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

Integral of sqrt(1+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  1 + x   dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{x^{2} + 1}\, dx$$ 
Integral(sqrt(1 + x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=1, b=0, c=1, context=sqrt(x**2 + 1), symbol=x)

  1. Add the constant of integration:

The answer is:

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

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

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