3.1384 \(\int \frac{x^5}{\sqrt{2+x^6}} \, dx\)

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

[Out]

Sqrt[2 + x^6]/3

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Rubi [A]  time = 0.00669852, 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 \[ \frac{\sqrt{x^6+2}}{3} \]

Antiderivative was successfully verified.

[In]  Int[x^5/Sqrt[2 + x^6],x]

[Out]

Sqrt[2 + x^6]/3

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Rubi in Sympy [A]  time = 1.68731, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{6} + 2}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5/(x**6+2)**(1/2),x)

[Out]

sqrt(x**6 + 2)/3

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Mathematica [A]  time = 0.00409162, size = 13, normalized size = 1. \[ \frac{\sqrt{x^6+2}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/Sqrt[2 + x^6],x]

[Out]

Sqrt[2 + x^6]/3

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(x^6+2)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.41662, 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/sqrt(x^6 + 2),x, algorithm="maxima")

[Out]

1/3*sqrt(x^6 + 2)

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Fricas [A]  time = 0.224036, 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/sqrt(x^6 + 2),x, algorithm="fricas")

[Out]

1/3*sqrt(x^6 + 2)

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Sympy [A]  time = 0.693858, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{6} + 2}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(x**6+2)**(1/2),x)

[Out]

sqrt(x**6 + 2)/3

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GIAC/XCAS [A]  time = 0.220357, 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/sqrt(x^6 + 2),x, algorithm="giac")

[Out]

1/3*sqrt(x^6 + 2)