Calculus: What happened? (From the first highlight to the second)

Question

mpj4 · Answer

attachment

usukidoll · Answer

it's been a while since I've done this... but I know that it's using trig identities and substitution .... second to the last are antiderivative.

usukidoll · Answer

it also have something to do with the powers too.. like if m and n are both even or m and n are both odd or m is odd and n is even or vice version

mpj4 · Answer

hmm, about the powers, my main concern was what happened to these two exponents

usukidoll · Answer

$$(1+\cos(2x))(1+\cos(2x) ) $$

mpj4 · Answer

OHHHHH

mpj4 · Answer

THANKS!!

mpj4 · Answer

I really didn't see that. Thanks a lot man.

usukidoll · Answer

it's another way of writing any trig to the second power there is A HUGE DIFFERENCE BETWEEN $$\sin (2x)$$ and $$\sin^2(x) = \sin(x) \sin(x) $$

usukidoll · Answer

$$(\sin(x))^2 = (\sin(x))(\sin(x))$$

usukidoll · Answer

means the same thing. ^

mpj4 · Answer

I got my answer usuki, thanks for the extra info though. Feel free to leave anytime :)

usukidoll · Answer

ok

mpj4 · Answer

Sorry if I sound ungrateful. I really do appreciate it.