Optimal. Leaf size=33 \[ -\frac{x^3}{6 \sqrt{x^6+2}}-\frac{1}{6 \sqrt{x^6+2} x^3} \]
[Out]
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Rubi [A] time = 0.0243014, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{x^3}{6 \sqrt{x^6+2}}-\frac{1}{6 \sqrt{x^6+2} x^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(2 + x^6)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 3.20135, size = 29, normalized size = 0.88 \[ - \frac{x^{3}}{6 \sqrt{x^{6} + 2}} - \frac{1}{6 x^{3} \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(x**6+2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.01267, size = 21, normalized size = 0.64 \[ -\frac{x^6+1}{6 x^3 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(2 + x^6)^(3/2)),x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.6 \[ -{\frac{{x}^{6}+1}{6\,{x}^{3}}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(x^6+2)^(3/2),x)
[Out]
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Maxima [A] time = 1.44011, size = 34, normalized size = 1.03 \[ -\frac{x^{3}}{12 \, \sqrt{x^{6} + 2}} - \frac{\sqrt{x^{6} + 2}}{12 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218174, size = 39, normalized size = 1.18 \[ \frac{1}{6 \,{\left (x^{12} + 2 \, x^{6} -{\left (x^{9} + x^{3}\right )} \sqrt{x^{6} + 2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.82349, size = 31, normalized size = 0.94 \[ - \frac{1}{6 \sqrt{1 + \frac{2}{x^{6}}}} - \frac{1}{6 x^{6} \sqrt{1 + \frac{2}{x^{6}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(x**6+2)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (x^{6} + 2\right )}^{\frac{3}{2}} x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 2)^(3/2)*x^4),x, algorithm="giac")
[Out]