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sqrt(x^2-6x-7)
Solving integrals/ sqrt(x^2-6x-7)

Integral of sqrt(x^2-6x-7) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  \/  x  - 6*x - 7  dx
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∫01x2−6x−7 dx\int\limits_{0}^{1} \sqrt{x^{2} - 6 x - 7}\, dx 
Integral(sqrt(x^2 - 6*x - 1*7), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=-7, b=-6, c=1, context=sqrt(x**2 - 6*x - 1*7), symbol=x)

  1. Now simplify:

    (x−3)x2−6x−72−8log⁡(2x+2x2−6x−7−6)\frac{\left(x - 3\right) \sqrt{x^{2} - 6 x - 7}}{2} - 8 \log{\left(2 x + 2 \sqrt{x^{2} - 6 x - 7} - 6 \right)}

  2. Add the constant of integration:

    (x−3)x2−6x−72−8log⁡(2x+2x2−6x−7−6)+constant\frac{\left(x - 3\right) \sqrt{x^{2} - 6 x - 7}}{2} - 8 \log{\left(2 x + 2 \sqrt{x^{2} - 6 x - 7} - 6 \right)}+ \mathrm{constant}

The answer is:

(x−3)x2−6x−72−8log⁡(2x+2x2−6x−7−6)+constant\frac{\left(x - 3\right) \sqrt{x^{2} - 6 x - 7}}{2} - 8 \log{\left(2 x + 2 \sqrt{x^{2} - 6 x - 7} - 6 \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                                                
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 |    ______________               /                _______________\      _______________          
 |   /  2                          |               /       2       |     /       2        /  3   x\
 | \/  x  - 6*x - 7  dx = C - 8*log\-6 + 2*x + 2*\/  -7 + x  - 6*x / + \/  -7 + x  - 6*x *|- - + -|
 |                                                                                        \  2   2/
/
−8 log⁡(2 x2−6 x−7+2 x−6)+x x2−6 x−72−3 x2−6 x−72-8\,\log \left(2\,\sqrt{x^2-6\,x-7}+2\,x-6\right)+{{x\,\sqrt{x^2-6 \,x-7}}\over{2}}-{{3\,\sqrt{x^2-6\,x-7}}\over{2}}
Simplify
The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
Plot the graph f(x)
The answer [src] 
                                                                ___
                 /           ___\         ___   16*pi*I   3*I*\/ 7 
-8*log(8) + 8*log\-6 + 2*I*\/ 7 / - 2*I*\/ 3  - ------- + ---------
                                                   3          2
8 log⁡(2 7 i−6)−8 log⁡(4 3 i−4)+3 7 i2−2 3 i8\,\log \left(2\,\sqrt{7}\,i-6\right)-8\,\log \left(4\,\sqrt{3}\,i- 4\right)+{{3\,\sqrt{7}\,i}\over{2}}-2\,\sqrt{3}\,i 
=
= 
                                                                ___
                 /           ___\         ___   16*pi*I   3*I*\/ 7 
-8*log(8) + 8*log\-6 + 2*I*\/ 7 / - 2*I*\/ 3  - ------- + ---------
                                                   3          2
−8log⁡(8)−16iπ3−23i+37i2+8log⁡(−6+27i)- 8 \log{\left(8 \right)} - \frac{16 i \pi}{3} - 2 \sqrt{3} i + \frac{3 \sqrt{7} i}{2} + 8 \log{\left(-6 + 2 \sqrt{7} i \right)}
Simplify
Numerical answer [src] 
(0.0 + 3.10023177852459j)
(0.0 + 3.10023177852459j)
The graph
Integral of sqrt(x^2-6x-7) dx

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

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