Rewriting f(x) to Simplify an Integral Problem

[wr1985]

Homework Statement

∫1/((√x)+x))dx

Homework Equations

The Attempt at a Solution

I understand the calculus but not the algebra, it's been a while. How can I write f(x) differently to make the problem seem easier?

 

[micromass]

Do a suitable substitution.

 

[SammyS]

Homework Statement

∫1/((√x)+x))dx

Homework Equations

The Attempt at a Solution

I understand the calculus but not the algebra, it's been a while. How can I write f(x) differently to make the problem seem easier?

Hello wr1985. Welcome to PF !

What have you tried?

Where are you stuck?

 

[wr1985]

I feel like I have to rearrange the function to get a good u value but my algebra is rusty and using x or sqrt x aren't giving me a clean answer.

 

[algebrat]

you should break it up, into ∫√x dx and ∫x dx, and use technique on one of them. Do you know the technique? It is a less known method, but Stewart's Calculus lists it as a good method.

 

[Bohrok]

You mean using either of the substitutions u=x or u=√x aren't giving you a clean answer?
The first one doesn't help you at all, but the second one should give you something you can integrate after simplification.

 

[wr1985]

the simplification is the only problem. my algebra is in the toilet.

 

[dimension10]

Homework Statement

∫1/((√x)+x))dx

Homework Equations

The Attempt at a Solution

I understand the calculus but not the algebra, it's been a while. How can I write f(x) differently to make the problem seem easier?

Let u=sqrt x. Then x = u^2. Then use partial fractions to solve.

Edit: I just realized that algebrat was saying exactly what I'm saying right now.

 

[Bohrok]

So what did you get after the substitution?

 

[dimension10]

So what did you get after the substitution?

I don't think I can give the whole answer in the homework help section.

 

[alan2]

Your algebra can't be that far in the toilet. Make the substitution suggested, don't forget to find the proper substitution for dx, and the integral is elementary.

 

[SammyS]

So what did you get after the substitution?

I don't think I can give the whole answer in the homework help section.

dimension10,

I'm pretty sure that Bohrok was addressing that to OP, wr1985.

 

[Jorriss]

'Factor' the denominator

∫1/(√x(1+√x))dx

Maybe it would be clearer this way.

∫[1/(1+√x)](dx/√x)

 

[dimension10]

Homework Statement

∫1/((√x)+x))dx

Homework Equations

The Attempt at a Solution

I understand the calculus but not the algebra, it's been a while. How can I write f(x) differently to make the problem seem easier?

So what did you get after the substitution?

I don't think I can give the whole answer in the homework help section.

dimension10,

I'm pretty sure that Bohrok was addressing that to OP, wr1985.

Oh..