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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                 
01x2+5dx\int\limits_{0}^{1} \sqrt{x^{2} + 5}\, dx
Integral(sqrt(x^2 + 5), (x, 0, 1))
The answer (Indefinite) [src]
  /                            /    ___\                
 |                             |x*\/ 5 |        ________
 |    ________          5*asinh|-------|       /      2 
 |   /  2                      \   5   /   x*\/  5 + x  
 | \/  x  + 5  dx = C + ---------------- + -------------
 |                             2                 2      
/                                                       
x2+5dx=C+xx2+52+5asinh(5x5)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}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.5
The answer [src]
               /  ___\
               |\/ 5 |
  ___   5*asinh|-----|
\/ 6           \  5  /
----- + --------------
  2           2       
5asinh(55)2+62\frac{5 \operatorname{asinh}{\left(\frac{\sqrt{5}}{5} \right)}}{2} + \frac{\sqrt{6}}{2}
=
=
               /  ___\
               |\/ 5 |
  ___   5*asinh|-----|
\/ 6           \  5  /
----- + --------------
  2           2       
5asinh(55)2+62\frac{5 \operatorname{asinh}{\left(\frac{\sqrt{5}}{5} \right)}}{2} + \frac{\sqrt{6}}{2}
sqrt(6)/2 + 5*asinh(sqrt(5)/5)/2
Numerical answer [src]
2.3085132795048
2.3085132795048
The graph
Integral of sqrt(x^2+5) dx

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