# Thread: Antiderivative

1. ## Antiderivative

How do you find this antiderivative?

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

I see that the $x^2 +1$ looks like the derivative of $tan^{-1}(x)$, but I don't know how to antidifferentiate that equation. :/

2. Originally Posted by Cursed
How do you find this antiderivative?

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

I see that the $x^2 +1$ looks like the derivative of $tan^{-1}(x)$, but I don't know how to antidifferentiate that equation. :/
Add 1 and subtract 1 to get:

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

$\ldots$