# Thread: Integration by subs. or parts?

1. ## 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

2. 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
$\int dx \, xe^{x^2}$

Let $y = x^2$, then $dy = 2x dx$

Then
$\int dx \, xe^{x^2} = \int \frac{dy}{2}e^y$

$= \frac{1}{2}e^y + C = \frac{1}{2}e^{x^2} + C$

I don't know of a way to do this using integration by parts because $\int dx \, e^{x^2}$ can't be done exactly.

-Dan

3. 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

4. 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

5. 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

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

-Dan