Answer
$\int(2x-1)e^{2x^2-2x}dx=\frac{1}{2}e^{2x^2-2x}+C$
Work Step by Step
Substitution:
$u=2x^2-2x$
$\frac{du}{dx}=4x-2=2(2x-1)$
$dx=\frac{1}{2(2x-1)}du$
$\int(2x-1)e^{2x^2-2x}dx=\int(2x-1)e^{u}\frac{1}{2(2x-1)}du=\int\frac{1}{2}e^udu=\frac{1}{2}e^u+C=\frac{1}{2}e^{2x^2-2x}+C$
