Simplify the quotient of powers $\frac{\left(x^{-\frac{1}{5}}y^{\frac{3}{2}}\right)^{10}}{\left(y^{\frac{1\cdot -2}{5}}\sqrt[3]{x^{2}}\right)^5}$

Compute the integral

$\int e^x\cos\left(x\right)dx$

Compute the integral

$\int xe^{2x}dx$

Compute the integral

$\int xe^{3x}dx$

Compute the integral

$\int3\cdot e^x\cdot xdx$

Compute the integral

$\int7\cdot e^{8x}\cdot xdx$

Compute the integral

$\int y^2 e^{2y}dy$

Compute the integral

$\int\sin\left(x\right)e^xdx$