Prove
Question:

$\frac{x^{2}}{\sqrt{x^{6}+a^{6}}}$

Solution:

Let $x^{3}=t$

$\Rightarrow 3 x^{2} d x=d t$

$\therefore \int \frac{x^{2}}{\sqrt{x^{6}+a^{6}}} d x=\frac{1}{3} \int \frac{d t}{\sqrt{t^{2}+\left(a^{3}\right)^{2}}}$

$=\frac{1}{3} \log \left|t+\sqrt{t^{2}+a^{6}}\right|+\mathrm{C}$

$=\frac{1}{3} \log \left|x^{3}+\sqrt{x^{6}+a^{6}}\right|+\mathrm{C}$

Administrator

Leave a comment

Please enter comment.
Please enter your name.