Integrate the function $\sin\left(2u\right)\left(1+\cot\left(2u\right)\right)$

Find the integral

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

Find the integral

$\int xsinx\:dx$

Find the integral

$\int\left(x^3+2\right)^23x^2dx$

Find the integral

$\int\left(x^2sen\left(2x\right)\right)dx$

Find the integral

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

Find the integral

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

Find the integral

$\int a^{4x}dx$