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Identical expressions
X^3sqrt(twenty-five -x^ two)
X cubed square root of (25 minus x squared )
X cubed square root of (twenty minus five minus x to the power of two)
X^3√(25-x^2)
X3sqrt(25-x2)
X3sqrt25-x2
X³sqrt(25-x²)
X to the power of 3sqrt(25-x to the power of 2)
X^3sqrt25-x^2
X^3sqrt(25-x^2)dx
Similar expressions
X^3sqrt(25+x^2)

Solving integrals/ X^3sqrt(25-x^2)

Integral of X^3sqrt(25-x^2) dx

The solution

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  0                   
  /                   
 |                    
 |        _________   
 |   3   /       2    
 |  x *\/  25 - x   dx
 |                    
/                     
5

$$\int\limits_{5}^{0} x^{3} \sqrt{25 - x^{2}}\, dx$$

Integral(x^3*sqrt(25 - x^2), (x, 5, 0))

Detail solution

Rewrite the integrand:

$x^{3} \sqrt{25 - x^{2}} = \frac{- x^{5} + 25 x^{3}}{\sqrt{25 - x^{2}}}$

SqrtQuadraticDenomRule(a=25, b=0, c=-1, coeffs=[-1, 0, 25, 0, 0, 0], context=(-x**5 + 25*x**3)/sqrt(25 - x**2), symbol=x)
Now simplify:

$\frac{\sqrt{25 - x^{2}} \cdot \left(3 x^{4} - 25 x^{2} - 1250\right)}{15}$
Add the constant of integration:

$\frac{\sqrt{25 - x^{2}} \cdot \left(3 x^{4} - 25 x^{2} - 1250\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{25 - x^{2}} \cdot \left(3 x^{4} - 25 x^{2} - 1250\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                         
 |                                                          
 |       _________             _________ /           2    4\
 |  3   /       2             /       2  |  250   5*x    x |
 | x *\/  25 - x   dx = C + \/  25 - x  *|- --- - ---- + --|
 |                                       \   3     3     5 /
/

$$-{{x^2\,\left(25-x^2\right)^{{{3}\over{2}}}}\over{5}}-{{10\,\left( 25-x^2\right)^{{{3}\over{2}}}}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1250/3

$$-{{1250}\over{3}}$$

-1250/3

$$- \frac{1250}{3}$$

Упростить

Numerical answer [src]

-416.666666666667

-416.666666666667

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

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Integral of X^3sqrt(25-x^2) dx

Limits of integration:

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Piecewise:

The solution