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

Find the integral

$\int arctanxdx$

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

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

Find the integral

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

Find the integral

$\int arctan\:x\:dx$