Thread: Integration by subs. or parts?

I have this question in a quiz for uni:



They show the exact same question in my lecture notes equalling:

1/2 e^x^2 + C , though im confused on how they get rid of the x in front: xe^x^2

any help would be appreciated

Originally Posted by sterps

I have this question in a quiz for uni:



They show the exact same question in my lecture notes equalling:

1/2 e^x^2 + C , though im confused on how they get rid of the x in front: xe^x^2

any help would be appreciated

Let , then

Then




I don't know of a way to do this using integration by parts because can't be done exactly.

-Dan

You can do this without needing to integrate.

Just differentiate (a) through (d), one of these derivatives will be the
integrand, and that will be the correct solution.

RonL

Originally Posted by CaptainBlack

You can do this without needing to integrate.

Just differentiate (a) through (d), one of these derivatives will be the
integrand, and that will be the correct solution.

RonL

Yes, but that doesn't help integrating techniques much

Originally Posted by Jameson

Yes, but that doesn't help integrating techniques much

It does if it teaches the student that they are allowed to spot the derivative
under the integral sign, or to use the fundamental theorem where they might
not have thought of it.

RonL

And solving the problem backwards is always a good trick to have when doing multiple choice tests.


-Dan