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1/(xsqrt(x-1))
Solving integrals/ 1/(xsqrt(x-1))

Integral of 1/(xsqrt(x-1)) dx

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The solution

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  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |      _______   
 |  x*\/ x - 1    
 |                
/                 
0
∫011xx−1 dx\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 1}}\, dx 
Integral(1/(x*sqrt(x - 1)), (x, 0, 1))
The answer (Indefinite) [src] 
                        //         /  1  \       1     \
  /                     ||2*I*acosh|-----|  for --- > 1|
 |                      ||         |  ___|      |x|    |
 |      1               ||         \\/ x /             |
 | ----------- dx = C + |<                             |
 |     _______          ||        /  1  \              |
 | x*\/ x - 1           || -2*asin|-----|    otherwise |
 |                      ||        |  ___|              |
/                       \\        \\/ x /              /
∫1xx−1 dx=C+{2iacosh⁡(1x)for 1∣x∣>1−2asin⁡(1x)otherwise\int \frac{1}{x \sqrt{x - 1}}\, dx = C + \begin{cases} 2 i \operatorname{acosh}{\left(\frac{1}{\sqrt{x}} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} > 1 \\- 2 \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)} & \text{otherwise} \end{cases}
Simplify
The graph
1.0000000.9997500.9997750.9998000.9998250.9998500.9998750.9999000.9999250.9999500.999975-3.15-3.13
Plot the graph f(x)
The answer [src] 
-oo*I
−∞i- \infty i 
=
= 
-oo*I
−∞i- \infty i 
-oo*i
Numerical answer [src] 
(0.0 - 45.4767404945823j)
(0.0 - 45.4767404945823j)
The graph
Integral of 1/(xsqrt(x-1)) dx

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

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