\[\int \frac {1}{x^2+a^2} \d x = \frac {1}{a} \arctan \left (\frac {x}{a}\right ) +C, \]
which will recur frequently in the course. Using this formula and the rules for antidifferentiation, find the following:
(Use \(C\) for the constant of integration)
\begin{align*} \int \frac {4}{x^2+1} \d x &= \answer {4\arctan (x)+C}\\ \int \frac {1}{x^2+4} \d x &= \answer {\frac {1}{2}\arctan \left (\frac {x}{2}\right )+C}\\ \int \frac {1}{4x^2+1} \d x &= \answer {\frac {1}{2} \arctan (2x)+C}\\ \end{align*}
Now, try one a little more complicated:
\[ \int \frac {3}{9x^2+16} \d x = \answer {\frac {1}{4}\arctan \left (\frac {3x}{4}\right )+C} \]
Use \(C\) for the constant of integration.