Question

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

Answer 1

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

Answer 2

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)

Answer 3

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

Answer 4

Not to mention a constant....

Answer 5

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