## u substitution

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?
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus Do a suitable substitution.

Mentor
 Quote by 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?
Hello wr1985. Welcome to PF !

What have you tried?

Where are you stuck?

## u substitution

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

 Quote by 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?
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.
 So what did you get after the substitution?

 Quote by Bohrok So what did you get after the substitution?
I don't think I can give the whole answer in the homework help section.
 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.

Mentor
 Quote by Bohrok So what did you get after the substitution?
 Quote by dimension10 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.
 Recognitions: Gold Member 'Factor' the denominator ∫1/(√x(1+√x))dx Maybe it would be clearer this way. ∫[1/(1+√x)](dx/√x)

Quote by SammyS
Quote by dimension10
Quote by Bohrok
 Quote by 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?

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..

 Tags algebra, antiderivative, calculus, substitution