1. ## Integral help needed.

I get stuck on this one.

$\displaystyle{ \int 8 x e^{2 x^2} \, dx}$
$
u=2x^2$

$du=4x$

$8 \int 4x{e}^{u}$

$\frac{8}{4}\int du{e}^{u}$

$\frac{1}{2}\int du{e}^{u}$

$\frac{1}{2}{e}^{2x^2}$

But I feel it's wrong.

This natural number always screws me up.

2. Originally Posted by Zanderist
I get stuck on this one.

$\displaystyle{ \int 8 x e^{2 x^2} \, dx}$
$
u=2x^2$

$du=4x \, dx$

$2 \int 4x{e}^{2x^2} \, dx$ ... fixed this

$2 \int e^u \, du$ ... and this.
finish it.

3. Why does the 8 turn into a 2?

4. Originally Posted by Zanderist
I get stuck on this one.

$\displaystyle{ \int 8 x e^{2 x^2} \, dx}$
$
u=2x^2$

$du=4x$dx => dx = du/4x

2 $\int 4x{e}^{u}$du/4x

2 $\int {e}^{u}$du

[snip]

2 ${e}^{2x^2}$

But I feel it's wrong. Mr F says: Yes it was.

This natural number always screws me up.
I have made corrections and annotations in red. If you were not so sloppy with your notation you probably would not have made all these mistakes.

5. Originally Posted by Zanderist
Why does the 8 turn into a 2?
the 8 turned into 2 times 4 ... not 2.

then, note that $4x \, dx$ changed to $du$

6. Originally Posted by skeeter
the 8 turned into 2 times 4 ... not 2.
Ah!

Thanks everyone.