Optimal. Leaf size=18 \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
[Out]
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Rubi [A] time = 0.0158401, antiderivative size = 18, 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 \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*Sqrt[16 - x^4]),x]
[Out]
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Rubi in Sympy [A] time = 2.54028, size = 14, normalized size = 0.78 \[ - \frac{\sqrt{- x^{4} + 16}}{32 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0104609, size = 18, normalized size = 1. \[ -\frac{\sqrt{16-x^4}}{32 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*Sqrt[16 - x^4]),x]
[Out]
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Maple [A] time = 0.006, size = 26, normalized size = 1.4 \[{\frac{ \left ( -2+x \right ) \left ( 2+x \right ) \left ({x}^{2}+4 \right ) }{32\,{x}^{2}}{\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(-x^4+16)^(1/2),x)
[Out]
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Maxima [A] time = 1.43896, size = 19, normalized size = 1.06 \[ -\frac{\sqrt{-x^{4} + 16}}{32 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.272571, size = 53, normalized size = 2.94 \[ \frac{x^{4} + 4 \, \sqrt{-x^{4} + 16} - 16}{32 \,{\left (\sqrt{-x^{4} + 16} x^{2} - 4 \, x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.89374, size = 34, normalized size = 1.89 \[ \begin{cases} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{32} & \text{for}\: 16 \left |{\frac{1}{x^{4}}}\right | > 1 \\- \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{32} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214497, size = 15, normalized size = 0.83 \[ -\frac{1}{32} \, \sqrt{\frac{16}{x^{4}} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^3),x, algorithm="giac")
[Out]