Question

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

Answer 1

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

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

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

$=x-2{\tan }^{-1}x+c$ (Ans)