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# How do you find the integral of cos(3x) dx?

Apr 14, 2016

I found: $\int \cos \left(3 x\right) \mathrm{dx} = \frac{1}{3} \sin \left(3 x\right) + c$

#### Explanation:

Considering:
$\int \cos \left(3 x\right) \mathrm{dx} =$

we can set $3 x = t$

so: $x = \frac{t}{3}$

and: $\mathrm{dx} = \frac{1}{3} \mathrm{dt}$

The integral becomes:

$\int \frac{1}{3} \cos \left(t\right) \mathrm{dt} = \frac{1}{3} \sin \left(t\right) + c$

going back to $x$:

we know that $t = 3 x$:

$= \frac{1}{3} \sin \left(3 x\right) + c$