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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               
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0
∫01x2−1 dx\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:

    xx2−12−log⁡(2x+2x2−1)2+constant\frac{x \sqrt{x^{2} - 1}}{2} - \frac{\log{\left(2 x + 2 \sqrt{x^{2} - 1} \right)}}{2}+ \mathrm{constant}

The answer is:

xx2−12−log⁡(2x+2x2−1)2+constant\frac{x \sqrt{x^{2} - 1}}{2} - \frac{\log{\left(2 x + 2 \sqrt{x^{2} - 1} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                               
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 |    ________             |          /       2 |       /       2 
 |   /  2               log\2*x + 2*\/  -1 + x  /   x*\/  -1 + x  
 | \/  x  - 1  dx = C - ------------------------- + --------------
 |                                  2                     2       
/
x x2−12−log⁡(2 x2−1+2 x)2{{x\,\sqrt{x^2-1}}\over{2}}-{{\log \left(2\,\sqrt{x^2-1}+2\,x \right)}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9001
Plot the graph f(x)
The answer [src] 
pi*I
----
 4
log⁡(2 i)2−log⁡22{{\log \left(2\,i\right)}\over{2}}-{{\log 2}\over{2}} 
=
= 
pi*I
----
 4
iπ4\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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