Question

anti derivative of the integral xe^x^2 dx

Answer 1

\[\int\limits_{}^{} xe ^{x ^{2}} dx \] I have no idea how to do it with e in it.

Answer 2

Use the substitution
\[u = x^2 \implies du = 2x dx \implies \frac{du}{2} = x dx\]
Replace this in the integral, this gives:
\[\frac{1}{2} \int\limits e^u du =\frac{1}{2}e^u + C = \frac{1}{2} e^{x^2}+C\]

Answer 3

where does the 1/2 come from thats in front of the integral?