Find the integral $\int2x\left(\cot\left(x\right)^2\right)^2dx$

Find the integral

$\int\frac{1}{1-cos\left(x\right)}dx$

Find the integral

$\int\frac{1}{\sin\left(x\right)-1}dx$

Find the integral

$\int\sin^4x\cos xdx$

Find the integral

$\int\left(\sin\left(x^2\right)\right)dx$

Find the integral

$\int cos\left(x^2\right)dx$

Find the integral

$\int\left(sin\left(x^2\right)\right)dx$

Find the integral

$\int\sin\left(x^2\right)\:dx$