$\int \frac{1}{(2 x-7) \sqrt{x^2-7 x+12}} d x$ is equal to
Answer & explanation
Correct answer: option 2
Let
$I=\int \frac{1}{(2 x-7) \sqrt{x^2-7 x+12}} d x$
$\Rightarrow I=\int \frac{2}{(2 x-7) \sqrt{4 x^2-28 x+48}} d x$
$\Rightarrow I=\int \frac{1}{(2 x-7) \sqrt{(2 x-7)^2-12}} d(2 x-7)=\sec ^{-1}(2 x-7)+C$