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

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

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /  2        
 |  \/  x  - 1    
 |  ----------- dx
 |       x        
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/                 
0
∫01x2−1x dx\int\limits_{0}^{1} \frac{\sqrt{x^{2} - 1}}{x}\, dx 
Integral(sqrt(x^2 - 1)/x, (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sec(_theta), rewritten=tan(_theta)**2, substep=RewriteRule(rewritten=sec(_theta)**2 - 1, substep=AddRule(substeps=[TrigRule(func='sec**2', arg=_theta, context=sec(_theta)**2, symbol=_theta), ConstantRule(constant=-1, context=-1, symbol=_theta)], context=sec(_theta)**2 - 1, symbol=_theta), context=tan(_theta)**2, symbol=_theta), restriction=(x > -1) & (x < 1), context=sqrt(x**2 - 1)/x, symbol=x)

  1. Add the constant of integration:

    {x2−1−acos⁡(1x)for x>−1∧x<1+constant\begin{cases} \sqrt{x^{2} - 1} - \operatorname{acos}{\left(\frac{1}{x} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}+ \mathrm{constant}

The answer is:

{x2−1−acos⁡(1x)for x>−1∧x<1+constant\begin{cases} \sqrt{x^{2} - 1} - \operatorname{acos}{\left(\frac{1}{x} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                      
 |                                                                       
 |    ________                                                           
 |   /  2               //   _________                                  \
 | \/  x  - 1           ||  /       2        /1\                        |
 | ----------- dx = C + |<\/  -1 + x   - acos|-|  for And(x > -1, x < 1)|
 |      x               ||                   \x/                        |
 |                      \\                                              /
/
∫x2−1x dx=C+{x2−1−acos⁡(1x)for x>−1∧x<1\int \frac{\sqrt{x^{2} - 1}}{x}\, dx = C + \begin{cases} \sqrt{x^{2} - 1} - \operatorname{acos}{\left(\frac{1}{x} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}
Simplify
The graph
0.999800.999820.999840.999860.999880.999900.999920.999940.999960.9999801
Plot the graph f(x)
Numerical answer [src] 
(0.0 + 43.7835933145528j)
(0.0 + 43.7835933145528j)
The graph
Integral of sqrt(x^2-1)/x dx

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

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