Consider the integrals

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the integrals (I)

\displaystyle\int e^{-x^{2}}\,dx

(II)

\displaystyle\int x\,e^{-x^{2}}\,dx

Indicate which integral possesses an elementary antiderivative and write that antiderivative (up to an additive constant).