Question

Integrate the function: $x \sqrt {1+2x^2}$

Answer 1

Let 1 + 2x2 = t

∴ 4xdx = dt

$\Rightarrow \int x \sqrt{1+2x^2}dx = \int \frac { \sqrt t dt}{4}$
= $\frac{1}{4}\int t^{\frac{1}{2}}dt$

= $\frac{1}{4}\bigg(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\bigg)+C$

=$\frac{1}{6}(1+2x^2)^{\frac{3}{2}}+C$