Optimal. Leaf size=29 \[ \frac{1}{6} \left (16-x^4\right )^{3/2}-8 \sqrt{16-x^4} \]
[Out]
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Rubi [A] time = 0.0404775, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{6} \left (16-x^4\right )^{3/2}-8 \sqrt{16-x^4} \]
Antiderivative was successfully verified.
[In] Int[x^7/Sqrt[16 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 4.79858, size = 19, normalized size = 0.66 \[ \frac{\left (- x^{4} + 16\right )^{\frac{3}{2}}}{6} - 8 \sqrt{- x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0128521, size = 20, normalized size = 0.69 \[ -\frac{1}{6} \sqrt{16-x^4} \left (x^4+32\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^7/Sqrt[16 - x^4],x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 1. \[{\frac{ \left ( -2+x \right ) \left ( 2+x \right ) \left ({x}^{2}+4 \right ) \left ({x}^{4}+32 \right ) }{6}{\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(-x^4+16)^(1/2),x)
[Out]
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Maxima [A] time = 1.43153, size = 31, normalized size = 1.07 \[ \frac{1}{6} \,{\left (-x^{4} + 16\right )}^{\frac{3}{2}} - 8 \, \sqrt{-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(-x^4 + 16),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262264, size = 22, normalized size = 0.76 \[ -\frac{1}{6} \,{\left (x^{4} + 32\right )} \sqrt{-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(-x^4 + 16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.28591, size = 26, normalized size = 0.9 \[ - \frac{x^{4} \sqrt{- x^{4} + 16}}{6} - \frac{16 \sqrt{- x^{4} + 16}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21355, size = 31, normalized size = 1.07 \[ \frac{1}{6} \,{\left (-x^{4} + 16\right )}^{\frac{3}{2}} - 8 \, \sqrt{-x^{4} + 16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/sqrt(-x^4 + 16),x, algorithm="giac")
[Out]