# How do you integrate (5)/(1+3x)^3?

Aug 23, 2015

The answer is $- \frac{5}{6 {\left(1 + 3 x\right)}^{2}}$

#### Explanation:

Rewrite as : $\frac{5}{3} \int \frac{3}{1 + 3 x} ^ 3 \mathrm{dx}$

Now let's : $u = 1 + 3 x$
then $\mathrm{du} = 3$

So we have :

$\frac{5}{3} \int \frac{1}{u} ^ 3 \mathrm{du} = \frac{5}{3} \int {u}^{- 3} \mathrm{du}$

$\implies \frac{5}{3} \left[- \frac{1}{2} {u}^{- 2}\right] = - \frac{5}{6} \left[\frac{1}{u} ^ 2\right]$

Dont forget $u = 1 + 3 x$

Finally : $- \frac{5}{6 {\left(1 + 3 x\right)}^{2}}$