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sqrt(4x^2-1)
Solving integrals/ sqrt(4x^2-1)

Integral of sqrt(4x^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
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 |     __________   
 |    /    2        
 |  \/  4*x  - 1  dx
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0
∫014x2−1 dx\int\limits_{0}^{1} \sqrt{4 x^{2} - 1}\, dx 
Integral(sqrt(4*x^2 - 1*1), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=-1, b=0, c=4, context=sqrt(4*x**2 - 1*1), symbol=x)

  1. Add the constant of integration:

    x4x2−12−log⁡(8x+44x2−1)4+constant\frac{x \sqrt{4 x^{2} - 1}}{2} - \frac{\log{\left(8 x + 4 \sqrt{4 x^{2} - 1} \right)}}{4}+ \mathrm{constant}

The answer is:

x4x2−12−log⁡(8x+44x2−1)4+constant\frac{x \sqrt{4 x^{2} - 1}}{2} - \frac{\log{\left(8 x + 4 \sqrt{4 x^{2} - 1} \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                     
 |                           /     ___________      \        ___________
 |    __________             |    /         2       |       /         2 
 |   /    2               log\4*\/  -1 + 4*x   + 8*x/   x*\/  -1 + 4*x  
 | \/  4*x  - 1  dx = C - --------------------------- + ----------------
 |                                     4                       2        
/
x 4 x2−12−log⁡(4 4 x2−1+8 x)4{{x\,\sqrt{4\,x^2-1}}\over{2}}-{{\log \left(4\,\sqrt{4\,x^2-1}+8\,x \right)}\over{4}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
  ___      /      ___\       
\/ 3    log\2 + \/ 3 /   pi*I
----- - -------------- + ----
  2           4           8
log⁡(4 i)4−log⁡(4 3+8)−2 34{{\log \left(4\,i\right)}\over{4}}-{{\log \left(4\,\sqrt{3}+8 \right)-2\,\sqrt{3}}\over{4}} 
=
= 
  ___      /      ___\       
\/ 3    log\2 + \/ 3 /   pi*I
----- - -------------- + ----
  2           4           8
−log⁡(3+2)4+32+iπ8- \frac{\log{\left(\sqrt{3} + 2 \right)}}{4} + \frac{\sqrt{3}}{2} + \frac{i \pi}{8}
Simplify
Numerical answer [src] 
(0.536220266948917 + 0.392134269538859j)
(0.536220266948917 + 0.392134269538859j)
The graph
Integral of sqrt(4x^2-1) dx

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

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