How do I find the integral #int(ln(x))^2dx# ?
1 Answer
Our objective is to reduce the power of
We can accomplish this by using integration by parts. Keep in mind the IBP formula:
Now, we will let
Therefore,
and
Now, assembling the pieces together, we get:
This new integral looks a lot better! Simplifying a bit, and bringing the constant out front, yields:
Now, to get rid of this next integral, we will do a second integration by parts, letting
Thus,
Assembling gives us:
Now, all that's left to do is simplify, keeping in mind to add the constant of integration:
And there we have it. Remember, integration by parts is all about picking