# How do you find the indefinite integral of int (4sinx)/(3tanx)dx?

Dec 7, 2016

The answer is $= \frac{4}{3} \sin x + C$

#### Explanation:

We use $\tan x = \sin \frac{x}{\cos} x$

$\frac{4 \sin x}{3 \tan x}$

$= \frac{4 \sin x}{3 \sin \frac{x}{\cos} x}$

$= \frac{4}{3} \cos x$

So,

$\int \frac{4 \tan x \mathrm{dx}}{3 \cos x} = \frac{4}{3} \int \cos x \mathrm{dx}$

$= \frac{4}{3} \sin x + C$