How do you calculate the antiderivative of ##sin(2x)/cos(x) dx##?

The integral/antiderivative you require is

##I = intsin(2x)/cos(x)dx##

The easiest way to solve it is to use trigonometric identities and expand the numerator, like this

##sin(2x) = 2sinxcosx##

This transforms the integral in this way

##I = int2sinxcosx/cosxdx## ##=> I = 2intsinxdx## ##=> I = -2cosx + C##