Optimal. Leaf size=37 \[ -\frac{\sqrt{16-x^4}}{96 x^6}-\frac{\sqrt{16-x^4}}{768 x^2} \]
[Out]
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Rubi [A] time = 0.0289965, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{\sqrt{16-x^4}}{96 x^6}-\frac{\sqrt{16-x^4}}{768 x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^7*Sqrt[16 - x^4]),x]
[Out]
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Rubi in Sympy [A] time = 3.54588, size = 27, normalized size = 0.73 \[ - \frac{\sqrt{- x^{4} + 16}}{768 x^{2}} - \frac{\sqrt{- x^{4} + 16}}{96 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0130572, size = 23, normalized size = 0.62 \[ -\frac{\sqrt{16-x^4} \left (x^4+8\right )}{768 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^7*Sqrt[16 - x^4]),x]
[Out]
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Maple [A] time = 0.007, size = 31, normalized size = 0.8 \[{\frac{ \left ( -2+x \right ) \left ( 2+x \right ) \left ({x}^{2}+4 \right ) \left ({x}^{4}+8 \right ) }{768\,{x}^{6}}{\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(-x^4+16)^(1/2),x)
[Out]
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Maxima [A] time = 1.43925, size = 39, normalized size = 1.05 \[ -\frac{\sqrt{-x^{4} + 16}}{512 \, x^{2}} - \frac{{\left (-x^{4} + 16\right )}^{\frac{3}{2}}}{1536 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26191, size = 99, normalized size = 2.68 \[ -\frac{x^{12} - 72 \, x^{8} + 384 \, x^{4} + 4 \,{\left (3 \, x^{8} - 40 \, x^{4} - 512\right )} \sqrt{-x^{4} + 16} + 8192}{768 \,{\left (12 \, x^{10} - 256 \, x^{6} -{\left (x^{10} - 64 \, x^{6}\right )} \sqrt{-x^{4} + 16}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.10299, size = 66, normalized size = 1.78 \[ \begin{cases} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{768} - \frac{\sqrt{-1 + \frac{16}{x^{4}}}}{96 x^{4}} & \text{for}\: 16 \left |{\frac{1}{x^{4}}}\right | > 1 \\- \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{768} - \frac{i \sqrt{1 - \frac{16}{x^{4}}}}{96 x^{4}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214914, size = 31, normalized size = 0.84 \[ -\frac{1}{1536} \,{\left (\frac{16}{x^{4}} - 1\right )}^{\frac{3}{2}} - \frac{1}{512} \, \sqrt{\frac{16}{x^{4}} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^7),x, algorithm="giac")
[Out]