3.1409 \(\int \frac{x^5}{\left (2+x^6\right )^{3/2}} \, dx\)

Optimal. Leaf size=13 \[ -\frac{1}{3 \sqrt{x^6+2}} \]

[Out]

-1/(3*Sqrt[2 + x^6])

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Rubi [A]  time = 0.00679804, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{3 \sqrt{x^6+2}} \]

Antiderivative was successfully verified.

[In]  Int[x^5/(2 + x^6)^(3/2),x]

[Out]

-1/(3*Sqrt[2 + x^6])

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Rubi in Sympy [A]  time = 1.67277, size = 12, normalized size = 0.92 \[ - \frac{1}{3 \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5/(x**6+2)**(3/2),x)

[Out]

-1/(3*sqrt(x**6 + 2))

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Mathematica [A]  time = 0.00474151, size = 13, normalized size = 1. \[ -\frac{1}{3 \sqrt{x^6+2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(2 + x^6)^(3/2),x]

[Out]

-1/(3*Sqrt[2 + x^6])

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Maple [A]  time = 0.005, size = 10, normalized size = 0.8 \[ -{\frac{1}{3}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(x^6+2)^(3/2),x)

[Out]

-1/3/(x^6+2)^(1/2)

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Maxima [A]  time = 1.44099, size = 12, normalized size = 0.92 \[ -\frac{1}{3 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^6 + 2)^(3/2),x, algorithm="maxima")

[Out]

-1/3/sqrt(x^6 + 2)

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Fricas [A]  time = 0.216788, size = 12, normalized size = 0.92 \[ -\frac{1}{3 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^6 + 2)^(3/2),x, algorithm="fricas")

[Out]

-1/3/sqrt(x^6 + 2)

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Sympy [A]  time = 1.75664, size = 12, normalized size = 0.92 \[ - \frac{1}{3 \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(x**6+2)**(3/2),x)

[Out]

-1/(3*sqrt(x**6 + 2))

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GIAC/XCAS [A]  time = 0.217841, size = 12, normalized size = 0.92 \[ -\frac{1}{3 \, \sqrt{x^{6} + 2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^6 + 2)^(3/2),x, algorithm="giac")

[Out]

-1/3/sqrt(x^6 + 2)