3.1383 \(\int \frac{x^{11}}{\sqrt{2+x^6}} \, dx\)

Optimal. Leaf size=27 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{2 \sqrt{x^6+2}}{3} \]

[Out]

(-2*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9

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Rubi [A]  time = 0.0298919, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{2 \sqrt{x^6+2}}{3} \]

Antiderivative was successfully verified.

[In]  Int[x^11/Sqrt[2 + x^6],x]

[Out]

(-2*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9

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Rubi in Sympy [A]  time = 3.63401, size = 20, normalized size = 0.74 \[ \frac{\left (x^{6} + 2\right )^{\frac{3}{2}}}{9} - \frac{2 \sqrt{x^{6} + 2}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**11/(x**6+2)**(1/2),x)

[Out]

(x**6 + 2)**(3/2)/9 - 2*sqrt(x**6 + 2)/3

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Mathematica [A]  time = 0.00886449, size = 18, normalized size = 0.67 \[ \frac{1}{9} \left (x^6-4\right ) \sqrt{x^6+2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^11/Sqrt[2 + x^6],x]

[Out]

((-4 + x^6)*Sqrt[2 + x^6])/9

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Maple [A]  time = 0.007, size = 15, normalized size = 0.6 \[{\frac{{x}^{6}-4}{9}\sqrt{{x}^{6}+2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^11/(x^6+2)^(1/2),x)

[Out]

1/9*(x^6+2)^(1/2)*(x^6-4)

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Maxima [A]  time = 1.45242, size = 26, normalized size = 0.96 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{6} + 2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^11/sqrt(x^6 + 2),x, algorithm="maxima")

[Out]

1/9*(x^6 + 2)^(3/2) - 2/3*sqrt(x^6 + 2)

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Fricas [A]  time = 0.22047, size = 19, normalized size = 0.7 \[ \frac{1}{9} \, \sqrt{x^{6} + 2}{\left (x^{6} - 4\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^11/sqrt(x^6 + 2),x, algorithm="fricas")

[Out]

1/9*sqrt(x^6 + 2)*(x^6 - 4)

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Sympy [A]  time = 4.00364, size = 24, normalized size = 0.89 \[ \frac{x^{6} \sqrt{x^{6} + 2}}{9} - \frac{4 \sqrt{x^{6} + 2}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**11/(x**6+2)**(1/2),x)

[Out]

x**6*sqrt(x**6 + 2)/9 - 4*sqrt(x**6 + 2)/9

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GIAC/XCAS [A]  time = 0.219433, size = 26, normalized size = 0.96 \[ \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{6} + 2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^11/sqrt(x^6 + 2),x, algorithm="giac")

[Out]

1/9*(x^6 + 2)^(3/2) - 2/3*sqrt(x^6 + 2)