Question

Evaluate the integral \( \displaystyle \int \frac{x^2}{(x^2 + 1)(x^2 + 4)} \, dx \) using partial fractions.

Hint:

For quadratic denominators: \( \int \frac{dx}{x^2 + a^2} = \frac{1}{a}\tan^{-1}(x/a) \). Always split using partial fractions first.

Answer 1