Integrate the function $\frac{x}{1-x^2}$ from 0 to $1$

Evaluate the integral

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

Evaluate the integral

$\int_0^1\left(\frac{x}{1-x^2}\right)dx$

Evaluate the integral

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

Evaluate the integral

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

Find the integral

$\int\frac{1}{\left(x^4+1\right)}dx$

Evaluate the integral

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

Evaluate the integral

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