Evaluate the following integral

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

Problem

Evaluate the following integral, showing every algebraic step used to introduce or remove constants: (i)

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

. (ii) Verify your result by differentiating the antiderivative obtained in part (i).