Basic integration

1. Apr 16, 2006

mathmathmath

i've been having trouble solving this one for highschool math:

it's under the substitution section

integrate:

[e^(x^0.5) ] / (x^0.5)

do you guys think you can help me with this one?

thanks

2. Apr 16, 2006

nocturnal

Have you tried a substitution?? There are only a couple of choices to choose from, and one is really obvious.

And the LaTex for this equation is

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

you can click on the equation to see the LaTex code.

Last edited: Apr 16, 2006
3. Apr 16, 2006

Actually, once you have more experience integrating exponential functions, you will realize a substitution is not really necessary.

4. Apr 16, 2006

mathmathmath

i'm still lost, and this is supposed to be a routine question :(

i think there is a property of e that i am not familiar with that might be holding me back. any hints?

i've looked at two ways, neither of which seem to be any good.

1. tried substituting u for x^.5, which seemed to do no good as it didnt offer a du/dx.
2. tried substiuting u for e^x^.5, using the idea that ln u = x^.5 for the denominator. again, this didn't offer me much help.

the answer for this one is 2e^x^.5, and working backwards didn't seem to give me any more ideas. sorry if i'm missing something blatant :(

Last edited: Apr 16, 2006
5. Apr 16, 2006

To solve the problem via substitution, what substitution should you try?

To solve it in a more direct manner, try differentiating the numerator. What do you realize?

6. Apr 16, 2006

pocoman

Let $$u=x^\frac{1}{2}$$,
so $$x=u^2 ;dx=2udu$$
substitutes them into your integral, it become:
$$\int \frac{e^u}{u}2udu$$

Last edited: Apr 16, 2006
7. Apr 16, 2006

mathmathmath

ah. :( after all the fuss about that root of x... thanks very much for all the help