how can i solve the indefinite integral cos (3x) using substitution?

Question

anonymous · Answer

1st use cos 3x formula, then simpify
or just use integration by parts by treating u = 1, v = cos 3x

anonymous · Answer

or i can guess, that the general integration of cos(x) is sin(x), and thus reason that cos (3x) would be sin(3x), but then i have to account for the 3x produced by the chain upon differentation, and write it as 1/3 sin(3x)

anonymous · Answer

true it'll be sin3x / 3, you are right

anonymous · Answer

Not to mention a constant....

anonymous · Answer

For substitution, let u = 3x. Therefore, du = 3dx; du/3 = dx..So you have...$$\int\limits_{}^{}\cos 3xdx = \ \frac{1}{3} \ \int\limits_{}^{}\cos udu =  \ \frac{1}{3} \ \sin u =  \ \frac{1}{3} \ \sin 3x$$