Factor by completing the square $\frac{-5m^5n^2-\frac{1}{2}m^4n^4+\frac{2}{3}m^3n-4mn^4}{-4m^5n^3}$

Evaluate the integral

$\int_2^{\infty}\left(\frac{1}{x^2+6x+5}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{\sqrt{x}+x^2}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{x}{1+x^3}\right)dx$

Evaluate the integral

$\int_{-\infty}^{\infty}\left(\frac{1}{2x^2\left(x-1\right)}\right)dx$

Evaluate the integral

$\int_2^{\infty}\left(\frac{1}{x^2+6x+5}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{\sqrt{x}+x^2}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{x}{1+x^3}\right)dx$