Find the derivative of $\ln\left(x\right)$ using the definition

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Find the integral

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

Evaluate the integral

$\int_{-1}^2\frac{3x}{x+4}dx$

Evaluate the integral

$\int_9^4\left(\frac{x^2}{x+1}\right)dx$