is there a certain rule for integrating something like 2cos4x? When integrating cos x, I'm aware it goes to sin x + C. But isn't dividing by the coefficient of x or something involved when it comes to integrating something like 2cos4x?
(Original post by Hashshashin)
And how are you planning on doing that? Using a trig identity is the only (quick) method of solving this integral.
Like I said I'm a weirdo and I know what that equals off the top of my head. Believe it or not it's useful to know things like that, they may not be trig identitities per se but if you know them they save time.
EDIT: actually I'm lying to be frank I already know what the derivative of the original is or at least 1/2 or d/dx of sec(x)^2 of it so in actuality, so I wouldn't of even bothered using anything, I'd of just written the answer out. After a while of doing problems you tend to get a hang of looking for simple methods that don't necessarily involve basic rules.
Once you know how to derive the trig functions and have done a truck load there's no point in grinding out an answer, unless you want a bit of practice. That's what function tables and books are for, as long as you can derive them when you have to, you don't have to mess about. Of course this is absolutely no use or interest to the op, but then that's already answered.