Question

Evaluate $\int \frac{x^6+1}{x^2+1}dx$?

Answer 1

When integrating a rational function where the numerator has a degree equal to or higher than the denominator, start by doing "algebraic division" of the numerator by the denominator figure (i).
In this unusual trick question the remainder is zero, so the denominator was a factor of the numerator, so the fraction is the polynomial $x^4-x^2+1$ which trivially integrates to the answer given.