Question

Integrate the following function with respect to $x$
$\frac{4x-6}{(x^2-3x+5{)}^{3/2}}$

Answer 1

Let,

$x^2-3x+5=t$

$⟹(2x-3)dx=dt$

Substituting these values, we get

$\int \frac{2dt}{t^{3/2}}$

$⟹\frac{-2\times 2}{t^{1/2}}+C$

$⟹\frac{-4}{(x^2-3x+5{)}^{1/2}}+C$