# Math Help - Integration by Substitution

1. ## Integration by Substitution

How do I find the indefinite integral:

$

\int\frac{5}{{(3x-1)}^3} dx
$

2. Originally Posted by millerst
How do I find the indefinite integral:

$

\int\frac{5}{(3x-1)^3} dx
$
I've aded the brackets that should have been included. Substitute u = 3x - 1.

3. make $u = 3x-1 \Rightarrow \frac{du}{dx} = 3$

therefore

$\frac{5}{3}\int \frac{du}{dx}\frac{1}{u^3}~dx$

Can you take it from here?

4. $

\int\frac{5}{(3x-1)^3} dx
$

So the answer works out to?

$

\frac{-5}{6(3x-1)^2} + C
$