Question

Solve: $\int \frac{1}{(2x-3)(x-4)}dx$

Answer 1

Now,

$\int \frac{1}{(2x-3)(x-4)}dx$

$=\frac{1}{5}[\int \frac{1}{(x-4)}dx-$$\int \frac{2}{(2x-3)}dx]$

$=\frac{1}{5}\left[\log |\right(x-4)|-\log |(2x-3\left)|\right]+c$ [ Where $c$ is integrating constant]

$=\frac{1}{5}\log \left|\frac{x-4}{2x-3}\right|+c$