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√(x^2-1)
Solving integrals/ √(x^2-1)

Integral of √(x^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    SqrtQuadraticRule(a=-1, b=0, c=1, context=sqrt(x**2 - 1*1), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                               
 |                         /           _________\        _________
 |    ________             |          /       2 |       /       2 
 |   /  2               log\2*x + 2*\/  -1 + x  /   x*\/  -1 + x  
 | \/  x  - 1  dx = C - ------------------------- + --------------
 |                                  2                     2       
/
$${{x\,\sqrt{x^2-1}}\over{2}}-{{\log \left(2\,\sqrt{x^2-1}+2\,x \right)}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi*I
----
 4
$${{\log \left(2\,i\right)}\over{2}}-{{\log 2}\over{2}}$$ 
=
= 
pi*I
----
 4
$$\frac{i \pi}{4}$$
Simplify
Numerical answer [src] 
(0.0 + 0.785398163397448j)
(0.0 + 0.785398163397448j)
The graph
Integral of √(x^2-1) dx

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

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