Find the integral $\int x^2\sqrt{\left(x-2\right)^{3}}dx$

Find the integral

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

Find the integral

$\int\left(\frac{arctan\left(2x\right)}{x}\right)dx$

Find the integral

$\int\left(8x-12\right)\left(4x^2-12x\right)^4dx$

Find the integral

$\int\left(5x-1\right)^3dx$

Find the integral

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

Find the integral

$\int\left(7x+8\right)^{10}7dx$

Find the integral

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