Question

integrate cos x = sin x.......ok
integrate cos 2x = what is my formula here?
integrate cos 3x...isn't there some formula for all of these?

Answer 1

there is a technique called substitution ...
let \( 2x = u\) then \( 2 dx = du \) or \( dx = du/2\)
Then,
\[ \int \cos2x\;dx = \int \cos u \;du/2 = 1/2 * \sin u = 1/2 * \sin 2x\]

Answer 2

Try these substitution for others, you will get general formula!!
\[ \int \cos nx \;dx = \frac{\sin nx}{n} + c\]

Answer 3

ok think i am there ---was putting in the question wrong over at wolfram, remember square brackets after the cos or sin or -cos or -sin