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

$\int\frac{\left(3x-5\right)}{\left(x-1\right)\left(x^2-1\right)}dx$

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

$\int\frac{x+7}{x^2+2x-3}dx$

$\int\frac{4}{x^2-4}dx$

$\int\frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)}dx$

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

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