Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution:

To integrate the given function first convert it into integrable form

$\int\frac{3x}{1+2x^4}dx \\ \\ 3\int\frac{x}{1+ (\sqrt{2}{x}^{2}) ^2}dx$
let

$\sqrt{2} {x}^{2} = t \\ \\ 2 \sqrt{2} xdx = dt \\ \\ xdx = \frac{dt}{2 \sqrt{2} }$
substitute these values

$\frac{3}{2 \sqrt{2} } \int\frac{1}{1+ (t) ^2}dt \\ \\ = \frac{3}{2 \sqrt{2} } {tan}^{ - 1}t + C$
Redo substitution

$\int\frac{3x}{1+2x^4}dx= \frac{3}{2 \sqrt{2} } {tan}^{ - 1}( \sqrt{2} {x}^{2} ) + C$
Hope it helps you.