Find the anti-derivative. Help please!!

Question

anonymous · Answer

$$4xe ^{-x ^{2}}$$ how would you find the derivative of that?

anonymous · Answer

anti derivative ***

jhannybean · Answer

$$\sf \text{antiderivative} = \int 4xe^{-x^2}dx$$

jhannybean · Answer

Most likely you'll have to integrate by parts.

ganeshie8 · Answer

or there is an obvious u-substitution : $\large u =-x^2$

anonymous · Answer

How could U = -x^2 if the du=4x? 
Am I allowed to multiplay the U by -2?

jhannybean · Answer

Actually... let's see.

jhannybean · Answer

What the heck... @ganeshie8  haha

anonymous · Answer

I'm terrible at taking antiderivatives of e because of the relationship it has with ln and it gets me all confused :(. I don't know how to take the anti derivative of e^(x^2

jhannybean · Answer

You could pull out the 4 since it's a constant?

jhannybean · Answer

$$4\int xe^{-x^2}dx$$

jhannybean · Answer

So now what ganeshie said about making a u sub makes sense !!

jhannybean · Answer

Letting $u=-x^2$, $du = -2xdx \implies -\dfrac{du}{2}=xdx$

jhannybean · Answer

So you would have $$4 \cdot \left(-\frac{1}{2}\right) \int e^udu$$

anonymous · Answer

OHH I see now!! Thank you so much !! @Jhannybean

jhannybean · Answer

Np :)

thomas5267 · Answer

I don't think $\int e^{-x^2}dx$ has a closed form solution.