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