Question

$\int \frac{(\sqrt{x}{)}^3}{(\sqrt{x}{)}^3+x^{7/2}}dx$

Answer 1

We have,

$I=\int \frac{(\sqrt{x}{)}^3}{(\sqrt{x}{)}^3+x^{7/2}}dx$

$I=\int \frac{(\sqrt{x}{)}^3}{\left(\sqrt{x}{)}^3\right(1+x^2)}dx$

$I=\int \frac{1}{(1+x^2)}dx$

$I={\tan }^{-1}x+C$

Hence, this si the answer.