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Solving integrals/ sqrt(a^2+x^2)dx

Integral of sqrt(a^2+x^2)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     _________   
 |    /  2    2    
 |  \/  a  + x   dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \sqrt{a^{2} + x^{2}}\, dx$$ 
Integral(sqrt(a^2 + x^2), (x, 0, 1))
The answer (Indefinite) [src] 
                                                 ________
                                                /      2 
  /                                            /      x  
 |                        2      /x\   a*x*   /   1 + -- 
 |    _________          a *asinh|-|         /         2 
 |   /  2    2                   \a/       \/         a  
 | \/  a  + x   dx = C + ----------- + ------------------
 |                            2                2         
/
$$\int \sqrt{a^{2} + x^{2}}\, dx = C + \frac{a^{2} \operatorname{asinh}{\left(\frac{x}{a} \right)}}{2} + \frac{a x \sqrt{1 + \frac{x^{2}}{a^{2}}}}{2}$$
Simplify
The answer [src] 
       ________              
      /     1                
a*   /  1 + --     2      /1\
    /        2    a *asinh|-|
  \/        a             \a/
--------------- + -----------
       2               2
$$\frac{a^{2} \operatorname{asinh}{\left(\frac{1}{a} \right)}}{2} + \frac{a \sqrt{1 + \frac{1}{a^{2}}}}{2}$$ 
=
= 
       ________              
      /     1                
a*   /  1 + --     2      /1\
    /        2    a *asinh|-|
  \/        a             \a/
--------------- + -----------
       2               2
$$\frac{a^{2} \operatorname{asinh}{\left(\frac{1}{a} \right)}}{2} + \frac{a \sqrt{1 + \frac{1}{a^{2}}}}{2}$$ 
a*sqrt(1 + a^(-2))/2 + a^2*asinh(1/a)/2

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

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