Question

Evaluate:
$\int \frac{2x}{(x^2+1)(x^2+3)}dx$.

Answer 1

$\int \frac{2x}{(x^2+1)(x^2+3)}dx$

$x^2=m$

$2xdx=dm$

$\int \frac{dm}{(m+1)(m+3)}$

$\frac{1}{2}\int [\frac{dm}{(m+1)}-\frac{dm}{m+3}]$

$=\frac{1}{2}[In|m+1|-In|m+3|]+c$

$=\frac{1}{2}[In|x^2+1|-In|x^2+3|]+c$