# Thread: integration with trig substitution

1. ## integration with trig substitution

integrate:

2x^2 / x^2 + 4 dx

how do know which substitution to use here and what happens to the numerator???

2. Originally Posted by razorfever
integrate:

2x^2 / x^2 + 4 dx

how do know which substitution to use here and what happens to the numerator???
First do some long division to turn the integrand into

$2 - \frac{8}{x^2 + 4}$.

Then you work with the fact that $\int{\frac{1}{a^2 + x^2}\,dx} = \frac{1}{a}\arctan{\left ( \frac{x}{a} \right )} + C$.