U substitution or substitution by parts?

[mickellowery]

Homework Statement

∫〖e^√x/√x dx〗
would this be a u substitution or a substitution by parts?

Homework Equations

The Attempt at a Solution

 

[Mark44]

I would go with an ordinary substitution. The other technique you mentioned is usually called integration by parts.

 

[mickellowery]

oh oops I meant to say integration by parts. So would I let u= sqrt(x)?

 

[D H]

That would be a good thing to try. What does that lead to?

 

[mickellowery]

So if u= sqrt(x) du= 1/2 x^-1/2 and now I'm a little lost because the du doesn't look like it helps me.

 

[D H]

Better written as

$$du = \frac 1 {2\sqrt x}\, dx$$

Now take a look at what you are supposed to integrate. Does the integrand involve anything that looks like the above?

 

[mickellowery]

Alright I think I see it but I want to check. Would I write it as 1/2 ∫〖e^u du〗?

 

[D H]

Yes.

BTW, what's the deal with the brackets and parentheses?

 

[mickellowery]

Thanks so much for your help DH. I don't know the deal with the brackets and parentheses. I have been using microsoft word's equation writer because I'm not too sure how to use the equation writer on here. Thanks again!