Solve the trigonometric integral $\int\sin\left(nx\right)dx$

Find the integral

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

Find the integral

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

Find the integral

$\int\sec^4xdx$

Find the integral

$\int cos^23xdx$

Find the integral

$\int\sin^4\left(7x-2\right)dx$

Find the integral

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

Find the integral

$\int\cos^6\left(x\right)dx$