# Math Help - Finding an indefinite integral

1. ## Finding an indefinite integral

Find the integral of:

[g'(x)] / [g(x)]^2

I got as an anser:

[g(x)] / 1/3[g(x)]^3

...but I'm not sure if I broke some kind of rules.

2. Originally Posted by WartonMorton
Find the integral of:

[g'(x)] / [g(x)]^2

I got as an anser:

[g(x)] / 1/3[g(x)]^3

...but I'm not sure if I broke some kind of rules.
hi warton,..
i suggest you to use the substitution method

$\int \frac{g'(x)}{g^2(x)}~dx = \int \frac{~d(g(x))}{g^2(x)} = - \frac{1}{g(x)} + C$

3. Originally Posted by WartonMorton
Find the integral of:

[g'(x)] / [g(x)]^2

I got as an anser:

[g(x)] / 1/3[g(x)]^3

...but I'm not sure if I broke some kind of rules.
$u = g(x)$ therefore $du = g'(x) dx \: \: \rightarrow \: dx = \frac{du}{g'(x)}$

$
\int \frac{g'(x)}{u^2\,g'(x)}\,du = \int \frac{du}{u^2}$

$= -\frac{1}{u}+C = -\frac{1}{g(x)}+C$