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

Integral of sqrt(5+x^2) dx

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
  2               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  5 + x   dx
 |                
/                 
0
$$\int\limits_{0}^{2} \sqrt{x^{2} + 5}\, dx$$ 
Integral(sqrt(5 + x^2), (x, 0, 2))
The answer (Indefinite) [src] 
  /                            /    ___\                
 |                             |x*\/ 5 |        ________
 |    ________          5*asinh|-------|       /      2 
 |   /      2                  \   5   /   x*\/  5 + x  
 | \/  5 + x   dx = C + ---------------- + -------------
 |                             2                 2      
/
$$\int \sqrt{x^{2} + 5}\, dx = C + \frac{x \sqrt{x^{2} + 5}}{2} + \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{5} x}{5} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           /    ___\
           |2*\/ 5 |
    5*asinh|-------|
           \   5   /
3 + ----------------
           2
$$\frac{5 \operatorname{asinh}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} + 3$$ 
=
= 
           /    ___\
           |2*\/ 5 |
    5*asinh|-------|
           \   5   /
3 + ----------------
           2
$$\frac{5 \operatorname{asinh}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} + 3$$ 
3 + 5*asinh(2*sqrt(5)/5)/2
Numerical answer [src] 
5.01179739054263
5.01179739054263
The graph
Integral of sqrt(5+x^2) dx

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

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