Calcular la integral $\int\frac{1}{u\left(1+u\right)}du$

Calcular la integral

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

Calcular la integral

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

Calcular la integral

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

Calcular la integral

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

Calcular la integral

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

Calcular la integral

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

Calcular la integral

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