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sqrt(4x^2-4x+3)
Solving integrals/ sqrt(4x^2-4x+3)

Integral of sqrt(4x^2-4x+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                       
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 |  \/  4*x  - 4*x + 3  dx
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/                         
0
$$\int\limits_{0}^{1} \sqrt{4 x^{2} - 4 x + 3}\, dx$$ 
Integral(sqrt(4*x^2 - 4*x + 3), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=3, b=-4, c=4, context=sqrt(4*x**2 - 4*x + 3), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                                    
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 |    ________________               /  ___           \      ________________          
 |   /    2                     asinh\\/ 2 *(-1/2 + x)/     /              2  /  1   x\
 | \/  4*x  - 4*x + 3  dx = C + ----------------------- + \/  3 - 4*x + 4*x  *|- - + -|
 |                                         2                                  \  4   2/
/
$${{{\rm asinh}\; \left({{8\,x-4}\over{2^{{{5}\over{2}}}}}\right) }\over{2}}+{{x\,\sqrt{4\,x^2-4\,x+3}}\over{2}}-{{\sqrt{4\,x^2-4\,x+3 }}\over{4}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___        /  ___\
\/ 3         |\/ 2 |
----- + asinh|-----|
  2          \  2  /
$${{2\,{\rm asinh}\; \left({{1}\over{\sqrt{2}}}\right)+\sqrt{3} }\over{2}}$$ 
=
= 
  ___        /  ___\
\/ 3         |\/ 2 |
----- + asinh|-----|
  2          \  2  /
$$\operatorname{asinh}{\left(\frac{\sqrt{2}}{2} \right)} + \frac{\sqrt{3}}{2}$$
Simplify
Numerical answer [src] 
1.52450435224685
1.52450435224685
The graph
Integral of sqrt(4x^2-4x+3) dx

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

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