AP

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Determine

\displaystyle \int x^{2}\,(\ln x)^{2}\,dx

. (a)

x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}+\dfrac{2\,\ln x}{9}-\dfrac{2}{27}\Bigr)+C

(b)

\dfrac{x^{3}}{3}(\ln x)^{2}-\dfrac{2x^{3}\ln x}{3}+C

(c)

x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}-\dfrac{2\,\ln x}{9}+\dfrac{2}{27}\Bigr)+C

(d)

x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}-\dfrac{2\,\ln x}{9}+\dfrac{1}{27}\Bigr)+C