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sqrt(25+x^2)
Solving integrals/ sqrt(25+x^2)

Integral of sqrt(25+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  5                
  /                
 |                 
 |     _________   
 |    /       2    
 |  \/  25 + x   dx
 |                 
/                  
0
∫05x2+25 dx\int\limits_{0}^{5} \sqrt{x^{2} + 25}\, dx 
Integral(sqrt(25 + x^2), (x, 0, 5))
Detail solution

    SqrtQuadraticRule(a=25, b=0, c=1, context=sqrt(x**2 + 25), symbol=x)

  1. Add the constant of integration:

    xx2+252+25asinh⁡(x5)2+constant\frac{x \sqrt{x^{2} + 25}}{2} + \frac{25 \operatorname{asinh}{\left(\frac{x}{5} \right)}}{2}+ \mathrm{constant}

The answer is:

xx2+252+25asinh⁡(x5)2+constant\frac{x \sqrt{x^{2} + 25}}{2} + \frac{25 \operatorname{asinh}{\left(\frac{x}{5} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                  
 |                               /x\        _________
 |    _________          25*asinh|-|       /       2 
 |   /       2                   \5/   x*\/  25 + x  
 | \/  25 + x   dx = C + ----------- + --------------
 |                            2              2       
/
x x2+252+25 asinh  (x5)2{{x\,\sqrt{x^2+25}}\over{2}}+{{25\,{\rm asinh}\; \left({{x}\over{5 }}\right)}\over{2}}
Simplify
The graph
0.05.00.51.01.52.02.53.03.54.04.5050
Plot the graph f(x)
The answer [src] 
     ___         /      ___\
25*\/ 2    25*log\1 + \/ 2 /
-------- + -----------------
   2               2
25 asinh  1+25 22{{25\,{\rm asinh}\; 1+25\,\sqrt{2}}\over{2}} 
=
= 
     ___         /      ___\
25*\/ 2    25*log\1 + \/ 2 /
-------- + -----------------
   2               2
25log⁡(1+2)2+2522\frac{25 \log{\left(1 + \sqrt{2} \right)}}{2} + \frac{25 \sqrt{2}}{2}
Simplify
Numerical answer [src] 
28.694839367408
28.694839367408
The graph
Integral of sqrt(25+x^2) dx

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

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