\right)}^{6} b c + 42 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 70 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 70 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 42 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 14 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left(-14 i \, {\left(d \sqrt{x} + c\right)}^{6} b + 84 i \, {\left(d \sqrt{x} + c\right)}^{5} b c - 210 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} + 280 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} - 210 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} + 84 i \, {\left(d \sqrt{x} + c\right)} b c^{5} - 14 i \, b c^{6}\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 4 \, {\left(14 i \, {\left(d \sqrt{x} + c\right)}^{6} b - 84 i \, {\left(d \sqrt{x} + c\right)}^{5} b c + 210 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} - 280 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} + 210 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} - 84 i \, {\left(d \sqrt{x} + c\right)} b c^{5} + 14 i \, b c^{6}\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 4 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 4 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - 40320 i \, b {\rm Li}_{8}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 40320 i \, b {\rm Li}_{8}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 40320 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{7}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 40320 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{7}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 4 \, {\left(-5040 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 10080 i \, {\left(d \sqrt{x} + c\right)} b c - 5040 i \, b c^{2}\right)} {\rm Li}_{6}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 4 \, {\left(5040 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 10080 i \, {\left(d \sqrt{x} + c\right)} b c + 5040 i \, b c^{2}\right)} {\rm Li}_{6}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 6720 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 6720 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 4 \, {\left(420 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 1680 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 2520 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 1680 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 420 i \, b c^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 4 \, {\left(-420 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 1680 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 2520 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 1680 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 420 i \, b c^{4}\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 336 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4} - b c^{5}\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 336 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4} - b c^{5}\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)})}{4 \, d^{8}}"," ",0,"1/4*((d*sqrt(x) + c)^8*a - 8*(d*sqrt(x) + c)^7*a*c + 28*(d*sqrt(x) + c)^6*a*c^2 - 56*(d*sqrt(x) + c)^5*a*c^3 + 70*(d*sqrt(x) + c)^4*a*c^4 - 56*(d*sqrt(x) + c)^3*a*c^5 + 28*(d*sqrt(x) + c)^2*a*c^6 - 8*(d*sqrt(x) + c)*a*c^7 + 8*b*c^7*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 4*(2*I*(d*sqrt(x) + c)^7*b - 14*I*(d*sqrt(x) + c)^6*b*c + 42*I*(d*sqrt(x) + c)^5*b*c^2 - 70*I*(d*sqrt(x) + c)^4*b*c^3 + 70*I*(d*sqrt(x) + c)^3*b*c^4 - 42*I*(d*sqrt(x) + c)^2*b*c^5 + 14*I*(d*sqrt(x) + c)*b*c^6)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) - 4*(2*I*(d*sqrt(x) + c)^7*b - 14*I*(d*sqrt(x) + c)^6*b*c + 42*I*(d*sqrt(x) + c)^5*b*c^2 - 70*I*(d*sqrt(x) + c)^4*b*c^3 + 70*I*(d*sqrt(x) + c)^3*b*c^4 - 42*I*(d*sqrt(x) + c)^2*b*c^5 + 14*I*(d*sqrt(x) + c)*b*c^6)*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 4*(-14*I*(d*sqrt(x) + c)^6*b + 84*I*(d*sqrt(x) + c)^5*b*c - 210*I*(d*sqrt(x) + c)^4*b*c^2 + 280*I*(d*sqrt(x) + c)^3*b*c^3 - 210*I*(d*sqrt(x) + c)^2*b*c^4 + 84*I*(d*sqrt(x) + c)*b*c^5 - 14*I*b*c^6)*dilog(-e^(I*d*sqrt(x) + I*c)) - 4*(14*I*(d*sqrt(x) + c)^6*b - 84*I*(d*sqrt(x) + c)^5*b*c + 210*I*(d*sqrt(x) + c)^4*b*c^2 - 280*I*(d*sqrt(x) + c)^3*b*c^3 + 210*I*(d*sqrt(x) + c)^2*b*c^4 - 84*I*(d*sqrt(x) + c)*b*c^5 + 14*I*b*c^6)*dilog(e^(I*d*sqrt(x) + I*c)) - 4*((d*sqrt(x) + c)^7*b - 7*(d*sqrt(x) + c)^6*b*c + 21*(d*sqrt(x) + c)^5*b*c^2 - 35*(d*sqrt(x) + c)^4*b*c^3 + 35*(d*sqrt(x) + c)^3*b*c^4 - 21*(d*sqrt(x) + c)^2*b*c^5 + 7*(d*sqrt(x) + c)*b*c^6)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + 4*((d*sqrt(x) + c)^7*b - 7*(d*sqrt(x) + c)^6*b*c + 21*(d*sqrt(x) + c)^5*b*c^2 - 35*(d*sqrt(x) + c)^4*b*c^3 + 35*(d*sqrt(x) + c)^3*b*c^4 - 21*(d*sqrt(x) + c)^2*b*c^5 + 7*(d*sqrt(x) + c)*b*c^6)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) - 40320*I*b*polylog(8, -e^(I*d*sqrt(x) + I*c)) + 40320*I*b*polylog(8, e^(I*d*sqrt(x) + I*c)) - 40320*((d*sqrt(x) + c)*b - b*c)*polylog(7, -e^(I*d*sqrt(x) + I*c)) + 40320*((d*sqrt(x) + c)*b - b*c)*polylog(7, e^(I*d*sqrt(x) + I*c)) - 4*(-5040*I*(d*sqrt(x) + c)^2*b + 10080*I*(d*sqrt(x) + c)*b*c - 5040*I*b*c^2)*polylog(6, -e^(I*d*sqrt(x) + I*c)) - 4*(5040*I*(d*sqrt(x) + c)^2*b - 10080*I*(d*sqrt(x) + c)*b*c + 5040*I*b*c^2)*polylog(6, e^(I*d*sqrt(x) + I*c)) + 6720*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(5, -e^(I*d*sqrt(x) + I*c)) - 6720*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(5, e^(I*d*sqrt(x) + I*c)) - 4*(420*I*(d*sqrt(x) + c)^4*b - 1680*I*(d*sqrt(x) + c)^3*b*c + 2520*I*(d*sqrt(x) + c)^2*b*c^2 - 1680*I*(d*sqrt(x) + c)*b*c^3 + 420*I*b*c^4)*polylog(4, -e^(I*d*sqrt(x) + I*c)) - 4*(-420*I*(d*sqrt(x) + c)^4*b + 1680*I*(d*sqrt(x) + c)^3*b*c - 2520*I*(d*sqrt(x) + c)^2*b*c^2 + 1680*I*(d*sqrt(x) + c)*b*c^3 - 420*I*b*c^4)*polylog(4, e^(I*d*sqrt(x) + I*c)) - 336*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4 - b*c^5)*polylog(3, -e^(I*d*sqrt(x) + I*c)) + 336*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4 - b*c^5)*polylog(3, e^(I*d*sqrt(x) + I*c)))/d^8","B",0
32,1,956,0,0.886804," ","integrate(x^2*(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{6} a - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a c^{5} + 6 \, b c^{5} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - 3 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{5} b - 10 i \, {\left(d \sqrt{x} + c\right)}^{4} b c + 20 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 20 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 10 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{5} b - 10 i \, {\left(d \sqrt{x} + c\right)}^{4} b c + 20 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 20 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 10 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left(-10 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 40 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 60 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 40 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 10 i \, b c^{4}\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 3 \, {\left(10 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 40 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 60 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 40 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 10 i \, b c^{4}\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 3 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 720 i \, b {\rm Li}_{6}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 720 i \, b {\rm Li}_{6}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 720 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 720 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 3 \, {\left(120 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 240 i \, {\left(d \sqrt{x} + c\right)} b c + 120 i \, b c^{2}\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 3 \, {\left(-120 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 240 i \, {\left(d \sqrt{x} + c\right)} b c - 120 i \, b c^{2}\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 120 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 120 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)})}{3 \, d^{6}}"," ",0,"1/3*((d*sqrt(x) + c)^6*a - 6*(d*sqrt(x) + c)^5*a*c + 15*(d*sqrt(x) + c)^4*a*c^2 - 20*(d*sqrt(x) + c)^3*a*c^3 + 15*(d*sqrt(x) + c)^2*a*c^4 - 6*(d*sqrt(x) + c)*a*c^5 + 6*b*c^5*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 3*(2*I*(d*sqrt(x) + c)^5*b - 10*I*(d*sqrt(x) + c)^4*b*c + 20*I*(d*sqrt(x) + c)^3*b*c^2 - 20*I*(d*sqrt(x) + c)^2*b*c^3 + 10*I*(d*sqrt(x) + c)*b*c^4)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) - 3*(2*I*(d*sqrt(x) + c)^5*b - 10*I*(d*sqrt(x) + c)^4*b*c + 20*I*(d*sqrt(x) + c)^3*b*c^2 - 20*I*(d*sqrt(x) + c)^2*b*c^3 + 10*I*(d*sqrt(x) + c)*b*c^4)*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 3*(-10*I*(d*sqrt(x) + c)^4*b + 40*I*(d*sqrt(x) + c)^3*b*c - 60*I*(d*sqrt(x) + c)^2*b*c^2 + 40*I*(d*sqrt(x) + c)*b*c^3 - 10*I*b*c^4)*dilog(-e^(I*d*sqrt(x) + I*c)) - 3*(10*I*(d*sqrt(x) + c)^4*b - 40*I*(d*sqrt(x) + c)^3*b*c + 60*I*(d*sqrt(x) + c)^2*b*c^2 - 40*I*(d*sqrt(x) + c)*b*c^3 + 10*I*b*c^4)*dilog(e^(I*d*sqrt(x) + I*c)) - 3*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + 3*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) + 720*I*b*polylog(6, -e^(I*d*sqrt(x) + I*c)) - 720*I*b*polylog(6, e^(I*d*sqrt(x) + I*c)) + 720*((d*sqrt(x) + c)*b - b*c)*polylog(5, -e^(I*d*sqrt(x) + I*c)) - 720*((d*sqrt(x) + c)*b - b*c)*polylog(5, e^(I*d*sqrt(x) + I*c)) - 3*(120*I*(d*sqrt(x) + c)^2*b - 240*I*(d*sqrt(x) + c)*b*c + 120*I*b*c^2)*polylog(4, -e^(I*d*sqrt(x) + I*c)) - 3*(-120*I*(d*sqrt(x) + c)^2*b + 240*I*(d*sqrt(x) + c)*b*c - 120*I*b*c^2)*polylog(4, e^(I*d*sqrt(x) + I*c)) - 120*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(3, -e^(I*d*sqrt(x) + I*c)) + 120*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(3, e^(I*d*sqrt(x) + I*c)))/d^6","B",0
33,1,534,0,0.939598," ","integrate(x*(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{4} a - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a c^{3} + 4 \, b c^{3} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - 2 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} b - 6 i \, {\left(d \sqrt{x} + c\right)}^{2} b c + 6 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) - 2 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} b - 6 i \, {\left(d \sqrt{x} + c\right)}^{2} b c + 6 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 2 \, {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 12 i \, {\left(d \sqrt{x} + c\right)} b c - 6 i \, b c^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 2 \, {\left(6 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 12 i \, {\left(d \sqrt{x} + c\right)} b c + 6 i \, b c^{2}\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - 24 i \, b {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 24 i \, b {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 24 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 24 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)})}{2 \, d^{4}}"," ",0,"1/2*((d*sqrt(x) + c)^4*a - 4*(d*sqrt(x) + c)^3*a*c + 6*(d*sqrt(x) + c)^2*a*c^2 - 4*(d*sqrt(x) + c)*a*c^3 + 4*b*c^3*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 2*(2*I*(d*sqrt(x) + c)^3*b - 6*I*(d*sqrt(x) + c)^2*b*c + 6*I*(d*sqrt(x) + c)*b*c^2)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) - 2*(2*I*(d*sqrt(x) + c)^3*b - 6*I*(d*sqrt(x) + c)^2*b*c + 6*I*(d*sqrt(x) + c)*b*c^2)*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 2*(-6*I*(d*sqrt(x) + c)^2*b + 12*I*(d*sqrt(x) + c)*b*c - 6*I*b*c^2)*dilog(-e^(I*d*sqrt(x) + I*c)) - 2*(6*I*(d*sqrt(x) + c)^2*b - 12*I*(d*sqrt(x) + c)*b*c + 6*I*b*c^2)*dilog(e^(I*d*sqrt(x) + I*c)) - 2*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + 2*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) - 24*I*b*polylog(4, -e^(I*d*sqrt(x) + I*c)) + 24*I*b*polylog(4, e^(I*d*sqrt(x) + I*c)) - 24*((d*sqrt(x) + c)*b - b*c)*polylog(3, -e^(I*d*sqrt(x) + I*c)) + 24*((d*sqrt(x) + c)*b - b*c)*polylog(3, e^(I*d*sqrt(x) + I*c)))/d^4","B",0
34,0,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))/x,x, algorithm=""maxima"")","b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x}\,{d x} + b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1)*x), x) + b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1)*x), x) + a*log(x)","F",0
35,-1,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,1,6399,0,3.087078," ","integrate(x^3*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{8} a^{2} - 8 \, {\left(d \sqrt{x} + c\right)}^{7} a^{2} c + 28 \, {\left(d \sqrt{x} + c\right)}^{6} a^{2} c^{2} - 56 \, {\left(d \sqrt{x} + c\right)}^{5} a^{2} c^{3} + 70 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c^{4} - 56 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{5} + 28 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{6} - 8 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{7} + 16 \, a b c^{7} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) + \frac{8 \, {\left(4 \, b^{2} c^{7} + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 14 \, b^{2} c^{6} - 14 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 84 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 70 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 140 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 42 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 28 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, b^{2} c^{6} - 7 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 42 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 35 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 70 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 21 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 14 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{7} a b - 14 i \, b^{2} c^{6} + {\left(-28 i \, a b c - 14 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(84 i \, a b c^{2} + 84 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-140 i \, a b c^{3} - 210 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(140 i \, a b c^{4} + 280 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-84 i \, a b c^{5} - 210 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(28 i \, a b c^{6} + 84 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(14 \, b^{2} c^{6} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 14 i \, b^{2} c^{6} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 14 \, b^{2} c^{6}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) - 1\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 14 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 84 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 70 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 140 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 42 \, {\left(2 \, a b c^{5} - 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 28 \, {\left(a b c^{6} - 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 42 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 35 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 70 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 21 \, {\left(2 \, a b c^{5} - 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 14 \, {\left(a b c^{6} - 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + {\left(-28 i \, a b c + 14 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(84 i \, a b c^{2} - 84 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-140 i \, a b c^{3} + 210 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(140 i \, a b c^{4} - 280 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-84 i \, a b c^{5} + 210 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(28 i \, a b c^{6} - 84 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b^{2} - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(28 \, {\left(d \sqrt{x} + c\right)}^{6} a b + 28 \, a b c^{6} + 84 \, b^{2} c^{5} - 84 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 420 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} - 280 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 420 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} - 84 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)} - 28 \, {\left({\left(d \sqrt{x} + c\right)}^{6} a b + a b c^{6} + 3 \, b^{2} c^{5} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 15 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 15 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} - 3 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-28 i \, {\left(d \sqrt{x} + c\right)}^{6} a b - 28 i \, a b c^{6} - 84 i \, b^{2} c^{5} + {\left(168 i \, a b c + 84 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-420 i \, a b c^{2} - 420 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(560 i \, a b c^{3} + 840 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-420 i \, a b c^{4} - 840 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(168 i \, a b c^{5} + 420 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(28 \, {\left(d \sqrt{x} + c\right)}^{6} a b + 28 \, a b c^{6} - 84 \, b^{2} c^{5} - 84 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 420 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} - 280 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 420 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} - 84 \, {\left(2 \, a b c^{5} - 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)} - 28 \, {\left({\left(d \sqrt{x} + c\right)}^{6} a b + a b c^{6} - 3 \, b^{2} c^{5} - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 15 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} - 10 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 15 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} - 3 \, {\left(2 \, a b c^{5} - 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(28 i \, {\left(d \sqrt{x} + c\right)}^{6} a b + 28 i \, a b c^{6} - 84 i \, b^{2} c^{5} + {\left(-168 i \, a b c + 84 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(420 i \, a b c^{2} - 420 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-560 i \, a b c^{3} + 840 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(420 i \, a b c^{4} - 840 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-168 i \, a b c^{5} + 420 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{7} a b - 7 i \, b^{2} c^{6} + {\left(-14 i \, a b c - 7 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(42 i \, a b c^{2} + 42 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-70 i \, a b c^{3} - 105 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(70 i \, a b c^{4} + 140 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-42 i \, a b c^{5} - 105 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(14 i \, a b c^{6} + 42 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 7 i \, b^{2} c^{6} + {\left(14 i \, a b c + 7 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(-42 i \, a b c^{2} - 42 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(70 i \, a b c^{3} + 105 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-70 i \, a b c^{4} - 140 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(42 i \, a b c^{5} + 105 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-14 i \, a b c^{6} - 42 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, b^{2} c^{6} - 7 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 42 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 35 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 70 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 21 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 14 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{7} a b - 7 i \, b^{2} c^{6} + {\left(14 i \, a b c - 7 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(-42 i \, a b c^{2} + 42 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(70 i \, a b c^{3} - 105 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-70 i \, a b c^{4} + 140 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(42 i \, a b c^{5} - 105 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-14 i \, a b c^{6} + 42 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)} + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 7 i \, b^{2} c^{6} + {\left(-14 i \, a b c + 7 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(42 i \, a b c^{2} - 42 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-70 i \, a b c^{3} + 105 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(70 i \, a b c^{4} - 140 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-42 i \, a b c^{5} + 105 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(14 i \, a b c^{6} - 42 i \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{7} a b + 7 \, b^{2} c^{6} - 7 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 42 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{5} - 35 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 70 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 21 \, {\left(2 \, a b c^{5} - 5 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 14 \, {\left(a b c^{6} - 3 \, b^{2} c^{5}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - 20160 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{8}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 20160 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{8}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(20160 i \, {\left(d \sqrt{x} + c\right)} a b - 20160 i \, a b c - 10080 i \, b^{2} + {\left(-20160 i \, {\left(d \sqrt{x} + c\right)} a b + 20160 i \, a b c + 10080 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 10080 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{7}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-20160 i \, {\left(d \sqrt{x} + c\right)} a b + 20160 i \, a b c - 10080 i \, b^{2} + {\left(20160 i \, {\left(d \sqrt{x} + c\right)} a b - 20160 i \, a b c + 10080 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 10080 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{7}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(10080 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 10080 \, a b c^{2} + 10080 \, b^{2} c - 10080 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 10080 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-10080 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 10080 i \, a b c^{2} - 10080 i \, b^{2} c + {\left(20160 i \, a b c + 10080 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(10080 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 10080 \, a b c^{2} - 10080 \, b^{2} c - 10080 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 10080 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} - b^{2} c - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(10080 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 10080 i \, a b c^{2} - 10080 i \, b^{2} c + {\left(-20160 i \, a b c + 10080 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-3360 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 3360 i \, a b c^{3} + 5040 i \, b^{2} c^{2} + {\left(10080 i \, a b c + 5040 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-10080 i \, a b c^{2} - 10080 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(3360 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3360 i \, a b c^{3} - 5040 i \, b^{2} c^{2} + {\left(-10080 i \, a b c - 5040 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(10080 i \, a b c^{2} + 10080 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 1680 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} - 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(3360 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3360 i \, a b c^{3} + 5040 i \, b^{2} c^{2} + {\left(-10080 i \, a b c + 5040 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(10080 i \, a b c^{2} - 10080 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-3360 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 3360 i \, a b c^{3} - 5040 i \, b^{2} c^{2} + {\left(10080 i \, a b c - 5040 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-10080 i \, a b c^{2} + 10080 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1680 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} + 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(840 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 840 \, a b c^{4} + 1680 \, b^{2} c^{3} - 1680 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 5040 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 1680 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 840 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b + a b c^{4} + 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(840 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 840 i \, a b c^{4} + 1680 i \, b^{2} c^{3} + {\left(-3360 i \, a b c - 1680 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(5040 i \, a b c^{2} + 5040 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-3360 i \, a b c^{3} - 5040 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(840 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 840 \, a b c^{4} - 1680 \, b^{2} c^{3} - 1680 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 5040 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 1680 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 840 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b + a b c^{4} - 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-840 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 840 i \, a b c^{4} + 1680 i \, b^{2} c^{3} + {\left(3360 i \, a b c - 1680 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-5040 i \, a b c^{2} + 5040 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(3360 i \, a b c^{3} - 5040 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(168 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 168 i \, a b c^{5} - 420 i \, b^{2} c^{4} + {\left(-840 i \, a b c - 420 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(1680 i \, a b c^{2} + 1680 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-1680 i \, a b c^{3} - 2520 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(840 i \, a b c^{4} + 1680 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-168 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 168 i \, a b c^{5} + 420 i \, b^{2} c^{4} + {\left(840 i \, a b c + 420 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-1680 i \, a b c^{2} - 1680 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(1680 i \, a b c^{3} + 2520 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-840 i \, a b c^{4} - 1680 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 84 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 2 \, a b c^{5} - 5 \, b^{2} c^{4} - 5 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-168 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 168 i \, a b c^{5} - 420 i \, b^{2} c^{4} + {\left(840 i \, a b c - 420 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-1680 i \, a b c^{2} + 1680 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(1680 i \, a b c^{3} - 2520 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-840 i \, a b c^{4} + 1680 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left(168 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 168 i \, a b c^{5} + 420 i \, b^{2} c^{4} + {\left(-840 i \, a b c + 420 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(1680 i \, a b c^{2} - 1680 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-1680 i \, a b c^{3} + 2520 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(840 i \, a b c^{4} - 1680 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 84 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 2 \, a b c^{5} + 5 \, b^{2} c^{4} - 5 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{7} b^{2} - 28 i \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} c + 84 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c^{2} - 140 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{3} + 140 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{4} - 84 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{5} + 28 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-2 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 i}}{4 \, d^{8}}"," ",0,"1/4*((d*sqrt(x) + c)^8*a^2 - 8*(d*sqrt(x) + c)^7*a^2*c + 28*(d*sqrt(x) + c)^6*a^2*c^2 - 56*(d*sqrt(x) + c)^5*a^2*c^3 + 70*(d*sqrt(x) + c)^4*a^2*c^4 - 56*(d*sqrt(x) + c)^3*a^2*c^5 + 28*(d*sqrt(x) + c)^2*a^2*c^6 - 8*(d*sqrt(x) + c)*a^2*c^7 + 16*a*b*c^7*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) + 8*(4*b^2*c^7 + (4*(d*sqrt(x) + c)^7*a*b - 14*b^2*c^6 - 14*(2*a*b*c + b^2)*(d*sqrt(x) + c)^6 + 84*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^5 - 70*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 140*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 42*(2*a*b*c^5 + 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 28*(a*b*c^6 + 3*b^2*c^5)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^7*a*b - 7*b^2*c^6 - 7*(2*a*b*c + b^2)*(d*sqrt(x) + c)^6 + 42*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^5 - 35*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 70*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 21*(2*a*b*c^5 + 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 14*(a*b*c^6 + 3*b^2*c^5)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^7*a*b - 14*I*b^2*c^6 + (-28*I*a*b*c - 14*I*b^2)*(d*sqrt(x) + c)^6 + (84*I*a*b*c^2 + 84*I*b^2*c)*(d*sqrt(x) + c)^5 + (-140*I*a*b*c^3 - 210*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (140*I*a*b*c^4 + 280*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (-84*I*a*b*c^5 - 210*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (28*I*a*b*c^6 + 84*I*b^2*c^5)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) + (14*b^2*c^6*cos(2*d*sqrt(x) + 2*c) + 14*I*b^2*c^6*sin(2*d*sqrt(x) + 2*c) - 14*b^2*c^6)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) - 1) + (4*(d*sqrt(x) + c)^7*a*b - 14*(2*a*b*c - b^2)*(d*sqrt(x) + c)^6 + 84*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^5 - 70*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 140*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 42*(2*a*b*c^5 - 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 28*(a*b*c^6 - 3*b^2*c^5)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^7*a*b - 7*(2*a*b*c - b^2)*(d*sqrt(x) + c)^6 + 42*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^5 - 35*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 70*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 21*(2*a*b*c^5 - 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 14*(a*b*c^6 - 3*b^2*c^5)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^7*a*b + (-28*I*a*b*c + 14*I*b^2)*(d*sqrt(x) + c)^6 + (84*I*a*b*c^2 - 84*I*b^2*c)*(d*sqrt(x) + c)^5 + (-140*I*a*b*c^3 + 210*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (140*I*a*b*c^4 - 280*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (-84*I*a*b*c^5 + 210*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (28*I*a*b*c^6 - 84*I*b^2*c^5)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 4*((d*sqrt(x) + c)^7*b^2 - 7*(d*sqrt(x) + c)^6*b^2*c + 21*(d*sqrt(x) + c)^5*b^2*c^2 - 35*(d*sqrt(x) + c)^4*b^2*c^3 + 35*(d*sqrt(x) + c)^3*b^2*c^4 - 21*(d*sqrt(x) + c)^2*b^2*c^5 + 7*(d*sqrt(x) + c)*b^2*c^6)*cos(2*d*sqrt(x) + 2*c) - (28*(d*sqrt(x) + c)^6*a*b + 28*a*b*c^6 + 84*b^2*c^5 - 84*(2*a*b*c + b^2)*(d*sqrt(x) + c)^5 + 420*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^4 - 280*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^3 + 420*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c)^2 - 84*(2*a*b*c^5 + 5*b^2*c^4)*(d*sqrt(x) + c) - 28*((d*sqrt(x) + c)^6*a*b + a*b*c^6 + 3*b^2*c^5 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^5 + 15*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^4 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^3 + 15*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c)^2 - 3*(2*a*b*c^5 + 5*b^2*c^4)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-28*I*(d*sqrt(x) + c)^6*a*b - 28*I*a*b*c^6 - 84*I*b^2*c^5 + (168*I*a*b*c + 84*I*b^2)*(d*sqrt(x) + c)^5 + (-420*I*a*b*c^2 - 420*I*b^2*c)*(d*sqrt(x) + c)^4 + (560*I*a*b*c^3 + 840*I*b^2*c^2)*(d*sqrt(x) + c)^3 + (-420*I*a*b*c^4 - 840*I*b^2*c^3)*(d*sqrt(x) + c)^2 + (168*I*a*b*c^5 + 420*I*b^2*c^4)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(I*d*sqrt(x) + I*c)) + (28*(d*sqrt(x) + c)^6*a*b + 28*a*b*c^6 - 84*b^2*c^5 - 84*(2*a*b*c - b^2)*(d*sqrt(x) + c)^5 + 420*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^4 - 280*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^3 + 420*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c)^2 - 84*(2*a*b*c^5 - 5*b^2*c^4)*(d*sqrt(x) + c) - 28*((d*sqrt(x) + c)^6*a*b + a*b*c^6 - 3*b^2*c^5 - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^5 + 15*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^4 - 10*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^3 + 15*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c)^2 - 3*(2*a*b*c^5 - 5*b^2*c^4)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (28*I*(d*sqrt(x) + c)^6*a*b + 28*I*a*b*c^6 - 84*I*b^2*c^5 + (-168*I*a*b*c + 84*I*b^2)*(d*sqrt(x) + c)^5 + (420*I*a*b*c^2 - 420*I*b^2*c)*(d*sqrt(x) + c)^4 + (-560*I*a*b*c^3 + 840*I*b^2*c^2)*(d*sqrt(x) + c)^3 + (420*I*a*b*c^4 - 840*I*b^2*c^3)*(d*sqrt(x) + c)^2 + (-168*I*a*b*c^5 + 420*I*b^2*c^4)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(e^(I*d*sqrt(x) + I*c)) - (2*I*(d*sqrt(x) + c)^7*a*b - 7*I*b^2*c^6 + (-14*I*a*b*c - 7*I*b^2)*(d*sqrt(x) + c)^6 + (42*I*a*b*c^2 + 42*I*b^2*c)*(d*sqrt(x) + c)^5 + (-70*I*a*b*c^3 - 105*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (70*I*a*b*c^4 + 140*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (-42*I*a*b*c^5 - 105*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (14*I*a*b*c^6 + 42*I*b^2*c^5)*(d*sqrt(x) + c) + (-2*I*(d*sqrt(x) + c)^7*a*b + 7*I*b^2*c^6 + (14*I*a*b*c + 7*I*b^2)*(d*sqrt(x) + c)^6 + (-42*I*a*b*c^2 - 42*I*b^2*c)*(d*sqrt(x) + c)^5 + (70*I*a*b*c^3 + 105*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (-70*I*a*b*c^4 - 140*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (42*I*a*b*c^5 + 105*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (-14*I*a*b*c^6 - 42*I*b^2*c^5)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (2*(d*sqrt(x) + c)^7*a*b - 7*b^2*c^6 - 7*(2*a*b*c + b^2)*(d*sqrt(x) + c)^6 + 42*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^5 - 35*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 70*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 21*(2*a*b*c^5 + 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 14*(a*b*c^6 + 3*b^2*c^5)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) - (-2*I*(d*sqrt(x) + c)^7*a*b - 7*I*b^2*c^6 + (14*I*a*b*c - 7*I*b^2)*(d*sqrt(x) + c)^6 + (-42*I*a*b*c^2 + 42*I*b^2*c)*(d*sqrt(x) + c)^5 + (70*I*a*b*c^3 - 105*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (-70*I*a*b*c^4 + 140*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (42*I*a*b*c^5 - 105*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (-14*I*a*b*c^6 + 42*I*b^2*c^5)*(d*sqrt(x) + c) + (2*I*(d*sqrt(x) + c)^7*a*b + 7*I*b^2*c^6 + (-14*I*a*b*c + 7*I*b^2)*(d*sqrt(x) + c)^6 + (42*I*a*b*c^2 - 42*I*b^2*c)*(d*sqrt(x) + c)^5 + (-70*I*a*b*c^3 + 105*I*b^2*c^2)*(d*sqrt(x) + c)^4 + (70*I*a*b*c^4 - 140*I*b^2*c^3)*(d*sqrt(x) + c)^3 + (-42*I*a*b*c^5 + 105*I*b^2*c^4)*(d*sqrt(x) + c)^2 + (14*I*a*b*c^6 - 42*I*b^2*c^5)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*(d*sqrt(x) + c)^7*a*b + 7*b^2*c^6 - 7*(2*a*b*c - b^2)*(d*sqrt(x) + c)^6 + 42*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^5 - 35*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^4 + 70*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c)^3 - 21*(2*a*b*c^5 - 5*b^2*c^4)*(d*sqrt(x) + c)^2 + 14*(a*b*c^6 - 3*b^2*c^5)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) - 20160*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(8, -e^(I*d*sqrt(x) + I*c)) + 20160*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(8, e^(I*d*sqrt(x) + I*c)) - (20160*I*(d*sqrt(x) + c)*a*b - 20160*I*a*b*c - 10080*I*b^2 + (-20160*I*(d*sqrt(x) + c)*a*b + 20160*I*a*b*c + 10080*I*b^2)*cos(2*d*sqrt(x) + 2*c) + 10080*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c - b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(7, -e^(I*d*sqrt(x) + I*c)) - (-20160*I*(d*sqrt(x) + c)*a*b + 20160*I*a*b*c - 10080*I*b^2 + (20160*I*(d*sqrt(x) + c)*a*b - 20160*I*a*b*c + 10080*I*b^2)*cos(2*d*sqrt(x) + 2*c) - 10080*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c + b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(7, e^(I*d*sqrt(x) + I*c)) - (10080*(d*sqrt(x) + c)^2*a*b + 10080*a*b*c^2 + 10080*b^2*c - 10080*(2*a*b*c + b^2)*(d*sqrt(x) + c) - 10080*((d*sqrt(x) + c)^2*a*b + a*b*c^2 + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-10080*I*(d*sqrt(x) + c)^2*a*b - 10080*I*a*b*c^2 - 10080*I*b^2*c + (20160*I*a*b*c + 10080*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(6, -e^(I*d*sqrt(x) + I*c)) + (10080*(d*sqrt(x) + c)^2*a*b + 10080*a*b*c^2 - 10080*b^2*c - 10080*(2*a*b*c - b^2)*(d*sqrt(x) + c) - 10080*((d*sqrt(x) + c)^2*a*b + a*b*c^2 - b^2*c - (2*a*b*c - b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (10080*I*(d*sqrt(x) + c)^2*a*b + 10080*I*a*b*c^2 - 10080*I*b^2*c + (-20160*I*a*b*c + 10080*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(6, e^(I*d*sqrt(x) + I*c)) - (-3360*I*(d*sqrt(x) + c)^3*a*b + 3360*I*a*b*c^3 + 5040*I*b^2*c^2 + (10080*I*a*b*c + 5040*I*b^2)*(d*sqrt(x) + c)^2 + (-10080*I*a*b*c^2 - 10080*I*b^2*c)*(d*sqrt(x) + c) + (3360*I*(d*sqrt(x) + c)^3*a*b - 3360*I*a*b*c^3 - 5040*I*b^2*c^2 + (-10080*I*a*b*c - 5040*I*b^2)*(d*sqrt(x) + c)^2 + (10080*I*a*b*c^2 + 10080*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - 1680*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 - 3*b^2*c^2 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(5, -e^(I*d*sqrt(x) + I*c)) - (3360*I*(d*sqrt(x) + c)^3*a*b - 3360*I*a*b*c^3 + 5040*I*b^2*c^2 + (-10080*I*a*b*c + 5040*I*b^2)*(d*sqrt(x) + c)^2 + (10080*I*a*b*c^2 - 10080*I*b^2*c)*(d*sqrt(x) + c) + (-3360*I*(d*sqrt(x) + c)^3*a*b + 3360*I*a*b*c^3 - 5040*I*b^2*c^2 + (10080*I*a*b*c - 5040*I*b^2)*(d*sqrt(x) + c)^2 + (-10080*I*a*b*c^2 + 10080*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 1680*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 + 3*b^2*c^2 - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(5, e^(I*d*sqrt(x) + I*c)) + (840*(d*sqrt(x) + c)^4*a*b + 840*a*b*c^4 + 1680*b^2*c^3 - 1680*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 5040*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 1680*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c) - 840*((d*sqrt(x) + c)^4*a*b + a*b*c^4 + 2*b^2*c^3 - 2*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (840*I*(d*sqrt(x) + c)^4*a*b + 840*I*a*b*c^4 + 1680*I*b^2*c^3 + (-3360*I*a*b*c - 1680*I*b^2)*(d*sqrt(x) + c)^3 + (5040*I*a*b*c^2 + 5040*I*b^2*c)*(d*sqrt(x) + c)^2 + (-3360*I*a*b*c^3 - 5040*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(I*d*sqrt(x) + I*c)) - (840*(d*sqrt(x) + c)^4*a*b + 840*a*b*c^4 - 1680*b^2*c^3 - 1680*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 5040*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 1680*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c) - 840*((d*sqrt(x) + c)^4*a*b + a*b*c^4 - 2*b^2*c^3 - 2*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-840*I*(d*sqrt(x) + c)^4*a*b - 840*I*a*b*c^4 + 1680*I*b^2*c^3 + (3360*I*a*b*c - 1680*I*b^2)*(d*sqrt(x) + c)^3 + (-5040*I*a*b*c^2 + 5040*I*b^2*c)*(d*sqrt(x) + c)^2 + (3360*I*a*b*c^3 - 5040*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(4, e^(I*d*sqrt(x) + I*c)) - (168*I*(d*sqrt(x) + c)^5*a*b - 168*I*a*b*c^5 - 420*I*b^2*c^4 + (-840*I*a*b*c - 420*I*b^2)*(d*sqrt(x) + c)^4 + (1680*I*a*b*c^2 + 1680*I*b^2*c)*(d*sqrt(x) + c)^3 + (-1680*I*a*b*c^3 - 2520*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (840*I*a*b*c^4 + 1680*I*b^2*c^3)*(d*sqrt(x) + c) + (-168*I*(d*sqrt(x) + c)^5*a*b + 168*I*a*b*c^5 + 420*I*b^2*c^4 + (840*I*a*b*c + 420*I*b^2)*(d*sqrt(x) + c)^4 + (-1680*I*a*b*c^2 - 1680*I*b^2*c)*(d*sqrt(x) + c)^3 + (1680*I*a*b*c^3 + 2520*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-840*I*a*b*c^4 - 1680*I*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 84*(2*(d*sqrt(x) + c)^5*a*b - 2*a*b*c^5 - 5*b^2*c^4 - 5*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(I*d*sqrt(x) + I*c)) - (-168*I*(d*sqrt(x) + c)^5*a*b + 168*I*a*b*c^5 - 420*I*b^2*c^4 + (840*I*a*b*c - 420*I*b^2)*(d*sqrt(x) + c)^4 + (-1680*I*a*b*c^2 + 1680*I*b^2*c)*(d*sqrt(x) + c)^3 + (1680*I*a*b*c^3 - 2520*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-840*I*a*b*c^4 + 1680*I*b^2*c^3)*(d*sqrt(x) + c) + (168*I*(d*sqrt(x) + c)^5*a*b - 168*I*a*b*c^5 + 420*I*b^2*c^4 + (-840*I*a*b*c + 420*I*b^2)*(d*sqrt(x) + c)^4 + (1680*I*a*b*c^2 - 1680*I*b^2*c)*(d*sqrt(x) + c)^3 + (-1680*I*a*b*c^3 + 2520*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (840*I*a*b*c^4 - 1680*I*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - 84*(2*(d*sqrt(x) + c)^5*a*b - 2*a*b*c^5 + 5*b^2*c^4 - 5*(2*a*b*c - b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, e^(I*d*sqrt(x) + I*c)) - (4*I*(d*sqrt(x) + c)^7*b^2 - 28*I*(d*sqrt(x) + c)^6*b^2*c + 84*I*(d*sqrt(x) + c)^5*b^2*c^2 - 140*I*(d*sqrt(x) + c)^4*b^2*c^3 + 140*I*(d*sqrt(x) + c)^3*b^2*c^4 - 84*I*(d*sqrt(x) + c)^2*b^2*c^5 + 28*I*(d*sqrt(x) + c)*b^2*c^6)*sin(2*d*sqrt(x) + 2*c))/(-2*I*cos(2*d*sqrt(x) + 2*c) + 2*sin(2*d*sqrt(x) + 2*c) + 2*I))/d^8","B",0
37,1,3856,0,1.599542," ","integrate(x^2*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{6} a^{2} - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a^{2} c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{5} + 12 \, a b c^{5} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) + \frac{6 \, {\left(4 \, b^{2} c^{5} + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 10 \, b^{2} c^{4} - 10 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 40 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 20 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 20 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, b^{2} c^{4} - 5 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 10 i \, b^{2} c^{4} + {\left(-20 i \, a b c - 10 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(40 i \, a b c^{2} + 40 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-40 i \, a b c^{3} - 60 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(20 i \, a b c^{4} + 40 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(10 \, b^{2} c^{4} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 10 i \, b^{2} c^{4} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 10 \, b^{2} c^{4}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) - 1\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 10 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 40 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 20 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 20 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + {\left(-20 i \, a b c + 10 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(40 i \, a b c^{2} - 40 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-40 i \, a b c^{3} + 60 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(20 i \, a b c^{4} - 40 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b^{2} - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(20 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 20 \, a b c^{4} + 40 \, b^{2} c^{3} - 40 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 120 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 40 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 20 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b + a b c^{4} + 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-20 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 20 i \, a b c^{4} - 40 i \, b^{2} c^{3} + {\left(80 i \, a b c + 40 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-120 i \, a b c^{2} - 120 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(80 i \, a b c^{3} + 120 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(20 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 20 \, a b c^{4} - 40 \, b^{2} c^{3} - 40 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 120 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 40 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 20 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b + a b c^{4} - 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(20 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 20 i \, a b c^{4} - 40 i \, b^{2} c^{3} + {\left(-80 i \, a b c + 40 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(120 i \, a b c^{2} - 120 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-80 i \, a b c^{3} + 120 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 5 i \, b^{2} c^{4} + {\left(-10 i \, a b c - 5 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(20 i \, a b c^{2} + 20 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-20 i \, a b c^{3} - 30 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(10 i \, a b c^{4} + 20 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 5 i \, b^{2} c^{4} + {\left(10 i \, a b c + 5 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-20 i \, a b c^{2} - 20 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(20 i \, a b c^{3} + 30 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-10 i \, a b c^{4} - 20 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, b^{2} c^{4} - 5 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 5 i \, b^{2} c^{4} + {\left(10 i \, a b c - 5 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-20 i \, a b c^{2} + 20 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(20 i \, a b c^{3} - 30 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-10 i \, a b c^{4} + 20 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 5 i \, b^{2} c^{4} + {\left(-10 i \, a b c + 5 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(20 i \, a b c^{2} - 20 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-20 i \, a b c^{3} + 30 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(10 i \, a b c^{4} - 20 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{5} a b + 5 \, b^{2} c^{4} - 5 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 20 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a b c^{4} - 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 480 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{6}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 480 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{6}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-480 i \, {\left(d \sqrt{x} + c\right)} a b + 480 i \, a b c + 240 i \, b^{2} + {\left(480 i \, {\left(d \sqrt{x} + c\right)} a b - 480 i \, a b c - 240 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 240 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(480 i \, {\left(d \sqrt{x} + c\right)} a b - 480 i \, a b c + 240 i \, b^{2} + {\left(-480 i \, {\left(d \sqrt{x} + c\right)} a b + 480 i \, a b c - 240 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 240 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(240 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 240 \, a b c^{2} + 240 \, b^{2} c - 240 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 240 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(240 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 240 i \, a b c^{2} + 240 i \, b^{2} c + {\left(-480 i \, a b c - 240 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(240 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 240 \, a b c^{2} - 240 \, b^{2} c - 240 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 240 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} - b^{2} c - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-240 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 240 i \, a b c^{2} + 240 i \, b^{2} c + {\left(480 i \, a b c - 240 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(80 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 80 i \, a b c^{3} - 120 i \, b^{2} c^{2} + {\left(-240 i \, a b c - 120 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(240 i \, a b c^{2} + 240 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-80 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 80 i \, a b c^{3} + 120 i \, b^{2} c^{2} + {\left(240 i \, a b c + 120 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-240 i \, a b c^{2} - 240 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 40 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} - 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-80 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 80 i \, a b c^{3} - 120 i \, b^{2} c^{2} + {\left(240 i \, a b c - 120 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-240 i \, a b c^{2} + 240 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(80 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 80 i \, a b c^{3} + 120 i \, b^{2} c^{2} + {\left(-240 i \, a b c + 120 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(240 i \, a b c^{2} - 240 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 40 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} + 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} - 20 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c + 40 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} - 40 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} + 20 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-2 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 i}}{3 \, d^{6}}"," ",0,"1/3*((d*sqrt(x) + c)^6*a^2 - 6*(d*sqrt(x) + c)^5*a^2*c + 15*(d*sqrt(x) + c)^4*a^2*c^2 - 20*(d*sqrt(x) + c)^3*a^2*c^3 + 15*(d*sqrt(x) + c)^2*a^2*c^4 - 6*(d*sqrt(x) + c)*a^2*c^5 + 12*a*b*c^5*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) + 6*(4*b^2*c^5 + (4*(d*sqrt(x) + c)^5*a*b - 10*b^2*c^4 - 10*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 40*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 20*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 20*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^5*a*b - 5*b^2*c^4 - 5*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^5*a*b - 10*I*b^2*c^4 + (-20*I*a*b*c - 10*I*b^2)*(d*sqrt(x) + c)^4 + (40*I*a*b*c^2 + 40*I*b^2*c)*(d*sqrt(x) + c)^3 + (-40*I*a*b*c^3 - 60*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (20*I*a*b*c^4 + 40*I*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) + (10*b^2*c^4*cos(2*d*sqrt(x) + 2*c) + 10*I*b^2*c^4*sin(2*d*sqrt(x) + 2*c) - 10*b^2*c^4)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) - 1) + (4*(d*sqrt(x) + c)^5*a*b - 10*(2*a*b*c - b^2)*(d*sqrt(x) + c)^4 + 40*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^3 - 20*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 20*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^5*a*b - 5*(2*a*b*c - b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^5*a*b + (-20*I*a*b*c + 10*I*b^2)*(d*sqrt(x) + c)^4 + (40*I*a*b*c^2 - 40*I*b^2*c)*(d*sqrt(x) + c)^3 + (-40*I*a*b*c^3 + 60*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (20*I*a*b*c^4 - 40*I*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 4*((d*sqrt(x) + c)^5*b^2 - 5*(d*sqrt(x) + c)^4*b^2*c + 10*(d*sqrt(x) + c)^3*b^2*c^2 - 10*(d*sqrt(x) + c)^2*b^2*c^3 + 5*(d*sqrt(x) + c)*b^2*c^4)*cos(2*d*sqrt(x) + 2*c) - (20*(d*sqrt(x) + c)^4*a*b + 20*a*b*c^4 + 40*b^2*c^3 - 40*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 120*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 40*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c) - 20*((d*sqrt(x) + c)^4*a*b + a*b*c^4 + 2*b^2*c^3 - 2*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-20*I*(d*sqrt(x) + c)^4*a*b - 20*I*a*b*c^4 - 40*I*b^2*c^3 + (80*I*a*b*c + 40*I*b^2)*(d*sqrt(x) + c)^3 + (-120*I*a*b*c^2 - 120*I*b^2*c)*(d*sqrt(x) + c)^2 + (80*I*a*b*c^3 + 120*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(I*d*sqrt(x) + I*c)) + (20*(d*sqrt(x) + c)^4*a*b + 20*a*b*c^4 - 40*b^2*c^3 - 40*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 120*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 40*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c) - 20*((d*sqrt(x) + c)^4*a*b + a*b*c^4 - 2*b^2*c^3 - 2*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (20*I*(d*sqrt(x) + c)^4*a*b + 20*I*a*b*c^4 - 40*I*b^2*c^3 + (-80*I*a*b*c + 40*I*b^2)*(d*sqrt(x) + c)^3 + (120*I*a*b*c^2 - 120*I*b^2*c)*(d*sqrt(x) + c)^2 + (-80*I*a*b*c^3 + 120*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(e^(I*d*sqrt(x) + I*c)) - (2*I*(d*sqrt(x) + c)^5*a*b - 5*I*b^2*c^4 + (-10*I*a*b*c - 5*I*b^2)*(d*sqrt(x) + c)^4 + (20*I*a*b*c^2 + 20*I*b^2*c)*(d*sqrt(x) + c)^3 + (-20*I*a*b*c^3 - 30*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (10*I*a*b*c^4 + 20*I*b^2*c^3)*(d*sqrt(x) + c) + (-2*I*(d*sqrt(x) + c)^5*a*b + 5*I*b^2*c^4 + (10*I*a*b*c + 5*I*b^2)*(d*sqrt(x) + c)^4 + (-20*I*a*b*c^2 - 20*I*b^2*c)*(d*sqrt(x) + c)^3 + (20*I*a*b*c^3 + 30*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-10*I*a*b*c^4 - 20*I*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (2*(d*sqrt(x) + c)^5*a*b - 5*b^2*c^4 - 5*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) - (-2*I*(d*sqrt(x) + c)^5*a*b - 5*I*b^2*c^4 + (10*I*a*b*c - 5*I*b^2)*(d*sqrt(x) + c)^4 + (-20*I*a*b*c^2 + 20*I*b^2*c)*(d*sqrt(x) + c)^3 + (20*I*a*b*c^3 - 30*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-10*I*a*b*c^4 + 20*I*b^2*c^3)*(d*sqrt(x) + c) + (2*I*(d*sqrt(x) + c)^5*a*b + 5*I*b^2*c^4 + (-10*I*a*b*c + 5*I*b^2)*(d*sqrt(x) + c)^4 + (20*I*a*b*c^2 - 20*I*b^2*c)*(d*sqrt(x) + c)^3 + (-20*I*a*b*c^3 + 30*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (10*I*a*b*c^4 - 20*I*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*(d*sqrt(x) + c)^5*a*b + 5*b^2*c^4 - 5*(2*a*b*c - b^2)*(d*sqrt(x) + c)^4 + 20*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^3 - 10*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 10*(a*b*c^4 - 2*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) + 480*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(6, -e^(I*d*sqrt(x) + I*c)) - 480*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(6, e^(I*d*sqrt(x) + I*c)) - (-480*I*(d*sqrt(x) + c)*a*b + 480*I*a*b*c + 240*I*b^2 + (480*I*(d*sqrt(x) + c)*a*b - 480*I*a*b*c - 240*I*b^2)*cos(2*d*sqrt(x) + 2*c) - 240*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c - b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(5, -e^(I*d*sqrt(x) + I*c)) - (480*I*(d*sqrt(x) + c)*a*b - 480*I*a*b*c + 240*I*b^2 + (-480*I*(d*sqrt(x) + c)*a*b + 480*I*a*b*c - 240*I*b^2)*cos(2*d*sqrt(x) + 2*c) + 240*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c + b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(5, e^(I*d*sqrt(x) + I*c)) + (240*(d*sqrt(x) + c)^2*a*b + 240*a*b*c^2 + 240*b^2*c - 240*(2*a*b*c + b^2)*(d*sqrt(x) + c) - 240*((d*sqrt(x) + c)^2*a*b + a*b*c^2 + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (240*I*(d*sqrt(x) + c)^2*a*b + 240*I*a*b*c^2 + 240*I*b^2*c + (-480*I*a*b*c - 240*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(I*d*sqrt(x) + I*c)) - (240*(d*sqrt(x) + c)^2*a*b + 240*a*b*c^2 - 240*b^2*c - 240*(2*a*b*c - b^2)*(d*sqrt(x) + c) - 240*((d*sqrt(x) + c)^2*a*b + a*b*c^2 - b^2*c - (2*a*b*c - b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-240*I*(d*sqrt(x) + c)^2*a*b - 240*I*a*b*c^2 + 240*I*b^2*c + (480*I*a*b*c - 240*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(4, e^(I*d*sqrt(x) + I*c)) - (80*I*(d*sqrt(x) + c)^3*a*b - 80*I*a*b*c^3 - 120*I*b^2*c^2 + (-240*I*a*b*c - 120*I*b^2)*(d*sqrt(x) + c)^2 + (240*I*a*b*c^2 + 240*I*b^2*c)*(d*sqrt(x) + c) + (-80*I*(d*sqrt(x) + c)^3*a*b + 80*I*a*b*c^3 + 120*I*b^2*c^2 + (240*I*a*b*c + 120*I*b^2)*(d*sqrt(x) + c)^2 + (-240*I*a*b*c^2 - 240*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 40*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 - 3*b^2*c^2 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(I*d*sqrt(x) + I*c)) - (-80*I*(d*sqrt(x) + c)^3*a*b + 80*I*a*b*c^3 - 120*I*b^2*c^2 + (240*I*a*b*c - 120*I*b^2)*(d*sqrt(x) + c)^2 + (-240*I*a*b*c^2 + 240*I*b^2*c)*(d*sqrt(x) + c) + (80*I*(d*sqrt(x) + c)^3*a*b - 80*I*a*b*c^3 + 120*I*b^2*c^2 + (-240*I*a*b*c + 120*I*b^2)*(d*sqrt(x) + c)^2 + (240*I*a*b*c^2 - 240*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - 40*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 + 3*b^2*c^2 - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, e^(I*d*sqrt(x) + I*c)) - (4*I*(d*sqrt(x) + c)^5*b^2 - 20*I*(d*sqrt(x) + c)^4*b^2*c + 40*I*(d*sqrt(x) + c)^3*b^2*c^2 - 40*I*(d*sqrt(x) + c)^2*b^2*c^3 + 20*I*(d*sqrt(x) + c)*b^2*c^4)*sin(2*d*sqrt(x) + 2*c))/(-2*I*cos(2*d*sqrt(x) + 2*c) + 2*sin(2*d*sqrt(x) + 2*c) + 2*I))/d^6","B",0
38,1,1943,0,2.004244," ","integrate(x*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{4} a^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{3} + 8 \, a b c^{3} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) + \frac{4 \, {\left(4 \, b^{2} c^{3} + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 6 \, b^{2} c^{2} - 6 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 12 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 6 i \, b^{2} c^{2} + {\left(-12 i \, a b c - 6 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(12 i \, a b c^{2} + 12 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(6 \, b^{2} c^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 6 i \, b^{2} c^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 6 \, b^{2} c^{2}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) - 1\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 6 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 12 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + {\left(-12 i \, a b c + 6 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(12 i \, a b c^{2} - 12 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b^{2} - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 3 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(12 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 12 \, a b c^{2} + 12 \, b^{2} c - 12 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 12 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 12 i \, a b c^{2} - 12 i \, b^{2} c + {\left(24 i \, a b c + 12 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(12 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 12 \, a b c^{2} - 12 \, b^{2} c - 12 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 12 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} - b^{2} c - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 12 i \, a b c^{2} - 12 i \, b^{2} c + {\left(-24 i \, a b c + 12 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3 i \, b^{2} c^{2} + {\left(-6 i \, a b c - 3 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(6 i \, a b c^{2} + 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 3 i \, b^{2} c^{2} + {\left(6 i \, a b c + 3 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-6 i \, a b c^{2} - 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 3 i \, b^{2} c^{2} + {\left(6 i \, a b c - 3 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-6 i \, a b c^{2} + 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 3 i \, b^{2} c^{2} + {\left(-6 i \, a b c + 3 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(6 i \, a b c^{2} - 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b + 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - 24 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 24 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - a b\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(24 i \, {\left(d \sqrt{x} + c\right)} a b - 24 i \, a b c - 12 i \, b^{2} + {\left(-24 i \, {\left(d \sqrt{x} + c\right)} a b + 24 i \, a b c + 12 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 12 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-24 i \, {\left(d \sqrt{x} + c\right)} a b + 24 i \, a b c - 12 i \, b^{2} + {\left(24 i \, {\left(d \sqrt{x} + c\right)} a b - 24 i \, a b c + 12 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 12 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(4 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 12 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-2 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 i}}{2 \, d^{4}}"," ",0,"1/2*((d*sqrt(x) + c)^4*a^2 - 4*(d*sqrt(x) + c)^3*a^2*c + 6*(d*sqrt(x) + c)^2*a^2*c^2 - 4*(d*sqrt(x) + c)*a^2*c^3 + 8*a*b*c^3*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) + 4*(4*b^2*c^3 + (4*(d*sqrt(x) + c)^3*a*b - 6*b^2*c^2 - 6*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 12*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^3*a*b - 3*b^2*c^2 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^3*a*b - 6*I*b^2*c^2 + (-12*I*a*b*c - 6*I*b^2)*(d*sqrt(x) + c)^2 + (12*I*a*b*c^2 + 12*I*b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) + (6*b^2*c^2*cos(2*d*sqrt(x) + 2*c) + 6*I*b^2*c^2*sin(2*d*sqrt(x) + 2*c) - 6*b^2*c^2)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) - 1) + (4*(d*sqrt(x) + c)^3*a*b - 6*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 12*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c) - 2*(2*(d*sqrt(x) + c)^3*a*b - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)^3*a*b + (-12*I*a*b*c + 6*I*b^2)*(d*sqrt(x) + c)^2 + (12*I*a*b*c^2 - 12*I*b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 4*((d*sqrt(x) + c)^3*b^2 - 3*(d*sqrt(x) + c)^2*b^2*c + 3*(d*sqrt(x) + c)*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) - (12*(d*sqrt(x) + c)^2*a*b + 12*a*b*c^2 + 12*b^2*c - 12*(2*a*b*c + b^2)*(d*sqrt(x) + c) - 12*((d*sqrt(x) + c)^2*a*b + a*b*c^2 + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-12*I*(d*sqrt(x) + c)^2*a*b - 12*I*a*b*c^2 - 12*I*b^2*c + (24*I*a*b*c + 12*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(I*d*sqrt(x) + I*c)) + (12*(d*sqrt(x) + c)^2*a*b + 12*a*b*c^2 - 12*b^2*c - 12*(2*a*b*c - b^2)*(d*sqrt(x) + c) - 12*((d*sqrt(x) + c)^2*a*b + a*b*c^2 - b^2*c - (2*a*b*c - b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (12*I*(d*sqrt(x) + c)^2*a*b + 12*I*a*b*c^2 - 12*I*b^2*c + (-24*I*a*b*c + 12*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(e^(I*d*sqrt(x) + I*c)) - (2*I*(d*sqrt(x) + c)^3*a*b - 3*I*b^2*c^2 + (-6*I*a*b*c - 3*I*b^2)*(d*sqrt(x) + c)^2 + (6*I*a*b*c^2 + 6*I*b^2*c)*(d*sqrt(x) + c) + (-2*I*(d*sqrt(x) + c)^3*a*b + 3*I*b^2*c^2 + (6*I*a*b*c + 3*I*b^2)*(d*sqrt(x) + c)^2 + (-6*I*a*b*c^2 - 6*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (2*(d*sqrt(x) + c)^3*a*b - 3*b^2*c^2 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) - (-2*I*(d*sqrt(x) + c)^3*a*b - 3*I*b^2*c^2 + (6*I*a*b*c - 3*I*b^2)*(d*sqrt(x) + c)^2 + (-6*I*a*b*c^2 + 6*I*b^2*c)*(d*sqrt(x) + c) + (2*I*(d*sqrt(x) + c)^3*a*b + 3*I*b^2*c^2 + (-6*I*a*b*c + 3*I*b^2)*(d*sqrt(x) + c)^2 + (6*I*a*b*c^2 - 6*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*(d*sqrt(x) + c)^3*a*b + 3*b^2*c^2 - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) - 24*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(4, -e^(I*d*sqrt(x) + I*c)) + 24*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) - a*b)*polylog(4, e^(I*d*sqrt(x) + I*c)) - (24*I*(d*sqrt(x) + c)*a*b - 24*I*a*b*c - 12*I*b^2 + (-24*I*(d*sqrt(x) + c)*a*b + 24*I*a*b*c + 12*I*b^2)*cos(2*d*sqrt(x) + 2*c) + 12*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c - b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(I*d*sqrt(x) + I*c)) - (-24*I*(d*sqrt(x) + c)*a*b + 24*I*a*b*c - 12*I*b^2 + (24*I*(d*sqrt(x) + c)*a*b - 24*I*a*b*c + 12*I*b^2)*cos(2*d*sqrt(x) + 2*c) - 12*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c + b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, e^(I*d*sqrt(x) + I*c)) - (4*I*(d*sqrt(x) + c)^3*b^2 - 12*I*(d*sqrt(x) + c)^2*b^2*c + 12*I*(d*sqrt(x) + c)*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))/(-2*I*cos(2*d*sqrt(x) + 2*c) + 2*sin(2*d*sqrt(x) + 2*c) + 2*I))/d^4","B",0
39,0,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x,x, algorithm=""maxima"")","-\frac{4 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - \frac{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} {\left(2 \, a d \int \frac{x \sin\left(d \sqrt{x} + c\right)}{x^{2} \cos\left(d \sqrt{x} + c\right)^{2} + x^{2} \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, x^{2} \cos\left(d \sqrt{x} + c\right) + x^{2}}\,{d x} + b \int \frac{\sqrt{x} \sin\left(d \sqrt{x} + c\right)}{x^{2} \cos\left(d \sqrt{x} + c\right)^{2} + x^{2} \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, x^{2} \cos\left(d \sqrt{x} + c\right) + x^{2}}\,{d x}\right)} b x}{d} - {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x \int \frac{2 \, a b d x \sin\left(d \sqrt{x} + c\right) - b^{2} \sqrt{x} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x} - {\left(a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} d\right)} x \log\left(x\right)}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x}"," ",0,"-(4*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) - (d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 - 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x*integrate((2*a*b*d*x*sin(d*sqrt(x) + c) + b^2*sqrt(x)*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 + 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) + (d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 - 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x*integrate(-(2*a*b*d*x*sin(d*sqrt(x) + c) - b^2*sqrt(x)*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 - 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) - (a^2*d*cos(2*d*sqrt(x) + 2*c)^2 + a^2*d*sin(2*d*sqrt(x) + 2*c)^2 - 2*a^2*d*cos(2*d*sqrt(x) + 2*c) + a^2*d)*x*log(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 - 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x)","F",0
40,-1,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-2,0,0,0.000000," ","integrate(x^3/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
42,-2,0,0,0.000000," ","integrate(x^2/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
43,-2,0,0,0.000000," ","integrate(x/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
44,-1,0,0,0.000000," ","integrate(1/x/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,0,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))/x^2,x, algorithm=""maxima"")","\frac{{\left(b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x^{2}}\,{d x} + b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x^{2}}\,{d x}\right)} x - a}{x}"," ",0,"((b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1)*x^2), x) + b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1)*x^2), x))*x - a)/x","F",0
46,-2,0,0,0.000000," ","integrate(x^3/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
47,-2,0,0,0.000000," ","integrate(x^2/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
48,-2,0,0,0.000000," ","integrate(x/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
49,-1,0,0,0.000000," ","integrate(1/x/(a+b*csc(c+d*x^(1/2)))^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*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,1,730,0,0.566959," ","integrate(x^(3/2)*(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{2 \, {\left(d \sqrt{x} + c\right)}^{5} a - 10 \, {\left(d \sqrt{x} + c\right)}^{4} a c + 20 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{3} + 10 \, {\left(d \sqrt{x} + c\right)} a c^{4} - 10 \, b c^{4} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - 5 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 8 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 8 i \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) - 5 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 8 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 8 i \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 5 \, {\left(-8 i \, {\left(d \sqrt{x} + c\right)}^{3} b + 24 i \, {\left(d \sqrt{x} + c\right)}^{2} b c - 24 i \, {\left(d \sqrt{x} + c\right)} b c^{2} + 8 i \, b c^{3}\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 5 \, {\left(8 i \, {\left(d \sqrt{x} + c\right)}^{3} b - 24 i \, {\left(d \sqrt{x} + c\right)}^{2} b c + 24 i \, {\left(d \sqrt{x} + c\right)} b c^{2} - 8 i \, b c^{3}\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 5 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 5 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 240 \, b {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 240 \, b {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 5 \, {\left(48 i \, {\left(d \sqrt{x} + c\right)} b - 48 i \, b c\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 5 \, {\left(-48 i \, {\left(d \sqrt{x} + c\right)} b + 48 i \, b c\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 120 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c + b c^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 120 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c + b c^{2}\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)})}{5 \, d^{5}}"," ",0,"1/5*(2*(d*sqrt(x) + c)^5*a - 10*(d*sqrt(x) + c)^4*a*c + 20*(d*sqrt(x) + c)^3*a*c^2 - 20*(d*sqrt(x) + c)^2*a*c^3 + 10*(d*sqrt(x) + c)*a*c^4 - 10*b*c^4*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 5*(2*I*(d*sqrt(x) + c)^4*b - 8*I*(d*sqrt(x) + c)^3*b*c + 12*I*(d*sqrt(x) + c)^2*b*c^2 - 8*I*(d*sqrt(x) + c)*b*c^3)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) - 5*(2*I*(d*sqrt(x) + c)^4*b - 8*I*(d*sqrt(x) + c)^3*b*c + 12*I*(d*sqrt(x) + c)^2*b*c^2 - 8*I*(d*sqrt(x) + c)*b*c^3)*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 5*(-8*I*(d*sqrt(x) + c)^3*b + 24*I*(d*sqrt(x) + c)^2*b*c - 24*I*(d*sqrt(x) + c)*b*c^2 + 8*I*b*c^3)*dilog(-e^(I*d*sqrt(x) + I*c)) - 5*(8*I*(d*sqrt(x) + c)^3*b - 24*I*(d*sqrt(x) + c)^2*b*c + 24*I*(d*sqrt(x) + c)*b*c^2 - 8*I*b*c^3)*dilog(e^(I*d*sqrt(x) + I*c)) - 5*((d*sqrt(x) + c)^4*b - 4*(d*sqrt(x) + c)^3*b*c + 6*(d*sqrt(x) + c)^2*b*c^2 - 4*(d*sqrt(x) + c)*b*c^3)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + 5*((d*sqrt(x) + c)^4*b - 4*(d*sqrt(x) + c)^3*b*c + 6*(d*sqrt(x) + c)^2*b*c^2 - 4*(d*sqrt(x) + c)*b*c^3)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) + 240*b*polylog(5, -e^(I*d*sqrt(x) + I*c)) - 240*b*polylog(5, e^(I*d*sqrt(x) + I*c)) - 5*(48*I*(d*sqrt(x) + c)*b - 48*I*b*c)*polylog(4, -e^(I*d*sqrt(x) + I*c)) - 5*(-48*I*(d*sqrt(x) + c)*b + 48*I*b*c)*polylog(4, e^(I*d*sqrt(x) + I*c)) - 120*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c + b*c^2)*polylog(3, -e^(I*d*sqrt(x) + I*c)) + 120*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c + b*c^2)*polylog(3, e^(I*d*sqrt(x) + I*c)))/d^5","B",0
52,1,370,0,0.576960," ","integrate((a+b*csc(c+d*x^(1/2)))*x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(d \sqrt{x} + c\right)}^{3} a - 6 \, {\left(d \sqrt{x} + c\right)}^{2} a c + 6 \, {\left(d \sqrt{x} + c\right)} a c^{2} - 6 \, b c^{2} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - 3 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 4 i \, {\left(d \sqrt{x} + c\right)} b c\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 4 i \, {\left(d \sqrt{x} + c\right)} b c\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left(-4 i \, {\left(d \sqrt{x} + c\right)} b + 4 i \, b c\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 3 \, {\left(4 i \, {\left(d \sqrt{x} + c\right)} b - 4 i \, b c\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - 3 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) - 12 \, b {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 12 \, b {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)})}{3 \, d^{3}}"," ",0,"1/3*(2*(d*sqrt(x) + c)^3*a - 6*(d*sqrt(x) + c)^2*a*c + 6*(d*sqrt(x) + c)*a*c^2 - 6*b*c^2*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 3*(2*I*(d*sqrt(x) + c)^2*b - 4*I*(d*sqrt(x) + c)*b*c)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) - 3*(2*I*(d*sqrt(x) + c)^2*b - 4*I*(d*sqrt(x) + c)*b*c)*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) - 3*(-4*I*(d*sqrt(x) + c)*b + 4*I*b*c)*dilog(-e^(I*d*sqrt(x) + I*c)) - 3*(4*I*(d*sqrt(x) + c)*b - 4*I*b*c)*dilog(e^(I*d*sqrt(x) + I*c)) - 3*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + 3*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) - 12*b*polylog(3, -e^(I*d*sqrt(x) + I*c)) + 12*b*polylog(3, e^(I*d*sqrt(x) + I*c)))/d^3","B",0
53,1,31,0,0.352060," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(1/2),x, algorithm=""maxima"")","2 \, a \sqrt{x} - \frac{2 \, b \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right)}{d}"," ",0,"2*a*sqrt(x) - 2*b*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c))/d","A",0
54,0,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(3/2),x, algorithm=""maxima"")","\frac{{\left(b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x^{\frac{3}{2}}}\,{d x} + b \int \frac{\sin\left(d \sqrt{x} + c\right)}{{\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right)} x^{\frac{3}{2}}}\,{d x}\right)} \sqrt{x} - 2 \, a}{\sqrt{x}}"," ",0,"((b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1)*x^(3/2)), x) + b*integrate(sin(d*sqrt(x) + c)/((cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1)*x^(3/2)), x))*sqrt(x) - 2*a)/sqrt(x)","F",0
55,-1,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))/x^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,2815,0,0.607957," ","integrate(x^(3/2)*(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a^{2} - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{4} - 10 \, a b c^{4} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - \frac{5 \, {\left(2 \, b^{2} c^{4} - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 4 \, b^{2} c^{3} - 4 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 12 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 4 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b + 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 4 i \, b^{2} c^{3} + {\left(-8 i \, a b c - 4 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(12 i \, a b c^{2} + 12 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-8 i \, a b c^{3} - 12 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(4 \, b^{2} c^{3} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 i \, b^{2} c^{3} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 4 \, b^{2} c^{3}\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) - 1\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 12 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 4 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 2 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + {\left(-8 i \, a b c + 4 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(12 i \, a b c^{2} - 12 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-8 i \, a b c^{3} + 12 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(8 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 8 \, a b c^{3} - 12 \, b^{2} c^{2} - 12 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 24 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)} - 4 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} - 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-8 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 8 i \, a b c^{3} + 12 i \, b^{2} c^{2} + {\left(24 i \, a b c + 12 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-24 i \, a b c^{2} - 24 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(8 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 8 \, a b c^{3} + 12 \, b^{2} c^{2} - 12 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 24 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)} - 4 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 2 \, a b c^{3} + 3 \, b^{2} c^{2} - 3 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(8 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 8 i \, a b c^{3} + 12 i \, b^{2} c^{2} + {\left(-24 i \, a b c + 12 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(24 i \, a b c^{2} - 24 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 2 i \, b^{2} c^{3} + {\left(-4 i \, a b c - 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(6 i \, a b c^{2} + 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-4 i \, a b c^{3} - 6 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 2 i \, b^{2} c^{3} + {\left(4 i \, a b c + 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-6 i \, a b c^{2} - 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(4 i \, a b c^{3} + 6 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(d \sqrt{x} + c\right)}^{4} a b + 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 2 i \, b^{2} c^{3} + {\left(4 i \, a b c - 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-6 i \, a b c^{2} + 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(4 i \, a b c^{3} - 6 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 2 i \, b^{2} c^{3} + {\left(-4 i \, a b c + 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(6 i \, a b c^{2} - 6 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-4 i \, a b c^{3} + 6 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 2 \, b^{2} c^{3} - 2 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(a b c^{2} - b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 2 \, {\left(2 \, a b c^{3} - 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(48 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 48 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 48 i \, a b\right)} {\rm Li}_{5}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-48 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 48 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 48 i \, a b\right)} {\rm Li}_{5}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(48 \, {\left(d \sqrt{x} + c\right)} a b - 48 \, a b c - 24 \, b^{2} - 24 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(48 i \, {\left(d \sqrt{x} + c\right)} a b - 48 i \, a b c - 24 i \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(48 \, {\left(d \sqrt{x} + c\right)} a b - 48 \, a b c + 24 \, b^{2} - 24 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-48 i \, {\left(d \sqrt{x} + c\right)} a b + 48 i \, a b c - 24 i \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(24 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 24 i \, a b c^{2} + 24 i \, b^{2} c + {\left(-48 i \, a b c - 24 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 24 i \, a b c^{2} - 24 i \, b^{2} c + {\left(48 i \, a b c + 24 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 24 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 24 i \, a b c^{2} + 24 i \, b^{2} c + {\left(48 i \, a b c - 24 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(24 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 24 i \, a b c^{2} - 24 i \, b^{2} c + {\left(-48 i \, a b c + 24 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 24 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + a b c^{2} - b^{2} c - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 8 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 8 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + i}\right)}}{5 \, d^{5}}"," ",0,"2/5*((d*sqrt(x) + c)^5*a^2 - 5*(d*sqrt(x) + c)^4*a^2*c + 10*(d*sqrt(x) + c)^3*a^2*c^2 - 10*(d*sqrt(x) + c)^2*a^2*c^3 + 5*(d*sqrt(x) + c)*a^2*c^4 - 10*a*b*c^4*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 5*(2*b^2*c^4 - (2*(d*sqrt(x) + c)^4*a*b + 4*b^2*c^3 - 4*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 12*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 4*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c) - 2*((d*sqrt(x) + c)^4*a*b + 2*b^2*c^3 - 2*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*I*(d*sqrt(x) + c)^4*a*b + 4*I*b^2*c^3 + (-8*I*a*b*c - 4*I*b^2)*(d*sqrt(x) + c)^3 + (12*I*a*b*c^2 + 12*I*b^2*c)*(d*sqrt(x) + c)^2 + (-8*I*a*b*c^3 - 12*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) + (4*b^2*c^3*cos(2*d*sqrt(x) + 2*c) + 4*I*b^2*c^3*sin(2*d*sqrt(x) + 2*c) - 4*b^2*c^3)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) - 1) - (2*(d*sqrt(x) + c)^4*a*b - 4*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 12*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 4*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c) - 2*((d*sqrt(x) + c)^4*a*b - 2*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*I*(d*sqrt(x) + c)^4*a*b + (-8*I*a*b*c + 4*I*b^2)*(d*sqrt(x) + c)^3 + (12*I*a*b*c^2 - 12*I*b^2*c)*(d*sqrt(x) + c)^2 + (-8*I*a*b*c^3 + 12*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) + 2*((d*sqrt(x) + c)^4*b^2 - 4*(d*sqrt(x) + c)^3*b^2*c + 6*(d*sqrt(x) + c)^2*b^2*c^2 - 4*(d*sqrt(x) + c)*b^2*c^3)*cos(2*d*sqrt(x) + 2*c) + (8*(d*sqrt(x) + c)^3*a*b - 8*a*b*c^3 - 12*b^2*c^2 - 12*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 24*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c) - 4*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 - 3*b^2*c^2 - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (-8*I*(d*sqrt(x) + c)^3*a*b + 8*I*a*b*c^3 + 12*I*b^2*c^2 + (24*I*a*b*c + 12*I*b^2)*(d*sqrt(x) + c)^2 + (-24*I*a*b*c^2 - 24*I*b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(I*d*sqrt(x) + I*c)) - (8*(d*sqrt(x) + c)^3*a*b - 8*a*b*c^3 + 12*b^2*c^2 - 12*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 24*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c) - 4*(2*(d*sqrt(x) + c)^3*a*b - 2*a*b*c^3 + 3*b^2*c^2 - 3*(2*a*b*c - b^2)*(d*sqrt(x) + c)^2 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (8*I*(d*sqrt(x) + c)^3*a*b - 8*I*a*b*c^3 + 12*I*b^2*c^2 + (-24*I*a*b*c + 12*I*b^2)*(d*sqrt(x) + c)^2 + (24*I*a*b*c^2 - 24*I*b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(e^(I*d*sqrt(x) + I*c)) + (I*(d*sqrt(x) + c)^4*a*b + 2*I*b^2*c^3 + (-4*I*a*b*c - 2*I*b^2)*(d*sqrt(x) + c)^3 + (6*I*a*b*c^2 + 6*I*b^2*c)*(d*sqrt(x) + c)^2 + (-4*I*a*b*c^3 - 6*I*b^2*c^2)*(d*sqrt(x) + c) + (-I*(d*sqrt(x) + c)^4*a*b - 2*I*b^2*c^3 + (4*I*a*b*c + 2*I*b^2)*(d*sqrt(x) + c)^3 + (-6*I*a*b*c^2 - 6*I*b^2*c)*(d*sqrt(x) + c)^2 + (4*I*a*b*c^3 + 6*I*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + ((d*sqrt(x) + c)^4*a*b + 2*b^2*c^3 - 2*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + (-I*(d*sqrt(x) + c)^4*a*b + 2*I*b^2*c^3 + (4*I*a*b*c - 2*I*b^2)*(d*sqrt(x) + c)^3 + (-6*I*a*b*c^2 + 6*I*b^2*c)*(d*sqrt(x) + c)^2 + (4*I*a*b*c^3 - 6*I*b^2*c^2)*(d*sqrt(x) + c) + (I*(d*sqrt(x) + c)^4*a*b - 2*I*b^2*c^3 + (-4*I*a*b*c + 2*I*b^2)*(d*sqrt(x) + c)^3 + (6*I*a*b*c^2 - 6*I*b^2*c)*(d*sqrt(x) + c)^2 + (-4*I*a*b*c^3 + 6*I*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - ((d*sqrt(x) + c)^4*a*b - 2*b^2*c^3 - 2*(2*a*b*c - b^2)*(d*sqrt(x) + c)^3 + 6*(a*b*c^2 - b^2*c)*(d*sqrt(x) + c)^2 - 2*(2*a*b*c^3 - 3*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) + (48*I*a*b*cos(2*d*sqrt(x) + 2*c) - 48*a*b*sin(2*d*sqrt(x) + 2*c) - 48*I*a*b)*polylog(5, -e^(I*d*sqrt(x) + I*c)) + (-48*I*a*b*cos(2*d*sqrt(x) + 2*c) + 48*a*b*sin(2*d*sqrt(x) + 2*c) + 48*I*a*b)*polylog(5, e^(I*d*sqrt(x) + I*c)) - (48*(d*sqrt(x) + c)*a*b - 48*a*b*c - 24*b^2 - 24*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c - b^2)*cos(2*d*sqrt(x) + 2*c) - (48*I*(d*sqrt(x) + c)*a*b - 48*I*a*b*c - 24*I*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(I*d*sqrt(x) + I*c)) + (48*(d*sqrt(x) + c)*a*b - 48*a*b*c + 24*b^2 - 24*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c + b^2)*cos(2*d*sqrt(x) + 2*c) + (-48*I*(d*sqrt(x) + c)*a*b + 48*I*a*b*c - 24*I*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(4, e^(I*d*sqrt(x) + I*c)) + (24*I*(d*sqrt(x) + c)^2*a*b + 24*I*a*b*c^2 + 24*I*b^2*c + (-48*I*a*b*c - 24*I*b^2)*(d*sqrt(x) + c) + (-24*I*(d*sqrt(x) + c)^2*a*b - 24*I*a*b*c^2 - 24*I*b^2*c + (48*I*a*b*c + 24*I*b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 24*((d*sqrt(x) + c)^2*a*b + a*b*c^2 + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(I*d*sqrt(x) + I*c)) + (-24*I*(d*sqrt(x) + c)^2*a*b - 24*I*a*b*c^2 + 24*I*b^2*c + (48*I*a*b*c - 24*I*b^2)*(d*sqrt(x) + c) + (24*I*(d*sqrt(x) + c)^2*a*b + 24*I*a*b*c^2 - 24*I*b^2*c + (-48*I*a*b*c + 24*I*b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - 24*((d*sqrt(x) + c)^2*a*b + a*b*c^2 - b^2*c - (2*a*b*c - b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, e^(I*d*sqrt(x) + I*c)) + (2*I*(d*sqrt(x) + c)^4*b^2 - 8*I*(d*sqrt(x) + c)^3*b^2*c + 12*I*(d*sqrt(x) + c)^2*b^2*c^2 - 8*I*(d*sqrt(x) + c)*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))/(-I*cos(2*d*sqrt(x) + 2*c) + sin(2*d*sqrt(x) + 2*c) + I))/d^5","B",0
57,1,1221,0,0.767629," ","integrate((a+b*csc(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a^{2} - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c + 3 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{2} - 6 \, a b c^{2} \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right) - \frac{3 \, {\left(2 \, b^{2} c^{2} - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 2 \, b^{2} c - 2 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 2 i \, b^{2} c + {\left(-4 i \, a b c - 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(2 \, b^{2} c \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 i \, b^{2} c \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, b^{2} c\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), \cos\left(d \sqrt{x} + c\right) - 1\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + {\left(-4 i \, a b c + 2 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(d \sqrt{x} + c\right), -\cos\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b^{2} - 2 \, {\left(d \sqrt{x} + c\right)} b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)} a b - 4 \, a b c - 2 \, b^{2} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-4 i \, {\left(d \sqrt{x} + c\right)} a b + 4 i \, a b c + 2 i \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(4 \, {\left(d \sqrt{x} + c\right)} a b - 4 \, a b c + 2 \, b^{2} - 2 \, {\left(2 \, {\left(d \sqrt{x} + c\right)} a b - 2 \, a b c + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(4 i \, {\left(d \sqrt{x} + c\right)} a b - 4 i \, a b c + 2 i \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(i \, {\left(d \sqrt{x} + c\right)}^{2} a b + i \, b^{2} c + {\left(-2 i \, a b c - i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{2} a b - i \, b^{2} c + {\left(2 i \, a b c + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(d \sqrt{x} + c\right)}^{2} a b + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{2} a b + i \, b^{2} c + {\left(2 i \, a b c - i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(i \, {\left(d \sqrt{x} + c\right)}^{2} a b - i \, b^{2} c + {\left(-2 i \, a b c + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left({\left(d \sqrt{x} + c\right)}^{2} a b - b^{2} c - {\left(2 \, a b c - b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \cos\left(d \sqrt{x} + c\right) + 1\right) + {\left(-4 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 i \, a b\right)} {\rm Li}_{3}(-e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(4 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 4 i \, a b\right)} {\rm Li}_{3}(e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 4 i \, {\left(d \sqrt{x} + c\right)} b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + i}\right)}}{3 \, d^{3}}"," ",0,"2/3*((d*sqrt(x) + c)^3*a^2 - 3*(d*sqrt(x) + c)^2*a^2*c + 3*(d*sqrt(x) + c)*a^2*c^2 - 6*a*b*c^2*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c)) - 3*(2*b^2*c^2 - (2*(d*sqrt(x) + c)^2*a*b + 2*b^2*c - 2*(2*a*b*c + b^2)*(d*sqrt(x) + c) - 2*((d*sqrt(x) + c)^2*a*b + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*I*(d*sqrt(x) + c)^2*a*b + 2*I*b^2*c + (-4*I*a*b*c - 2*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) + 1) + (2*b^2*c*cos(2*d*sqrt(x) + 2*c) + 2*I*b^2*c*sin(2*d*sqrt(x) + 2*c) - 2*b^2*c)*arctan2(sin(d*sqrt(x) + c), cos(d*sqrt(x) + c) - 1) - (2*(d*sqrt(x) + c)^2*a*b - 2*(2*a*b*c - b^2)*(d*sqrt(x) + c) - 2*((d*sqrt(x) + c)^2*a*b - (2*a*b*c - b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (2*I*(d*sqrt(x) + c)^2*a*b + (-4*I*a*b*c + 2*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(d*sqrt(x) + c), -cos(d*sqrt(x) + c) + 1) + 2*((d*sqrt(x) + c)^2*b^2 - 2*(d*sqrt(x) + c)*b^2*c)*cos(2*d*sqrt(x) + 2*c) + (4*(d*sqrt(x) + c)*a*b - 4*a*b*c - 2*b^2 - 2*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c - b^2)*cos(2*d*sqrt(x) + 2*c) + (-4*I*(d*sqrt(x) + c)*a*b + 4*I*a*b*c + 2*I*b^2)*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(I*d*sqrt(x) + I*c)) - (4*(d*sqrt(x) + c)*a*b - 4*a*b*c + 2*b^2 - 2*(2*(d*sqrt(x) + c)*a*b - 2*a*b*c + b^2)*cos(2*d*sqrt(x) + 2*c) - (4*I*(d*sqrt(x) + c)*a*b - 4*I*a*b*c + 2*I*b^2)*sin(2*d*sqrt(x) + 2*c))*dilog(e^(I*d*sqrt(x) + I*c)) + (I*(d*sqrt(x) + c)^2*a*b + I*b^2*c + (-2*I*a*b*c - I*b^2)*(d*sqrt(x) + c) + (-I*(d*sqrt(x) + c)^2*a*b - I*b^2*c + (2*I*a*b*c + I*b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + ((d*sqrt(x) + c)^2*a*b + b^2*c - (2*a*b*c + b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*cos(d*sqrt(x) + c) + 1) + (-I*(d*sqrt(x) + c)^2*a*b + I*b^2*c + (2*I*a*b*c - I*b^2)*(d*sqrt(x) + c) + (I*(d*sqrt(x) + c)^2*a*b - I*b^2*c + (-2*I*a*b*c + I*b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - ((d*sqrt(x) + c)^2*a*b - b^2*c - (2*a*b*c - b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*cos(d*sqrt(x) + c) + 1) + (-4*I*a*b*cos(2*d*sqrt(x) + 2*c) + 4*a*b*sin(2*d*sqrt(x) + 2*c) + 4*I*a*b)*polylog(3, -e^(I*d*sqrt(x) + I*c)) + (4*I*a*b*cos(2*d*sqrt(x) + 2*c) - 4*a*b*sin(2*d*sqrt(x) + 2*c) - 4*I*a*b)*polylog(3, e^(I*d*sqrt(x) + I*c)) + (2*I*(d*sqrt(x) + c)^2*b^2 - 4*I*(d*sqrt(x) + c)*b^2*c)*sin(2*d*sqrt(x) + 2*c))/(-I*cos(2*d*sqrt(x) + 2*c) + sin(2*d*sqrt(x) + 2*c) + I))/d^3","B",0
58,1,52,0,0.331616," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""maxima"")","2 \, a^{2} \sqrt{x} - \frac{4 \, a b \log\left(\cot\left(d \sqrt{x} + c\right) + \csc\left(d \sqrt{x} + c\right)\right)}{d} - \frac{2 \, b^{2}}{d \tan\left(d \sqrt{x} + c\right)}"," ",0,"2*a^2*sqrt(x) - 4*a*b*log(cot(d*sqrt(x) + c) + csc(d*sqrt(x) + c))/d - 2*b^2/(d*tan(d*sqrt(x) + c))","A",0
59,0,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""maxima"")","-\frac{4 \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) - b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left(d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) - b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, {\left(d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) - b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) + b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{a b d \sqrt{x} \sin\left(d \sqrt{x} + c\right) - b^{2} \sin\left(d \sqrt{x} + c\right)}{{\left(d \cos\left(d \sqrt{x} + c\right)^{2} + d \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, d \cos\left(d \sqrt{x} + c\right) + d\right)} x^{2}}\,{d x}\right)} x + 2 \, {\left(a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} d\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x}"," ",0,"-(4*b^2*sin(2*d*sqrt(x) + 2*c) - ((d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) + b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 + 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) + d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) - b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 - 2*d*cos(d*sqrt(x) + c) + d)*x^2), x))*cos(2*d*sqrt(x) + 2*c)^2 + (d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) + b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 + 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) + d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) - b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 - 2*d*cos(d*sqrt(x) + c) + d)*x^2), x))*sin(2*d*sqrt(x) + 2*c)^2 - 2*(d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) + b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 + 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) + d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) - b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 - 2*d*cos(d*sqrt(x) + c) + d)*x^2), x))*cos(2*d*sqrt(x) + 2*c) + d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) + b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 + 2*d*cos(d*sqrt(x) + c) + d)*x^2), x) + d*integrate(2*(a*b*d*sqrt(x)*sin(d*sqrt(x) + c) - b^2*sin(d*sqrt(x) + c))/((d*cos(d*sqrt(x) + c)^2 + d*sin(d*sqrt(x) + c)^2 - 2*d*cos(d*sqrt(x) + c) + d)*x^2), x))*x + 2*(a^2*d*cos(2*d*sqrt(x) + 2*c)^2 + a^2*d*sin(2*d*sqrt(x) + 2*c)^2 - 2*a^2*d*cos(2*d*sqrt(x) + 2*c) + a^2*d)*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 - 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x)","F",0
60,-1,0,0,0.000000," ","integrate((a+b*csc(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,1,34,0,0.442392," ","integrate(csc(x^(1/2))^3/x^(1/2),x, algorithm=""maxima"")","\frac{\cos\left(\sqrt{x}\right)}{\cos\left(\sqrt{x}\right)^{2} - 1} - \frac{1}{2} \, \log\left(\cos\left(\sqrt{x}\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(\sqrt{x}\right) - 1\right)"," ",0,"cos(sqrt(x))/(cos(sqrt(x))^2 - 1) - 1/2*log(cos(sqrt(x)) + 1) + 1/2*log(cos(sqrt(x)) - 1)","A",0
62,-2,0,0,0.000000," ","integrate(x^(3/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
63,-2,0,0,0.000000," ","integrate(x^(1/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
64,-2,0,0,0.000000," ","integrate(1/(a+b*csc(c+d*x^(1/2)))/x^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
65,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(a+b*csc(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-2,0,0,0.000000," ","integrate(x^(3/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
68,-2,0,0,0.000000," ","integrate(x^(1/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
69,-2,0,0,0.000000," ","integrate(1/(a+b*csc(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
70,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(a+b*csc(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*csc(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \csc\left(d x^{n} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*csc(d*x^n + c) + a)^p, x)","F",0
73,1,128,0,0.464428," ","integrate((e*x)^(-1+n)*(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","\frac{\left(e x\right)^{n} a}{e n} - \frac{{\left(e^{n} \log\left(\cos\left(d x^{n}\right)^{2} + 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} - 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - e^{n} \log\left(\cos\left(d x^{n}\right)^{2} - 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} + 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)\right)} b}{2 \, d e n}"," ",0,"(e*x)^n*a/(e*n) - 1/2*(e^n*log(cos(d*x^n)^2 + 2*cos(d*x^n)*cos(c) + cos(c)^2 + sin(d*x^n)^2 - 2*sin(d*x^n)*sin(c) + sin(c)^2) - e^n*log(cos(d*x^n)^2 - 2*cos(d*x^n)*cos(c) + cos(c)^2 + sin(d*x^n)^2 + 2*sin(d*x^n)*sin(c) + sin(c)^2))*b/(d*e*n)","B",0
74,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","{\left(e^{2 \, n + 1} \int \frac{x^{2 \, n} \sin\left(d x^{n} + c\right)}{e^{2} x \cos\left(d x^{n} + c\right)^{2} + e^{2} x \sin\left(d x^{n} + c\right)^{2} + 2 \, e^{2} x \cos\left(d x^{n} + c\right) + e^{2} x}\,{d x} + e^{2 \, n + 1} \int \frac{x^{2 \, n} \sin\left(d x^{n} + c\right)}{e^{2} x \cos\left(d x^{n} + c\right)^{2} + e^{2} x \sin\left(d x^{n} + c\right)^{2} - 2 \, e^{2} x \cos\left(d x^{n} + c\right) + e^{2} x}\,{d x}\right)} b + \frac{\left(e x\right)^{2 \, n} a}{2 \, e n}"," ",0,"(e^(2*n + 1)*integrate(x^(2*n)*sin(d*x^n + c)/(e^2*x*cos(d*x^n + c)^2 + e^2*x*sin(d*x^n + c)^2 + 2*e^2*x*cos(d*x^n + c) + e^2*x), x) + e^(2*n + 1)*integrate(x^(2*n)*sin(d*x^n + c)/(e^2*x*cos(d*x^n + c)^2 + e^2*x*sin(d*x^n + c)^2 - 2*e^2*x*cos(d*x^n + c) + e^2*x), x))*b + 1/2*(e*x)^(2*n)*a/(e*n)","F",0
75,0,0,0,0.000000," ","integrate((e*x)^(-1+3*n)*(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","{\left(e^{3 \, n + 1} \int \frac{x^{3 \, n} \sin\left(d x^{n} + c\right)}{e^{2} x \cos\left(d x^{n} + c\right)^{2} + e^{2} x \sin\left(d x^{n} + c\right)^{2} + 2 \, e^{2} x \cos\left(d x^{n} + c\right) + e^{2} x}\,{d x} + e^{3 \, n + 1} \int \frac{x^{3 \, n} \sin\left(d x^{n} + c\right)}{e^{2} x \cos\left(d x^{n} + c\right)^{2} + e^{2} x \sin\left(d x^{n} + c\right)^{2} - 2 \, e^{2} x \cos\left(d x^{n} + c\right) + e^{2} x}\,{d x}\right)} b + \frac{\left(e x\right)^{3 \, n} a}{3 \, e n}"," ",0,"(e^(3*n + 1)*integrate(x^(3*n)*sin(d*x^n + c)/(e^2*x*cos(d*x^n + c)^2 + e^2*x*sin(d*x^n + c)^2 + 2*e^2*x*cos(d*x^n + c) + e^2*x), x) + e^(3*n + 1)*integrate(x^(3*n)*sin(d*x^n + c)/(e^2*x*cos(d*x^n + c)^2 + e^2*x*sin(d*x^n + c)^2 - 2*e^2*x*cos(d*x^n + c) + e^2*x), x))*b + 1/3*(e*x)^(3*n)*a/(e*n)","F",0
76,1,207,0,1.253097," ","integrate((e*x)^(-1+n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","-\frac{2 \, b^{2} e^{n} \sin\left(2 \, d x^{n} + 2 \, c\right)}{d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n} + \frac{\left(e x\right)^{n} a^{2}}{e n} - \frac{{\left(e^{n} \log\left(\cos\left(d x^{n}\right)^{2} + 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} - 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - e^{n} \log\left(\cos\left(d x^{n}\right)^{2} - 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} + 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)\right)} a b}{d e n}"," ",0,"-2*b^2*e^n*sin(2*d*x^n + 2*c)/(d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n) + (e*x)^n*a^2/(e*n) - (e^n*log(cos(d*x^n)^2 + 2*cos(d*x^n)*cos(c) + cos(c)^2 + sin(d*x^n)^2 - 2*sin(d*x^n)*sin(c) + sin(c)^2) - e^n*log(cos(d*x^n)^2 - 2*cos(d*x^n)*cos(c) + cos(c)^2 + sin(d*x^n)^2 + 2*sin(d*x^n)*sin(c) + sin(c)^2))*a*b/(d*e*n)","B",0
77,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{2 \, n} a^{2}}{2 \, e n} - \frac{2 \, b^{2} e^{2 \, n} x^{n} \sin\left(2 \, d x^{n} + 2 \, c\right) - \frac{1}{2} \, {\left(4 \, a b d^{2} e^{2 \, n + 1} \int \frac{x^{2 \, n} \sin\left(d x^{n} + c\right)}{d^{2} e^{2} x \cos\left(d x^{n} + c\right)^{2} + d^{2} e^{2} x \sin\left(d x^{n} + c\right)^{2} + 2 \, d^{2} e^{2} x \cos\left(d x^{n} + c\right) + d^{2} e^{2} x}\,{d x} + \frac{b^{2} e^{2 \, n - 1} \log\left(\cos\left(d x^{n}\right)^{2} + 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} - 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{d^{2} n}\right)} {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)} - \frac{1}{2} \, {\left(4 \, a b d^{2} e^{2 \, n + 1} \int \frac{x^{2 \, n} \sin\left(d x^{n} + c\right)}{d^{2} e^{2} x \cos\left(d x^{n} + c\right)^{2} + d^{2} e^{2} x \sin\left(d x^{n} + c\right)^{2} - 2 \, d^{2} e^{2} x \cos\left(d x^{n} + c\right) + d^{2} e^{2} x}\,{d x} + \frac{b^{2} e^{2 \, n - 1} \log\left(\cos\left(d x^{n}\right)^{2} - 2 \, \cos\left(d x^{n}\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x^{n}\right)^{2} + 2 \, \sin\left(d x^{n}\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{d^{2} n}\right)} {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)}}{d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n}"," ",0,"1/2*(e*x)^(2*n)*a^2/(e*n) - (2*b^2*e^(2*n)*x^n*sin(2*d*x^n + 2*c) - (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate((2*a*b*d*e^(2*n)*x^(2*n) - b^2*e^(2*n)*x^n)*sin(d*x^n + c)/(d*e*x*cos(d*x^n + c)^2 + d*e*x*sin(d*x^n + c)^2 + 2*d*e*x*cos(d*x^n + c) + d*e*x), x) - (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate((2*a*b*d*e^(2*n)*x^(2*n) + b^2*e^(2*n)*x^n)*sin(d*x^n + c)/(d*e*x*cos(d*x^n + c)^2 + d*e*x*sin(d*x^n + c)^2 - 2*d*e*x*cos(d*x^n + c) + d*e*x), x))/(d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)","F",0
78,0,0,0,0.000000," ","integrate((e*x)^(-1+3*n)*(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{3 \, n} a^{2}}{3 \, e n} - \frac{2 \, b^{2} e^{3 \, n} x^{2 \, n} \sin\left(2 \, d x^{n} + 2 \, c\right) - 2 \, {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)} \int \frac{{\left(a b d e^{3 \, n} x^{3 \, n} - b^{2} e^{3 \, n} x^{2 \, n}\right)} \sin\left(d x^{n} + c\right)}{d e x \cos\left(d x^{n} + c\right)^{2} + d e x \sin\left(d x^{n} + c\right)^{2} + 2 \, d e x \cos\left(d x^{n} + c\right) + d e x}\,{d x} - 2 \, {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)} \int \frac{{\left(a b d e^{3 \, n} x^{3 \, n} + b^{2} e^{3 \, n} x^{2 \, n}\right)} \sin\left(d x^{n} + c\right)}{d e x \cos\left(d x^{n} + c\right)^{2} + d e x \sin\left(d x^{n} + c\right)^{2} - 2 \, d e x \cos\left(d x^{n} + c\right) + d e x}\,{d x}}{d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} - 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n}"," ",0,"1/3*(e*x)^(3*n)*a^2/(e*n) - (2*b^2*e^(3*n)*x^(2*n)*sin(2*d*x^n + 2*c) - (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate(2*(a*b*d*e^(3*n)*x^(3*n) - b^2*e^(3*n)*x^(2*n))*sin(d*x^n + c)/(d*e*x*cos(d*x^n + c)^2 + d*e*x*sin(d*x^n + c)^2 + 2*d*e*x*cos(d*x^n + c) + d*e*x), x) - (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate(2*(a*b*d*e^(3*n)*x^(3*n) + b^2*e^(3*n)*x^(2*n))*sin(d*x^n + c)/(d*e*x*cos(d*x^n + c)^2 + d*e*x*sin(d*x^n + c)^2 - 2*d*e*x*cos(d*x^n + c) + d*e*x), x))/(d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 - 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)","F",0
79,-1,0,0,0.000000," ","integrate((e*x)^(-1+n)/(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((e*x)^(-1+2*n)/(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*csc(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*x)^(-1+n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((e*x)^(-1+2*n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*csc(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
