00:02
Okay, so let's start by letting you be equal to cosine of x.
00:07
And then we have du that's equal to negative sign of x dx, and now dv is a remaining, which is e to 2x, dx.
00:17
So then the integral of that, that's e to 2x over 2.
00:23
Okay, and now using our equation, we have u times v, so that's cosine of x, e to the 2x over 2, minus the integral of v, du.
00:34
Notice there's a negative here and a negative here.
00:37
So this turns positive.
00:39
And then we have one half and then a e to 2x, sine of x d x.
00:48
So looking at this integral, it seems like we're going to need to take our integration by parts again.
00:53
So this time, let's take u to be equal to our trig function again, just sign of x.
01:01
So d u is equal to cosine of x d x, and then dv is equal to e to 2x.
01:09
D x so then b is equal to e to the 2x over 2.
01:14
Okay, so we're writing this equation...