00:01
For this problem, you'll also use integration by parts, fg.
00:08
So we know the formula.
00:10
One function goes outside, one goes inside, minus function that's outside.
00:15
We take its derivative, take the integral of the inside function, apply the whole integral.
00:21
Okay, in this problem, let's take ln square x outside.
00:26
Let's keep x square inside.
00:28
Now, if you take the derivative of ln squared x, that is 2lnx and derivative of lnx is 1 over x.
00:39
Integral of x squared is x cube over 3, whole integral.
00:46
So, ln square x, integral of x square is x cube over 3.
00:56
Okay, here 2 and 3 are constants.
00:58
So let's bring the 2 over 3 outside because they are constants.
01:02
Things that go inside are this x cancels with this power of x so that is x square l and x so we should apply integration by parts again so that's x cube ln square x over three the first term for the second term it is negative two third again if we take the l and x outside for integration by parts keep the x square inside their way to of ln x is 1 over x integral of x square is x cube over 3 whole integral is x cube ln square x squared x over 3 minus this gives x cube ln x square x over 3 minus this one cancels one power of x cube so it becomes so x square over three integral.
02:17
One third is constant.
02:18
So it's outside...