00:01
In this question, we're looking to integrate e to the 2x times cosine of x dx.
00:05
So what do we have to do? we have to do integration by parts.
00:12
So i'm going to start by letting u equal e to the 2x, while my dv is equal to cosine of x dx.
00:24
I figure out my du and my v.
00:26
So my du is going to be 2e to the 2x dx, while my v, the antiderivative of dv, that's just cosine x.
00:39
So i'm going to apply my integration by parts formula.
00:42
I get u times v.
00:45
So e to the 2x times sine of x minus the integral of v du.
00:51
So minus the integral of 2e to the 2x times the sine of x dx.
01:01
And i can move the 2 through the interval sign.
01:06
So i've got e to the 2x sine x minus twice the integral of e to the 2x sine of x dx.
01:16
Now, i need an integration by parts on this guy.
01:21
So we're going to do the exact same thing that we did before.
01:25
So i let u equal e to the 2x, and my dv is equal to the sine of x dx.
01:37
What's my du? it's 2e to the 2x dx, and my v is negative cosine x.
01:46
So what do we get here? well, we get uv...