1. ## Integral

How do I find the indefinite integral to $\displaystyle \int e^{\sqrt x}dx$?

2. Consider the following

$\displaystyle \int e^{f( x)}dx = \frac{e^{f( x)}}{f'( x)}+c$

3. I must be an idiot, because I dismissed that idea immediately without even trying!

Maybe it was the star beside the question that screwed up my mind.

4. u = √x ---> uČ = x ---> 2 u du = dx
substitute then use integration by parts ..

5. Radicals do have a strange way of throwing people off track

6. Differentiate $\displaystyle 2e^{\sqrt x } \sqrt x - 2e^{\sqrt x }$.
What do you get?

7. Originally Posted by chengbin
How do I find the indefinite integral to $\displaystyle \int e^{\sqrt x}dx$?
$\displaystyle u = \sqrt{t}$

$\displaystyle du = \frac{1}{2\sqrt{t}} \, dt = \frac{1}{2u} \, dt$

$\displaystyle dt = 2u \, du$

$\displaystyle 2\int ue^u \, du$

integrate by parts ...

$\displaystyle 2e^u(u - 1) + C$

$\displaystyle 2e^{\sqrt{t}}(\sqrt{t} - 1) + C$

8. Originally Posted by pickslides
Radicals do have a strange way of throwing people off track
Is this for me ?

9. Originally Posted by TWiX
Is this for me ?

I'd say no, seeing as your method was correct.

10. Originally Posted by pickslides
Consider the following

$\displaystyle \int e^{f( x)}dx = \frac{e^{f( x)}}{f'( x)}+c$
that's a wrong formula.

11. Originally Posted by Krizalid
that's a wrong formula.
yep it is, was confused with $\displaystyle y= e^{f(x)} \Rightarrow \frac{dy}{dx}= f'(x)e^{f(x)}$

Gentle reminder to myself not to post on MHF the morning after a big night on the sauce.