How to Solve the Integral ∫√(1+x)/(1-x)

  • Thread starter blu3jam
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In summary, the conversation involves a person asking for help with solving the problem \int\sqrt{\frac{1+x}{1-x}}. Another person provides a hint to use the substitution u^2=(1+x)/(1-x) and another person suggests multiplying top and bottom by √(1 - x). The conversation ends with the first person expressing gratitude for the help and the second person reminding to follow forum rules.
  • #1
blu3jam
7
0
[tex]\int\sqrt{}\frac{1+x}{1-x}[/tex]

I am stuck on this problem. I have no idea about what to do , If you have any idea please share with me ... thanks in advance
 
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  • #2
Do you mean

[tex]\int\sqrt{\frac{1+x}{1-x}}[/tex] ?

I don't think there is any way to express that in terms of elementary functions.
 
  • #3
Feldoh said:
Do you mean

[tex]\int\sqrt{\frac{1+x}{1-x}}[/tex] ?

I don't think there is any way to express that in terms of elementary functions.

I think there actually is. Do the substitution u^2=(1+x)/(1-x). It just takes some patience.
 
  • #4
Your hint is excellent. Working the problem in full is strictly against the rules. I'm going to report this and see if it can be removed. READ THE FORUM RULES.
 
  • #5
janhaa, you can repost your hint. It's very good. Just leave out the full workings, ok?
 
  • #6
Hi blu3jam! :smile:

Alternative hint: multiply top and bottom by √(1 - x). :smile:
 
  • #7
Your hints works. Thanks for your help !
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to find the total value of a quantity over a certain interval.

2. What is the function of this integral: ∫√(1+x)/(1-x)?

This integral is used to find the area under the curve of the function f(x) = √(1+x)/(1-x). It represents the total value of the function over a given interval.

3. How do you solve this integral: ∫√(1+x)/(1-x)?

To solve this integral, you can use integration techniques such as u-substitution or integration by parts. It is important to also pay attention to the limits of integration while solving the integral.

4. What is the significance of the square root in this integral: ∫√(1+x)/(1-x)?

The square root in this integral represents the shape of the curve. It is important to consider the behavior of the square root function while solving the integral.

5. Can this integral be solved using a calculator?

Yes, this integral can be solved using a calculator or online integral calculator. However, it is important to have a basic understanding of integration and the concepts involved in solving the integral in order to correctly interpret the results.

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