# A tricky logarithmic integral

Evaluate the integral

Solution

Well, we all have the basic idea that we are going to kill the logarithm by inserting a parameter , call it , and then differentiate under the integral sign but doing so we have that if we define

then

And this is why the integral is tricky. You cannot find a general closed form for the derivative but that doesn’t matter because all you care about is to evaluate . Since we have that

Therefore,