3.1 Test file Number [5]

3.1.1 Maxima

Integral number [145] $$\int x\cos (k\csc (x))\cot (x)\csc (x)dx$$

[B]   time = 1.90275 (sec), size = 240 ,normalized size = 17.14 $$-\frac{(x{e}^{(\frac{4k\cos \left(2x\right)\cos \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1}+\frac{4k\sin \left(2x\right)\sin \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1})}+x{e}^{\left(\frac{4k\cos \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1}\right)})e^{(-\frac{2k\cos \left(2x\right)\cos \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1}-\frac{2k\sin \left(2x\right)\sin \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1}-\frac{2k\cos \left(x\right)}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1})}\sin \left(\frac{2(k\cos \left(x\right)\sin \left(2x\right)-k\cos \left(2x\right)\sin \left(x\right)+k\sin \left(x\right))}{\cos {\left(2x\right)}^2+\sin {\left(2x\right)}^2-2\cos \left(2x\right)+1}\right)}{2k}$$

[In]

integrate(x*cos(x)*cos(k/sin(x))/sin(x)^2,x, algorithm=""maxima"")

[Out]

-1/2*(x*e^(4*k*cos(2*x)*cos(x)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1) + 4*k*sin(2*x)*sin(x)/(cos(2*x)^2 +
sin(2*x)^2 - 2*cos(2*x) + 1)) + x*e^(4*k*cos(x)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)))*e^(-2*k*cos(2*x)*
cos(x)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1) - 2*k*sin(2*x)*sin(x)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x)
+ 1) - 2*k*cos(x)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1))*sin(2*(k*cos(x)*sin(2*x) - k*cos(2*x)*sin(x) + k
*sin(x))/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1))/k