00:01
So in this question we're integrating by parts.
00:03
So first of all, we've got part b, strangely, where our integral is the integral log x over x dx.
00:12
So let's take u equals log x, u dashed is 1 over x, v dashed is 1 over x, v is 1 over x, v is log x.
00:20
Then i is going to be log x squared plus c minus the integral of log x over x d x but this is i so we get 2 i is log x squared plus c so i is a half log x plus c prime sorry a half log x squared plus c prime okay uh so now now, c we've got i is the integral of x over e to the x squared, i think that says.
01:05
So that is the integral of x, e to the minus x squared, the x.
01:12
And actually, we don't need to integrate this by parts at all.
01:18
We can just integrate this by inspection...