Question

Evaluate : $\int \frac{x^4+1}{x^2+1}dx$.

Answer 1

Given $\int \frac{x^4+1}{x^2+1}dx$

$=\int (\frac{2}{x^2+1}+x^2-1)dx$

$=2\int \frac{1}{x^2+1}dx+\int x^{2}dx-\int 1dx$

$=2\left({\tan }^{-1}x\right)+\frac{x^3}{3}-x+C$

$=2{\tan }^{-1}x+\frac{x^3}{3}-x+C$