Find the derivative using the quotient rule $\frac{\left(\sqrt[5]{x}\sqrt{y^{3}}\right)^{10}}{\left(y^{- \frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$

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

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