Question

Evaluate:

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

Answer 1

Now,

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

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

$=\int \frac{dx}{(x^2+(\sqrt{3}{)}^2)}+$$\int \frac{dx}{(x^2-(\sqrt{2}{)}^2)}$

$=\frac{1}{\sqrt{3}}{\tan }^{-1}\frac{x}{\sqrt{3}}+\frac{1}{2\sqrt{2}}\log \left|\frac{x-\sqrt{2}}{x+\sqrt{2}}\right|+c$ [Where $c$ is integrating constant]