Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

Show that

Question:

$\frac{x^{3}}{\sqrt{1-x^{8}}}$

Solution:

$\frac{x^{3}}{\sqrt{1-x^{8}}}$

Let $x^{4}=t \Rightarrow 4 x^{3} d x=d t$

$\Rightarrow \int \frac{x^{3}}{\sqrt{1-x^{8}}} d x=\frac{1}{4} \int \frac{d t}{\sqrt{1-t^{2}}}$

$=\frac{1}{4} \sin ^{-1} t+C$

$=\frac{1}{4} \sin ^{-1}\left(x^{4}\right)+C$

Leave a comment

None
Free Study Material