Simplify the power of a power $\sqrt{\sqrt{x^{12}y^8\sqrt{x^2y}}}$

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

$\int arctan\:x\:dx$

Find the integral

$\int sin^4xdx$

Find the integral

$\int sin\left(x\right)\cdot\cos\left(x\right)dx$