Evaluate the following integrals: ∫ (x^2 tan^-1 x)/(1 + x^2) dx

Question

Evaluate the following integrals:

\(\int \frac{x^2\,tan^{-1}x}{(1+x^2)}dx\)

∫ (x² tan^-1 x)/(1 + x²) dx

Answer 1

Let tan^{- 1} x = t and x = tan t

Differentiating both sides, we get

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here t is the first function and sec²t as the second function.