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Solving integrals/ sqrt(x^(2)-5)

Integral of sqrt(x^(2)-5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /  2        
 |  \/  x  - 5  dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{x^{2} - 5}\, dx$$ 
Integral(sqrt(x^2 - 5), (x, 0, 1))
The answer (Indefinite) [src] 
  /                            /    ___\                 
 |                             |x*\/ 5 |        _________
 |    ________          5*acosh|-------|       /       2 
 |   /  2                      \   5   /   x*\/  -5 + x  
 | \/  x  - 5  dx = C - ---------------- + --------------
 |                             2                 2       
/
$$\int \sqrt{x^{2} - 5}\, dx = C + \frac{x \sqrt{x^{2} - 5}}{2} - \frac{5 \operatorname{acosh}{\left(\frac{\sqrt{5} x}{5} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           /  ___\         
           |\/ 5 |         
    5*acosh|-----|         
           \  5  /   5*pi*I
I - -------------- + ------
          2            4
$$- \frac{5 \operatorname{acosh}{\left(\frac{\sqrt{5}}{5} \right)}}{2} + i + \frac{5 i \pi}{4}$$ 
=
= 
           /  ___\         
           |\/ 5 |         
    5*acosh|-----|         
           \  5  /   5*pi*I
I - -------------- + ------
          2            4
$$- \frac{5 \operatorname{acosh}{\left(\frac{\sqrt{5}}{5} \right)}}{2} + i + \frac{5 i \pi}{4}$$ 
i - 5*acosh(sqrt(5)/5)/2 + 5*pi*i/4
Numerical answer [src] 
(0.0 + 2.15911902250202j)
(0.0 + 2.15911902250202j)

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

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