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Solving integrals/ 1/((sqrtx-1)x^2)

Integral of 1/((sqrtx-1)x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |  /  ___    \  2   
 |  \\/ x  - 1/*x    
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1
$$\int\limits_{1}^{\infty} \frac{1}{x^{2} \left(\sqrt{x} - 1\right)}\, dx$$ 
Integral(1/((sqrt(x) - 1)*x^2), (x, 1, oo))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. The integral of a constant times a function is the constant times the integral of the function:

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    Method #2

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. The integral of a constant times a function is the constant times the integral of the function:

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                              
 |                                                               
 |       1                 1              2          /       ___\
 | -------------- dx = C + - - log(x) + ----- + 2*log\-1 + \/ x /
 | /  ___    \  2          x              ___                    
 | \\/ x  - 1/*x                        \/ x                     
 |                                                               
/
$$\int \frac{1}{x^{2} \left(\sqrt{x} - 1\right)}\, dx = C - \log{\left(x \right)} + 2 \log{\left(\sqrt{x} - 1 \right)} + \frac{1}{x} + \frac{2}{\sqrt{x}}$$
Simplify
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo

    Use the examples entering the upper and lower limits of integration.

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