Question

Find the integral of 3/sqrt of 1-4x^2

Answer 1

$\int {\frac{3}{\sqrt{1-4x^{2}}}} \, dx$
$= 3\int {\frac{1}{\sqrt{1-4x^{2}}}} \, dx$
$= 3\int {\frac{1}{\sqrt{4(\frac{1}{4} - x^{2})}}} \, dx$
$= \frac{3}{2}\int {\frac{1}{\sqrt{\frac{1}{4} - x^{2}}}}\, dx$

$= \frac{3}{2}sin^{-1}(2x) + C$