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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Rewrite the integrand:

    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:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                       
 |                                                        
 |       ________             _________ /          2    4\
 |  3   /  2                 /       2  |  54   3*x    x |
 | x *\/  x  - 9  dx = C + \/  -9 + x  *|- -- - ---- + --|
 |                                      \  5     5     5 /
/
$${{x^2\,\left(x^2-9\right)^{{{3}\over{2}}}}\over{5}}+{{6\,\left(x^2- 9\right)^{{{3}\over{2}}}}\over{5}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                ___
162*I   112*I*\/ 2 
----- - -----------
  5          5
$${{162\,i}\over{5}}-{{7\,2^{{{9}\over{2}}}\,i}\over{5}}$$ 
=
= 
                ___
162*I   112*I*\/ 2 
----- - -----------
  5          5
$$- \frac{112 \sqrt{2} i}{5} + \frac{162 i}{5}$$
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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