1. ## Integral

Determine

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

2. $\int \frac{1}{1+2x^2} dx = \int \frac{1}{1+(\sqrt{2}x)^{2}} dx = \frac{1}{\sqrt{2}} \int \frac{1}{1+u^{2}} du$ $= \frac{1}{\sqrt{2}} \tan^{-1} u + C = \frac{1}{\sqrt{2}} \tan^{-1} \sqrt{2}x + C$

For simple integrals like this one, Wolfram Alpha will give you all of the steps.

EDIT: Actually it doesn't for this one.