3.141 \(\int \frac{x \left (9-9 x+2 x^2\right )}{\sqrt [3]{(-3+x) x}} \, dx\)

Optimal. Leaf size=15 \[ \frac{3}{5} \left (x^2-3 x\right )^{5/3} \]

[Out]

(3*(-3*x + x^2)^(5/3))/5

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Rubi [A]  time = 0.0932254, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{3}{5} \left (x^2-3 x\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Int[(x*(9 - 9*x + 2*x^2))/((-3 + x)*x)^(1/3),x]

[Out]

(3*(-3*x + x^2)^(5/3))/5

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Rubi in Sympy [A]  time = 11.9661, size = 12, normalized size = 0.8 \[ \frac{3 \left (x^{2} - 3 x\right )^{\frac{5}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(2*x**2-9*x+9)/((-3+x)*x)**(1/3),x)

[Out]

3*(x**2 - 3*x)**(5/3)/5

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Mathematica [A]  time = 0.0103182, size = 13, normalized size = 0.87 \[ \frac{3}{5} ((x-3) x)^{5/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(x*(9 - 9*x + 2*x^2))/((-3 + x)*x)^(1/3),x]

[Out]

(3*((-3 + x)*x)^(5/3))/5

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Maple [A]  time = 0.005, size = 18, normalized size = 1.2 \[{\frac{3\, \left ( -3+x \right ) ^{2}{x}^{2}}{5}{\frac{1}{\sqrt [3]{ \left ( -3+x \right ) x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(2*x^2-9*x+9)/((-3+x)*x)^(1/3),x)

[Out]

3/5*(-3+x)^2*x^2/((-3+x)*x)^(1/3)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, x^{2} - 9 \, x + 9\right )} x}{\left ({\left (x - 3\right )} x\right )^{\frac{1}{3}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x + 9)*x/((x - 3)*x)^(1/3),x, algorithm="maxima")

[Out]

integrate((2*x^2 - 9*x + 9)*x/((x - 3)*x)^(1/3), x)

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Fricas [A]  time = 0.278864, size = 15, normalized size = 1. \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x + 9)*x/((x - 3)*x)^(1/3),x, algorithm="fricas")

[Out]

3/5*(x^2 - 3*x)^(5/3)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{x \left (x - 3\right ) \left (2 x - 3\right )}{\sqrt [3]{x \left (x - 3\right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(2*x**2-9*x+9)/((-3+x)*x)**(1/3),x)

[Out]

Integral(x*(x - 3)*(2*x - 3)/(x*(x - 3))**(1/3), x)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (2 \, x^{2} - 9 \, x + 9\right )} x}{\left ({\left (x - 3\right )} x\right )^{\frac{1}{3}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x + 9)*x/((x - 3)*x)^(1/3),x, algorithm="giac")

[Out]

integrate((2*x^2 - 9*x + 9)*x/((x - 3)*x)^(1/3), x)