3.14 \(\int \frac{x^5}{\sqrt{1-x^6}} \, dx\)

Optimal. Leaf size=15 \[ -\frac{1}{3} \sqrt{1-x^6} \]

[Out]

-Sqrt[1 - x^6]/3

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Rubi [A]  time = 0.00652509, 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 \[ -\frac{1}{3} \sqrt{1-x^6} \]

Antiderivative was successfully verified.

[In]  Int[x^5/Sqrt[1 - x^6],x]

[Out]

-Sqrt[1 - x^6]/3

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Rubi in Sympy [A]  time = 0.977442, size = 10, normalized size = 0.67 \[ - \frac{\sqrt{- x^{6} + 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-sqrt(-x**6 + 1)/3

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Mathematica [A]  time = 0.00535236, size = 15, normalized size = 1. \[ -\frac{1}{3} \sqrt{1-x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/Sqrt[1 - x^6],x]

[Out]

-Sqrt[1 - x^6]/3

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Maple [B]  time = 0.013, size = 32, normalized size = 2.1 \[{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+x+1 \right ) \left ({x}^{2}-x+1 \right ) }{3}{\frac{1}{\sqrt{-{x}^{6}+1}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(-x^6+1)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.3434, size = 15, normalized size = 1. \[ -\frac{1}{3} \, \sqrt{-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/sqrt(-x^6 + 1),x, algorithm="maxima")

[Out]

-1/3*sqrt(-x^6 + 1)

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Fricas [A]  time = 0.209514, size = 15, normalized size = 1. \[ -\frac{1}{3} \, \sqrt{-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/sqrt(-x^6 + 1),x, algorithm="fricas")

[Out]

-1/3*sqrt(-x^6 + 1)

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Sympy [A]  time = 0.341842, size = 10, normalized size = 0.67 \[ - \frac{\sqrt{- x^{6} + 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-sqrt(-x**6 + 1)/3

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GIAC/XCAS [A]  time = 0.214874, size = 15, normalized size = 1. \[ -\frac{1}{3} \, \sqrt{-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/sqrt(-x^6 + 1),x, algorithm="giac")

[Out]

-1/3*sqrt(-x^6 + 1)