Question

integrate 1/(4x^2+3)

Answer 1

\[
\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3}}\right)}{2
\sqrt{3}}
\]
This comes from the general formula\[

\int \frac{dx}{a x^2+b}=\frac{\tan ^{-1}\left(\frac{\sqrt{a}
x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}
\]
Try to prove the general formula