# How do you integrate (1/(25 + x^2) ) dx?

May 18, 2015

We can rewrite this as

$\int \left(\frac{1}{{5}^{2} + {x}^{2}}\right) \mathrm{dx}$

By definition, we know that the integration of the inverse of a sum of squares results in a trigonometric function as follows:

$\int \left(\frac{1}{{u}^{2} + {a}^{2}}\right) \mathrm{du} = \left(\frac{1}{a}\right) \arctan \left(\frac{u}{a}\right) + c$

Applying this formula to your function, we have this:

$\int \left(\frac{1}{{5}^{2} + {x}^{2}}\right) \mathrm{dx} = \textcolor{g r e e n}{\frac{\arctan \left(\frac{x}{5}\right)}{5} + c}$