Question

Integrate

xe^(x^2)

Answer 1

Use u-substitution.
\[u = x^2\]\[du = 2xdx\]
\[\frac{ du }{ 2 }=xdx\]
\[\int\limits \frac{ 1 }{ 2 }e^udu = \frac{ 1 }{ 2 } \int\limits e^udu\]
You can finish it from here.

Answer 2

so you can eliminate the x by the chain rule and not have to integrate it??

what is it was to integrate x^2 e^(x^2)? would only one x cancel and then you have to do the product of them?

Answer 3

Wait, is the function yo are being asked to integrate: \[\int\limits x^2 e^{x^2}dx \] OR \[\int\limits xe^{x^2}dx\]

Answer 4

the second one... i just want to make sure i got the rules right and understand in case it was the first one.

Answer 5

Well, you would use a different method for the first one (integration by parts), not substitution method.

Answer 6

which is to integrate the first times the second, plus integrate the second times the first?

Answer 7

Are you referring to parts? It's something like that. But not quite. It's something like this: \[fg - \int\limits gf'\]

Answer 8

okay well thank you for the help

Answer 9

I would follow the first method I showed you for the initial function you are integrating. It's definitely more cleaner than using parts.