Solve the trigonometric integral $\int\mathrm{arccot}\left(12y\right)dy$

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

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

Find the integral

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

Find the integral

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