Answer
$\frac{\sqrt 3}{15}arcsin(\frac{5x}{\sqrt 3})+C$
Work Step by Step
$\int\frac{1}{\sqrt (3+25x^{2})}dx$
The denominator looks like $arctan$.
$\int\frac{du}{a^{2}+u^{2}}=\frac{1}{a}arctan(\frac{u}{a})+C$
$a=\sqrt 3$
$u=5x$
$du=5dx$
$\frac{1}{5}\int\frac{5}{3+25x^{2}}$
$\frac{1}{5}[\frac{1}{\sqrt 3}arctan(\frac{5x}{\sqrt 3}]+C$
$\frac{1}{5\sqrt 3}(\frac{\sqrt 3}{\sqrt 3})arctan(\frac{5x}{\sqrt 3}+C$
$\frac{\sqrt 3}{15}arcsin(\frac{5x}{\sqrt 3})+C$
