Integrate dx/(x^(1/2)(x+1)) | 1 to 3

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In summary, the conversation revolved around solving the integration problem of (dx/((x^(1/2))(x+1)), with the individual trying different approaches such as substituting x = u and using integration by parts.
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Aerosion
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Homework Statement



(integrate: upper limit 3; lower limit 1)(dx/((x^(1/2))(x+1))

Homework Equations


The Attempt at a Solution



First of all, somebody needs to show me how to get the actual integration sign to show up on the forums.

Anyway, I was pretty confused with this one. I tried making u be x+1 and du=dx, but I was afraid this wouldn't solve for the radical x that I also had. Than I tried making u be x and du be dx, but then that wouldn't solve for the x+1 that I had. I don't think I can break this up into two different equations, so I'd like some help.
 
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  • #2
First line of attack in such cases: Remove the radical with a "square". Try x = u2.

Btw, making the "substitution" x = u does nothing more than change the letter denoting the dummy variable.

As for getting LaTeX to work, see this thread: https://www.physicsforums.com/showthread.php?t=8997
 
  • #3
After trying that x=u^2 substitution, try integration by parts.
 

What is the formula for integrating dx/(x^(1/2)(x+1)) from 1 to 3?

The formula for integrating dx/(x^(1/2)(x+1)) from 1 to 3 is ∫dx/(x^(1/2)(x+1)) = 2√x + 2ln|x+1| + C, where C is the constant of integration.

What is the meaning of the integral dx/(x^(1/2)(x+1)) from 1 to 3?

The integral dx/(x^(1/2)(x+1)) from 1 to 3 represents the area under the curve of the function f(x) = 1/(x^(1/2)(x+1)) between the limits of 1 and 3 on the x-axis.

What is the significance of the limits 1 and 3 in the integral dx/(x^(1/2)(x+1)) | 1 to 3?

The limits 1 and 3 in the integral dx/(x^(1/2)(x+1)) | 1 to 3 represent the starting and ending points of the integration, or the boundaries of the area under the curve that is being calculated.

What is the relationship between the function f(x) = 1/(x^(1/2)(x+1)) and the integral dx/(x^(1/2)(x+1)) | 1 to 3?

The function f(x) = 1/(x^(1/2)(x+1)) is the integrand of the integral dx/(x^(1/2)(x+1)) | 1 to 3. This means that the integral is the process of finding the antiderivative of the function f(x).

Can the integral dx/(x^(1/2)(x+1)) | 1 to 3 be evaluated using any other methods?

Yes, there are other methods that can be used to evaluate the integral dx/(x^(1/2)(x+1)) | 1 to 3, such as substitution or integration by parts. However, the formula given in the first question is the most straightforward and efficient method for this particular integral.

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