Find the indefinite integral .

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

Problem

Find the indefinite integral

\displaystyle \int x\,\ln x\,dx

. (a)

\dfrac{x^{2}}{2}\,\ln x + \dfrac{x^{2}}{4} + C

(b)

\dfrac{x^{2}}{2}\,\ln x - \dfrac{x^{2}}{2} + C

(c)

\dfrac{x^{2}}{2}\,\ln x - \dfrac{x^{2}}{4} + C

(d)

\dfrac{x^{2}}{4}\,\ln x - \dfrac{x^{2}}{2} + C