How to evaluate the following integral x^3*ln(x) with an upper bound of e and a lower bound of 1

Answer 1

Integrate by parts.

u=ln x

du=(1/x) dx

dv=x³

v=(x⁴)/4

Then the integral becomes (x⁴ ln x)/4 - (1/4)∫x³ dx

I think you should be able to finish it from here.