Question

Evaluate the ∫(t³+3t)/(t²+1)dt

Answer 1

Let $I=\int \dfrac{t^3+3t}{t^2+1} dt$

First performing long division, we get

$I=\int (t+\dfrac{2t}{t^2+1} )dt$

On integrating

$I=\dfrac{t^2}2+\log|t^2+1|+C$