Integrate the function $2x\sqrt{2x-1}$ from 0 to $12$

Compute the integral

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Compute the integral

$\int\frac{x}{x^2+1}dx$

Compute the integral

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

Compute the integral

$\int\frac{x}{\sqrt{x^2+9}}dx$

Compute the integral

$\int\frac{2x-1}{x^2-8x+15}dx$

Compute the integral

$\int\frac{x}{x^2+3x+2}dx$

Compute the integral

$\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx$