00:01
All right, so given this integral, we can do a substitution letting u be equal to sine of x.
00:09
Well, if u is sine of x, then we know the derivative of sine is just cosine, so du is then cosine of x.
00:17
Okay, so then looking at our integral, we can then rewrite our integral.
00:23
We have the integral of sine of x times cosine of x times e to the sine of x dx.
00:34
Well, if u is sine of x and du, the cosine of x dx, that whole mess just becomes du.
00:40
So therefore, our integral is just going to become the integral of just u e to the u du.
00:47
Oh, this is now simple to do by integration by parts.
00:51
Because we know if we have an integral in the form, right, integral of u dv is equal to u times v, and then minus the new integral of v du.
01:01
So in this case, we're letting v be equal to e to the u, and then du is going to be equal to u du...