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Solving integrals/ sqrt(10+x^2)

Integral of sqrt(10+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     _________   
 |    /       2    
 |  \/  10 + x   dx
 |                 
/                  
0
∫01x2+10 dx\int\limits_{0}^{1} \sqrt{x^{2} + 10}\, dx 
Integral(sqrt(10 + x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                        
 |                                                _________
 |    _________                 /    ____\       /       2 
 |   /       2                  |x*\/ 10 |   x*\/  10 + x  
 | \/  10 + x   dx = C + 5*asinh|--------| + --------------
 |                              \   10   /         2       
/
∫x2+10 dx=C+xx2+102+5asinh⁡(10x10)\int \sqrt{x^{2} + 10}\, dx = C + \frac{x \sqrt{x^{2} + 10}}{2} + 5 \operatorname{asinh}{\left(\frac{\sqrt{10} x}{10} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
  ____          /  ____\
\/ 11           |\/ 10 |
------ + 5*asinh|------|
  2             \  10  /
5asinh⁡(1010)+1125 \operatorname{asinh}{\left(\frac{\sqrt{10}}{10} \right)} + \frac{\sqrt{11}}{2} 
=
= 
  ____          /  ____\
\/ 11           |\/ 10 |
------ + 5*asinh|------|
  2             \  10  /
5asinh⁡(1010)+1125 \operatorname{asinh}{\left(\frac{\sqrt{10}}{10} \right)} + \frac{\sqrt{11}}{2} 
sqrt(11)/2 + 5*asinh(sqrt(10)/10)
Numerical answer [src] 
3.21421865446465
3.21421865446465

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

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