How do I integrate $$\int _0^T x^m B_1(\{ x\} ) dx$$, where $\{x\} $ denotes the fractional part of $x $?
Integrating by parts should work, but I can't get anything to simplify in a particularly nice way so I can't work out how to make an induction work.
Ultimately, I just want to show that Integrating the result with respect to T is small.
