Question

evaluate the integral: xe^(2x^2) dx

Answer 1

Let u=2x^2
then du=4xdx
so (1/4)du=xdx
So your integral becomes:
\[\frac{1}{4} \int\limits e^u du=\frac{1}{4}e^u+C=\frac{1}{4}e^{2x^2}+C\]