Integration of 1 Over a^2+x^2

In this tutorial we shall discuss the integration of 1 over x^2+a^2, and this is another important form of integration.

The integration of $\frac{1}{{{a^2} + {x^2}}}$ is of the form

To prove this formula, putting $x = a\tan t$ we have $dx = a{\sec ^2}tdt$, $t = {\tan ^{ - 1}}\left( {\frac{x}{a}} \right)$. So the given integral takes the form

Using the value $t = {\tan ^{ - 1}}\left( {\frac{x}{a}} \right)$, we have