Optimal. Leaf size=42 \[ \frac{\tanh ^{-1}\left (\frac{\sqrt{x^6+2}}{\sqrt{2}}\right )}{12 \sqrt{2}}-\frac{\sqrt{x^6+2}}{12 x^6} \]
[Out]
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Rubi [A] time = 0.0454894, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{\tanh ^{-1}\left (\frac{\sqrt{x^6+2}}{\sqrt{2}}\right )}{12 \sqrt{2}}-\frac{\sqrt{x^6+2}}{12 x^6} \]
Antiderivative was successfully verified.
[In] Int[1/(x^7*Sqrt[2 + x^6]),x]
[Out]
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Rubi in Sympy [A] time = 4.25512, size = 36, normalized size = 0.86 \[ \frac{\sqrt{2} \operatorname{atanh}{\left (\frac{\sqrt{2} \sqrt{x^{6} + 2}}{2} \right )}}{24} - \frac{\sqrt{x^{6} + 2}}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(x**6+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0365888, size = 42, normalized size = 1. \[ \frac{\tanh ^{-1}\left (\frac{\sqrt{x^6+2}}{\sqrt{2}}\right )}{12 \sqrt{2}}-\frac{\sqrt{x^6+2}}{12 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^7*Sqrt[2 + x^6]),x]
[Out]
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Maple [A] time = 0.035, size = 39, normalized size = 0.9 \[ -{\frac{1}{12\,{x}^{6}}\sqrt{{x}^{6}+2}}-{\frac{\sqrt{2}}{24}\ln \left ({1 \left ( \sqrt{{x}^{6}+2}-\sqrt{2} \right ){\frac{1}{\sqrt{{x}^{6}}}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(x^6+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.58517, size = 66, normalized size = 1.57 \[ -\frac{1}{48} \, \sqrt{2} \log \left (-\frac{2 \,{\left (\sqrt{2} - \sqrt{x^{6} + 2}\right )}}{2 \, \sqrt{2} + 2 \, \sqrt{x^{6} + 2}}\right ) - \frac{\sqrt{x^{6} + 2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225992, size = 66, normalized size = 1.57 \[ \frac{\sqrt{2}{\left (x^{6} \log \left (\frac{\sqrt{2}{\left (x^{6} + 4\right )} + 4 \, \sqrt{x^{6} + 2}}{x^{6}}\right ) - 2 \, \sqrt{2} \sqrt{x^{6} + 2}\right )}}{48 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.03888, size = 31, normalized size = 0.74 \[ \frac{\sqrt{2} \operatorname{asinh}{\left (\frac{\sqrt{2}}{x^{3}} \right )}}{24} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{12 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(x**6+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228356, size = 63, normalized size = 1.5 \[ -\frac{1}{48} \, \sqrt{2}{\rm ln}\left (-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right ) - \frac{\sqrt{x^{6} + 2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^7),x, algorithm="giac")
[Out]