00:01
All right, so this question wants us to evaluate this indefinite integral.
00:04
What i'm going to do first is just note a few things.
00:07
This integral is equivalent to saying sine of 2x all of the 5th power dx.
00:11
Then we can use trigon identities to rewrite this as 2, sine of 2, sorry, 2 sine of x, cosine of x, all to the 5th, dx.
00:23
So rewriting this, we get 32 on the outside and then sine to the 5th x, cosine to the 5th x.
00:29
Some nice things we can now do.
00:32
We can go ahead and rewrite sine to fifth x as the following.
00:38
We'll just get sign times one minus cosine squared.
00:43
Actually, i should write the other one.
00:44
I apologize.
00:44
I want to write cosine, excuse me.
00:47
So when i do cosine, i'm going to go ahead and rewrite it as the following.
00:51
So letting sine of feth x be this.
00:54
This will be cosine of x, and then it will be cosine to the fourth power of x dx...