#intergratoin
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integrating lnx is done with parts
It is generally advisable to know an antiderivative of ln by heart, just like any other common function
So I will give it to you, if you didn't see it at school already
An antiderivative for f : x l-> ln(x) is F : x l-> x ln(x) - x
You can check it for yourself: F is differentiable, on R+, and: