# How do you find the antiderivative of 1−cos(4x)?

Nov 1, 2016

Say that, as an example but not related to the problem:

$y = \frac{1}{k} \cdot \sin \left(k x\right)$

This would mean that:

$k y = \sin \left(k x\right)$

And ultimately that:

$k \cdot \frac{\mathrm{dy}}{\mathrm{dx}} = k \cdot \cos \left(k x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(k x\right)$

Because of the chain rule.

Now, if this is the case, when solving the problem :

$\int 1 - \cos \left(4 x\right) \mathrm{dx}$

$= x - \frac{1}{4} \sin \left(4 x\right) + C$