Solve the trigonometric integral $\int\sin\left(x\right)^4\cos\left(x\right)dx$

Find the integral

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

Find the integral

$\int\frac{1}{1-sinx}dx$

Find the integral

$\int x\left(x^2-3\right)dx$

Find the integral

$\int\csc^23x\cos3xdx$

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

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