Mathematics

Problem

Define

K=\displaystyle \int_{1}^{e} x^{2}\ln x\,dx.

(a) Find an explicit antiderivative of

x^{2}\ln x.

(b) Compute the exact value of

K.

x^{2}\ln x

to differentiate first when constructing their work. Explain why the choice you made in part (a) leads to fewer total algebraic terms than the opposite choice.

Browse the problem library