In my lecture notes there's this method for solving integrals of irational functions, but I can't find anything about it on the internet. Here it is
Let $R$ be a rational function, and let $m_1, \dots, m_i, n_1, \dots, n_i$ be natural numbers. The integral $$\int R \Bigl(x,\Bigl(\frac{ax+b}{cx+d}\Bigr)^\frac{m_1}{n_1}, \dots ,\Bigl(\frac{ax+b}{cx+d}\Bigr)^\frac{m_i}{n_i}\Bigr)dx$$ simplifies to an integral of a rational function, with the substitution $t^n=\frac{ax+b}{cx+d}$, where $n=lcm\{n_1, \dots, n_i\}$
If you know where I can find out more about it, please let me know.
