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(x^2+1)^(1/2)
Solving integrals/ (x^2+1)^(1/2)

Integral of (x^2+1)^(1/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
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 |     ________   
 |    /  2        
 |  \/  x  + 1  dx
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0
$$\int\limits_{0}^{1} \sqrt{x^{2} + 1}\, dx$$ 
Integral(sqrt(x^2 + 1), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                             
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 |    ________                         /      2 
 |   /  2               asinh(x)   x*\/  1 + x  
 | \/  x  + 1  dx = C + -------- + -------------
 |                         2             2      
/
$$\int \sqrt{x^{2} + 1}\, dx = C + \frac{x \sqrt{x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___      /      ___\
\/ 2    log\1 + \/ 2 /
----- + --------------
  2           2
$$\frac{\log{\left(1 + \sqrt{2} \right)}}{2} + \frac{\sqrt{2}}{2}$$ 
=
= 
  ___      /      ___\
\/ 2    log\1 + \/ 2 /
----- + --------------
  2           2
$$\frac{\log{\left(1 + \sqrt{2} \right)}}{2} + \frac{\sqrt{2}}{2}$$ 
sqrt(2)/2 + log(1 + sqrt(2))/2
Numerical answer [src] 
1.14779357469632
1.14779357469632
The graph
Integral of (x^2+1)^(1/2) dx

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

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