# 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

Staff Emeritus
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

### dimension10

Oh..

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