# What is the integral of 1/(x^2 + a^2)?

The integral of \frac{1}{x^2 + a^2} is \frac{1}{a}\tan^{-1}(\frac{x}{a}) + C.## Solution of the integral of 1/(x^2 + a^2)

**Solution:**While we could straightly use some integral techniques, the reader should remind itself that there is a function that if you take the derivative of that, then we get exactly the solution of \frac{1}{x^2 + a^2}. Indeed, we get the following from this article:

\begin{align*} \frac{d}{dx} \frac{1}{a}\tan^{-1}\bigg(\frac{x}{a}\bigg) = \frac{1}{x^2 + a^2}. \end{align*}

## Conclusion

Therefore, the integral of \frac{1}{x^2 + a^2} is \frac{1}{a}\tan^{-1}(\frac{x}{a}) + C, or in mathematical notation:\begin{align*} \int \frac{dx}{x^2 + a^2} = \frac{1}{a}\tan^{-1}\bigg(\frac{x}{a}\bigg) + C. \end{align*}