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√(1+x²)
Solving integrals/ √(1+x²)

Integral of √(1+x²) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  1 + x   dx
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0
$$\int\limits_{0}^{1} \sqrt{x^{2} + 1}\, dx$$ 
Integral(sqrt(1 + x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                             
 |                                      ________
 |    ________                         /      2 
 |   /      2           asinh(x)   x*\/  1 + x  
 | \/  1 + x   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 √(1+x²) dx

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

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