Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\frac{9e^{-5x}\cos\left(7x\right)^2}{8x^2-3x+1}\right)$

Compute the integral

$\int xdx$

$\frac{x^5-x^4+x^2-2}{x^2+1}$

$\frac{x^3+x+5}{x+1}$

Compute the integral

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

Compute the integral

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

Compute the integral

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

Compute the integral

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