AP

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

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.

Related theory

Integration by Parts
Integration Techniques
Integrals

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