Solve the trigonometric integral $\int\mathrm{arcsec}\left(x\right)dx$

Find the integral

$\int xarctan\left(4x\right)dx$

Find the integral

$\int arctanxdx$

Find the integral

$\int sec^3\left(x\right)dx$

Find the integral

$\int x\arcsin\left(x\right)dx$

Find the integral

$\int\sec^4xdx$

Find the integral

$\int cos^23xdx$

Find the integral

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