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sqrt(x^2+4)
Solving integrals/ sqrt(x^2+4)

Integral of sqrt(x^2+4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /  2        
 |  \/  x  + 4  dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{x^{2} + 4}\, dx$$ 
Integral(sqrt(x^2 + 4), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                               
 |                                        ________
 |    ________                           /      2 
 |   /  2                      /x\   x*\/  4 + x  
 | \/  x  + 4  dx = C + 2*asinh|-| + -------------
 |                             \2/         2      
/
$$\int \sqrt{x^{2} + 4}\, dx = C + \frac{x \sqrt{x^{2} + 4}}{2} + 2 \operatorname{asinh}{\left(\frac{x}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___               
\/ 5                
----- + 2*asinh(1/2)
  2
$$2 \operatorname{asinh}{\left(\frac{1}{2} \right)} + \frac{\sqrt{5}}{2}$$ 
=
= 
  ___               
\/ 5                
----- + 2*asinh(1/2)
  2
$$2 \operatorname{asinh}{\left(\frac{1}{2} \right)} + \frac{\sqrt{5}}{2}$$ 
sqrt(5)/2 + 2*asinh(1/2)
Numerical answer [src] 
2.0804576388691
2.0804576388691
The graph
Integral of sqrt(x^2+4) dx

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

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