# Assume function is integrable

I am having trouble with an integral that won't evaluate. The expression involves many terms, but, essentially, the problem boils down to having Mathematica evaluate the integral $$\int_a^b xf'(x)dx$$

I know from this answer that

Block[{f}, SetAttributes[f, {NumericFunction}]; Integrate[D[f[x],x], {x, a, b}]]


seems to work for that integrand, but not in my case. How can I add the assumption that my $f'(x)$ is integrable?

(Or, if such assumptions cannot be made, how to force Mathematica to make appropriate substitutions? I'd rather not do this step by hand since the original integrand is a bit tedious to work with.)

• What sort of answer are you looking for? That it integrate by parts? Without $f$ being a specific function, this doesn't have a simple answer that doesn't involve an integral. (Also minor technical note: you want the assumption that $f$ is absolutely continuous, a stronger condition than $f'$ being integrable. Not that Mathematica has a notion of absolute continuity.) – Itai Seggev Sep 24 '17 at 16:54
• Thanks, yes, I was looking for it to integrate by parts, but you made me realize that that's really not the evaluation of the integral. Sorry for taking your time (your comment has helped me, though). – Marijnn Sep 29 '17 at 11:48