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(1+4x^2)^(1/2)
Solving integrals/ (1+4x^2)^(1/2)

Integral of (1+4x^2)^(1/2) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  1 + 4*x   dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sqrt{4 x^{2} + 1}\, dx$$ 
Integral(sqrt(1 + 4*x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                          __________
 |    __________                           /        2 
 |   /        2           asinh(2*x)   x*\/  1 + 4*x  
 | \/  1 + 4*x   dx = C + ---------- + ---------------
 |                            4               2       
/
$$\int \sqrt{4 x^{2} + 1}\, dx = C + \frac{x \sqrt{4 x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(2 x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___           
\/ 5    asinh(2)
----- + --------
  2        4
$$\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}$$ 
=
= 
  ___           
\/ 5    asinh(2)
----- + --------
  2        4
$$\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}$$ 
sqrt(5)/2 + asinh(2)/4
Numerical answer [src] 
1.4789428575446
1.4789428575446
The graph
Integral of (1+4x^2)^(1/2) dx

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

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