3.17 \(\int x^2 \left (27+8 x^3\right )^{2/3} \, dx\)

Optimal. Leaf size=15 \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]

[Out]

(27 + 8*x^3)^(5/3)/40

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Rubi [A]  time = 0.00691163, antiderivative size = 15, 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 \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(27 + 8*x^3)^(2/3),x]

[Out]

(27 + 8*x^3)^(5/3)/40

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Rubi in Sympy [A]  time = 0.931484, size = 10, normalized size = 0.67 \[ \frac{\left (8 x^{3} + 27\right )^{\frac{5}{3}}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2*(8*x**3+27)**(2/3),x)

[Out]

(8*x**3 + 27)**(5/3)/40

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Mathematica [A]  time = 0.00629887, size = 15, normalized size = 1. \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(27 + 8*x^3)^(2/3),x]

[Out]

(27 + 8*x^3)^(5/3)/40

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Maple [B]  time = 0.006, size = 27, normalized size = 1.8 \[{\frac{ \left ( 3+2\,x \right ) \left ( 4\,{x}^{2}-6\,x+9 \right ) }{40} \left ( 8\,{x}^{3}+27 \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(8*x^3+27)^(2/3),x)

[Out]

1/40*(3+2*x)*(4*x^2-6*x+9)*(8*x^3+27)^(2/3)

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Maxima [A]  time = 1.36691, size = 15, normalized size = 1. \[ \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((8*x^3 + 27)^(2/3)*x^2,x, algorithm="maxima")

[Out]

1/40*(8*x^3 + 27)^(5/3)

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Fricas [A]  time = 0.20508, size = 15, normalized size = 1. \[ \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((8*x^3 + 27)^(2/3)*x^2,x, algorithm="fricas")

[Out]

1/40*(8*x^3 + 27)^(5/3)

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Sympy [A]  time = 0.45183, size = 27, normalized size = 1.8 \[ \frac{x^{3} \left (8 x^{3} + 27\right )^{\frac{2}{3}}}{5} + \frac{27 \left (8 x^{3} + 27\right )^{\frac{2}{3}}}{40} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(8*x**3+27)**(2/3),x)

[Out]

x**3*(8*x**3 + 27)**(2/3)/5 + 27*(8*x**3 + 27)**(2/3)/40

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GIAC/XCAS [A]  time = 0.216462, size = 15, normalized size = 1. \[ \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((8*x^3 + 27)^(2/3)*x^2,x, algorithm="giac")

[Out]

1/40*(8*x^3 + 27)^(5/3)