If your not the same person..then well someone got the same problem as you =P

  • Thread starter Kerbox
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    Integral
In summary, the conversation is about solving the integral \int \frac{x}{1+\sqrt{x}} dx. The person asking for help has tried various substitutions and manipulations but has not been able to find a solution. Suggestions for solving the integral include using the residue theorem from complex analysis, but this method is not applicable for finding antiderivatives. The person offering help suspects that the person asking for help is the same person they helped on a similar integral in a different forum.
  • #1
Kerbox
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Hey guys,

I could really use some hints on how to solve the integral [tex] \int \frac{x}{1+\sqrt{x}} dx [/tex]
I tried some substitutions, and doing some manipulations on the expression, with no solution. Any help would be much appreciated.

Regards,

Kerbox
 
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  • #2
[tex]1+\sqrt{x} = t[/tex]
 
  • #3
yea, tried that. but I end up with an expression where x can't be canceled. unless I am missing something here.
 
  • #4
Post your steps, and we can see if you made a mistake.
 
  • #5
Notice that x = (t - 1)^2.
 
  • #6
you could use the residue theorem from complex analysis (I think)
 
  • #7
thebuttonfreak said:
you could use the residue theorem from complex analysis (I think)

The residue theorem does not pertain to antiderivatives.
 
  • #8
I helped someone else on exactly the same integral in scienceforums.net and I have a really good feeling your the same person, since your post is identical..and your username is the same >.<

Just incase..: http://www.scienceforums.net/forum/showthread.php?t=24664

My name in scienceforums.net is Ragib btw.
 

1. What is the integral of x/1+sqrt(x)?

The integral of x/1+sqrt(x) is ln(2sqrt(x)+2x+4).

2. How do you solve the integral of x/1+sqrt(x)?

To solve the integral of x/1+sqrt(x), you can use the substitution method by letting u = sqrt(x) + 1. Then, you can rewrite the integral as 2∫(u-1)du/u, which can be solved using the logarithmic rule.

3. What is the domain of x/1+sqrt(x)?

The domain of x/1+sqrt(x) is all positive real numbers greater than 0.

4. Can the integral of x/1+sqrt(x) be simplified?

Yes, the integral of x/1+sqrt(x) can be simplified by using the substitution method or by using the partial fraction decomposition method.

5. What is the significance of the integral of x/1+sqrt(x)?

The integral of x/1+sqrt(x) has applications in calculus and physics, particularly in determining areas under curves and finding the work done by a variable force. It also has connections to the natural logarithm function, which is important in many areas of math and science.

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