3.495 \(\int \frac{x^2}{\sqrt{-1-x^3}} \, dx\)

Optimal. Leaf size=15 \[ -\frac{2}{3} \sqrt{-x^3-1} \]

[Out]

(-2*Sqrt[-1 - x^3])/3

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Rubi [A]  time = 0.00821236, 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 \[ -\frac{2}{3} \sqrt{-x^3-1} \]

Antiderivative was successfully verified.

[In]  Int[x^2/Sqrt[-1 - x^3],x]

[Out]

(-2*Sqrt[-1 - x^3])/3

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Rubi in Sympy [A]  time = 2.05736, size = 14, normalized size = 0.93 \[ - \frac{2 \sqrt{- x^{3} - 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2/(-x**3-1)**(1/2),x)

[Out]

-2*sqrt(-x**3 - 1)/3

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Mathematica [A]  time = 0.0052042, size = 15, normalized size = 1. \[ -\frac{2}{3} \sqrt{-x^3-1} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2/Sqrt[-1 - x^3],x]

[Out]

(-2*Sqrt[-1 - x^3])/3

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Maple [A]  time = 0.006, size = 23, normalized size = 1.5 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) }{3}{\frac{1}{\sqrt{-{x}^{3}-1}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2/(-x^3-1)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.44408, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(-x^3 - 1),x, algorithm="maxima")

[Out]

-2/3*sqrt(-x^3 - 1)

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Fricas [A]  time = 0.228327, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(-x^3 - 1),x, algorithm="fricas")

[Out]

-2/3*sqrt(-x^3 - 1)

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Sympy [A]  time = 0.339684, size = 14, normalized size = 0.93 \[ - \frac{2 \sqrt{- x^{3} - 1}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2/(-x**3-1)**(1/2),x)

[Out]

-2*sqrt(-x**3 - 1)/3

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GIAC/XCAS [A]  time = 0.211047, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(-x^3 - 1),x, algorithm="giac")

[Out]

-2/3*sqrt(-x^3 - 1)