Question

Find the anti-derivative. Help please!!

Answer 1

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

Answer 2

anti derivative ***

Answer 3

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

Answer 4

Most likely you'll have to integrate by parts.

Answer 5

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

Answer 6

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

Answer 7

Actually... let's see.

Answer 8

What the heck... @ganeshie8 haha

Answer 9

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

Answer 10

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

Answer 11

\[4\int xe^{-x^2}dx\]

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Np :)

Answer 17

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