Answer
$\int xe^{-x^2+1}dx=-\frac{1}{2}e^{-x^2+1}+C$
Work Step by Step
Substitution:
$u=-x^2+1$
$\frac{du}{dx}=-2x$
$dx=-\frac{1}{2x}du$
$\int xe^{-x^2+1}dx=\int xe^u(-\frac{1}{2x})du=\int-\frac{1}{2}e^udu=-\frac{1}{2}e^u+C=-\frac{1}{2}e^{-x^2+1}+C$
