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x^3sqrt(x^2-9)
Solving integrals/ x^3sqrt(x^2-9)

Integral of x^3sqrt(x^2-9) dx

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  x *\/  x  - 9  dx
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0
∫01x3x2−9 dx\int\limits_{0}^{1} x^{3} \sqrt{x^{2} - 9}\, dx 
Integral(x^3*sqrt(x^2 - 1*9), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    x3x2−9=x5−9x3x2−9x^{3} \sqrt{x^{2} - 9} = \frac{x^{5} - 9 x^{3}}{\sqrt{x^{2} - 9}}

    SqrtQuadraticDenomRule(a=-9, b=0, c=1, coeffs=[1, 0, -9, 0, 0, 0], context=(x**5 - 9*x**3)/sqrt(x**2 - 9), symbol=x)

  2. Now simplify:

    x2−9(x4−3x2−54)5\frac{\sqrt{x^{2} - 9} \left(x^{4} - 3 x^{2} - 54\right)}{5}

  3. Add the constant of integration:

    x2−9(x4−3x2−54)5+constant\frac{\sqrt{x^{2} - 9} \left(x^{4} - 3 x^{2} - 54\right)}{5}+ \mathrm{constant}

The answer is:

x2−9(x4−3x2−54)5+constant\frac{\sqrt{x^{2} - 9} \left(x^{4} - 3 x^{2} - 54\right)}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                       
 |                                                        
 |       ________             _________ /          2    4\
 |  3   /  2                 /       2  |  54   3*x    x |
 | x *\/  x  - 9  dx = C + \/  -9 + x  *|- -- - ---- + --|
 |                                      \  5     5     5 /
/
x2 (x2−9)325+6 (x2−9)325{{x^2\,\left(x^2-9\right)^{{{3}\over{2}}}}\over{5}}+{{6\,\left(x^2- 9\right)^{{{3}\over{2}}}}\over{5}}
Simplify
The graph
0.0000000.0000250.0000500.0000750.0001000.0001250.0001500.0001750.0002000.00022501
Plot the graph f(x)
The answer [src] 
                ___
162*I   112*I*\/ 2 
----- - -----------
  5          5
162 i5−7 292 i5{{162\,i}\over{5}}-{{7\,2^{{{9}\over{2}}}\,i}\over{5}} 
=
= 
                ___
162*I   112*I*\/ 2 
----- - -----------
  5          5
−1122i5+162i5- \frac{112 \sqrt{2} i}{5} + \frac{162 i}{5}
Simplify
Numerical answer [src] 
(0.0 + 0.721616202842671j)
(0.0 + 0.721616202842671j)
The graph
Integral of x^3sqrt(x^2-9) dx

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

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