Integrate the function $\frac{1}{\sqrt{x}+x^2}$ from 0 to $\infty $

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_e^{\infty}\left(\frac{1}{x\left(\ln\left(x\right)\right)^3}\right)dx$

Evaluate the integral

$\int_2^{\infty}\left(\frac{lnx}{x}\right)dx$

Evaluate the integral

$\int_0^1\left(\ln\left(1+x\right)\right)dx$