Question

Integrate the function: $\frac {3x}{1+2x^4}$

Answer 1

$Let \ \sqrt 2x^2 = t$

$∴ 2\sqrt2x\ dx = dt$

$⇒ ∫\frac {3x}{1+2x^4}\ dx = \frac {3}{2\sqrt2} ∫\frac {dt}{1+t^2}$

$= \frac {3}{2√2}[tan^{-1} t]+C$

$= \frac {3}{2√2}[tan^{-1} (\sqrt 2x^2)]+C$