3.139 \(\int ((-3+x) x)^{2/3} (-3+2 x) \, dx\)

Optimal. Leaf size=16 \[ \frac{3}{5} (-(3-x) x)^{5/3} \]

[Out]

(3*(-((3 - x)*x))^(5/3))/5

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Rubi [A]  time = 0.00818837, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{3}{5} (-(3-x) x)^{5/3} \]

Antiderivative was successfully verified.

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

[Out]

(3*(-((3 - x)*x))^(5/3))/5

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Rubi in Sympy [A]  time = 1.90351, size = 10, normalized size = 0.62 \[ \frac{3 \left (x \left (x - 3\right )\right )^{\frac{5}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*(x*(x - 3))**(5/3)/5

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Mathematica [A]  time = 0.00920367, size = 13, normalized size = 0.81 \[ \frac{3}{5} ((x-3) x)^{5/3} \]

Antiderivative was successfully verified.

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

[Out]

(3*((-3 + x)*x)^(5/3))/5

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Maple [A]  time = 0.004, size = 14, normalized size = 0.9 \[{\frac{ \left ( -9+3\,x \right ) x}{5} \left ( \left ( -3+x \right ) x \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Maxima [A]  time = 0.701904, size = 12, normalized size = 0.75 \[ \frac{3}{5} \, \left ({\left (x - 3\right )} x\right )^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*((x - 3)*x)^(5/3)

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Fricas [A]  time = 0.274239, size = 15, normalized size = 0.94 \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(x^2 - 3*x)^(5/3)

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Sympy [A]  time = 15.1847, size = 10, normalized size = 0.62 \[ \frac{3 \left (x \left (x - 3\right )\right )^{\frac{5}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*(x*(x - 3))**(5/3)/5

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GIAC/XCAS [A]  time = 0.270977, size = 15, normalized size = 0.94 \[ \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(x^2 - 3*x)^(5/3)