To evaluate $\int x\tan^{-1} x\,dx$ by parts, which should be taken as $u$, the function to differentiate?

Explanation

1. 01

   The order of preference for $u$ is inverse trigonometric, then logarithmic, algebraic, trigonometric, exponential.

2. 02

   $\tan^{-1} x$ comes first: its derivative $\frac{1}{1 + x^{2}}$ is simple, while $\int \tan^{-1} x\,dx$ is not.