Question:
$x \sqrt{1+2 x^{2}}$
Solution:
Let $1+2 x^{2}=t$
$\therefore 4 x d x=d t$
$\Rightarrow \int x \sqrt{1+2 x^{2}} d x=\int \frac{\sqrt{t} d t}{4}$
$=\frac{1}{4} \int t^{\frac{1}{2}} d t$
$=\frac{1}{4}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right)+\mathrm{C}$
$=\frac{1}{6}\left(1+2 x^{2}\right)^{\frac{3}{2}}+\mathrm{C}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.