Question

Evaluate the following integrals:
$\int \frac{x}{\sqrt{x^4+a^4}}dx$

Answer 1

Now,

$\int \frac{x}{\sqrt{x^4+a^4}}dx$

$=\frac{1}{2}\int \frac{2x}{\sqrt{x^4+a^4}}dx$

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

$=\frac{1}{2}\log |x^2+\sqrt{x^4+a^4}|+c$. [ Where $c$ is integrating constant]