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Solving integrals/ sqrt(16+5x^2)

Integral of sqrt(16+5x^2) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                  
  /                  
 |                   
 |     ___________   
 |    /         2    
 |  \/  16 + 5*x   dx
 |                   
/                    
0
$$\int\limits_{0}^{2} \sqrt{5 x^{2} + 16}\, dx$$ 
Integral(sqrt(16 + 5*x^2), (x, 0, 2))
The answer (Indefinite) [src] 
  /                                                        /    ___\
 |                              ___________       ___      |x*\/ 5 |
 |    ___________              /         2    8*\/ 5 *asinh|-------|
 |   /         2           x*\/  16 + 5*x                  \   4   /
 | \/  16 + 5*x   dx = C + ---------------- + ----------------------
 |                                2                     5           
/
$$\int \sqrt{5 x^{2} + 16}\, dx = C + \frac{x \sqrt{5 x^{2} + 16}}{2} + \frac{8 \sqrt{5} \operatorname{asinh}{\left(\frac{\sqrt{5} x}{4} \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                 /  ___\
        ___      |\/ 5 |
    8*\/ 5 *asinh|-----|
                 \  2  /
6 + --------------------
             5
$$\frac{8 \sqrt{5} \operatorname{asinh}{\left(\frac{\sqrt{5}}{2} \right)}}{5} + 6$$ 
=
= 
                 /  ___\
        ___      |\/ 5 |
    8*\/ 5 *asinh|-----|
                 \  2  /
6 + --------------------
             5
$$\frac{8 \sqrt{5} \operatorname{asinh}{\left(\frac{\sqrt{5}}{2} \right)}}{5} + 6$$ 
6 + 8*sqrt(5)*asinh(sqrt(5)/2)/5
Numerical answer [src] 
9.44327152771203
9.44327152771203

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

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