Homework Help: U substitution

1. Jun 4, 2012

wr1985

1. The problem statement, all variables and given/known data

∫1/((√x)+x))dx

2. Relevant equations

3. 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?

2. Jun 4, 2012

micromass

Do a suitable substitution.

3. Jun 4, 2012

SammyS

Staff Emeritus
Hello wr1985. Welcome to PF !

What have you tried?

Where are you stuck?

4. Jun 5, 2012

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.

5. Jun 5, 2012

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.

6. Jun 5, 2012

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.

7. Jun 5, 2012

wr1985

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

8. Jun 5, 2012

dimension10

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

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

9. Jun 5, 2012

Bohrok

So what did you get after the substitution?

10. Jun 5, 2012

dimension10

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

11. Jun 5, 2012

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.

12. Jun 5, 2012

SammyS

Staff Emeritus
dimension10,

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

13. Jun 5, 2012

Jorriss

'Factor' the denominator

∫1/(√x(1+√x))dx

Maybe it would be clearer this way.

∫[1/(1+√x)](dx/√x)

14. Jun 5, 2012

Oh..