00:01
So what we're going to be doing for this integral is an integration by parts, and we're going to be trying to reduce this natural log of x, or changed, i guess, into its derivative, 1 over x, which will make the integrals a lot easier to compute, since we already have a 1 over x squared term as part of our integral.
00:20
And so what we're going to do is we're going to let u equal the natural log of x, like i was saying, then du is equal to 1 over x, and we can even say multiplied by dx, and dv here.
00:31
Here is equal to 1 divided by x squared, which is equal to x the negative second power.
00:37
And so this is just a power rule integral.
00:40
We're going to add one to the power and then divide by that power.
00:46
And so these are the values for uv, du, and dv we're going to want to use for this integration by parts.
00:52
And so we're going to have u times v, which is going to be the negative natural log of x divided by x and then minus the integral of v times du.
01:00
This negative one here is going to cancel with this minus size.
01:03
And we're going to be left with plus the integral of 1 divided by x multiplied by 1 divided by x d x and we're looking from 1 to 2...