Answer
$-\frac{9}{4}$$\ln|5-4x|$ + C
Work Step by Step
$\int\frac{9}{5-4x} dx $
Let $u = 5-4x$
$\frac{du}{dx}$ = -4
$\frac{du}{-4}$ = $dx$
Substitute $u$ and $dx$ into the original equation
$\int\frac{9}{u}\frac{du}{-4}$
= $\int\frac{9}{-4}\frac{1}{u} du$
= $-\frac{9}{4}$$\int\frac{1}{u} du$
= $-\frac{9}{4}$$\ln|u|$ + C
Since $u = 5-4x$, substituting it back will give you
$-\frac{9}{4}$$\ln|5-4x|$ + C
