Question

Evaluate:
$\int \frac{x^2}{9+16x^6}dx$

Answer 1

'$\int \frac{x^2}{9+16x^6}dx$

$=\frac{1}{12}\int \frac{12x^2}{9+(4x^3{)}^2}dx$

$=\frac{1}{12}\int \frac{d\left(4x^3\right)}{9+(4x^3{)}^2}dx$

$=\frac{1}{12}\times \frac{1}{3}{\tan }^{-1}\frac{4x^3}{3}+c$ [ Where $c$ is integrating constant]

$=\frac{1}{36}{\tan }^{-1}\frac{4x^3}{3}+c$