Optimal. Leaf size=37 \[ -\frac{5}{12 x^6}+\frac{5}{4 x^2}+\frac{5}{4} \tan ^{-1}\left (x^2\right )+\frac{1}{4 x^6 \left (x^4+1\right )} \]
[Out]
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Rubi [A] time = 0.0417847, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.312 \[ -\frac{5}{12 x^6}+\frac{5}{4 x^2}+\frac{5}{4} \tan ^{-1}\left (x^2\right )+\frac{1}{4 x^6 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Int[1/(x^7*(1 + 2*x^4 + x^8)),x]
[Out]
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Rubi in Sympy [A] time = 9.52098, size = 32, normalized size = 0.86 \[ \frac{5 \operatorname{atan}{\left (x^{2} \right )}}{4} + \frac{5}{4 x^{2}} - \frac{5}{12 x^{6}} + \frac{1}{4 x^{6} \left (x^{4} + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(x**8+2*x**4+1),x)
[Out]
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Mathematica [A] time = 0.0163911, size = 33, normalized size = 0.89 \[ -\frac{1}{6 x^6}+\frac{1}{x^2}-\frac{5}{4} \tan ^{-1}\left (\frac{1}{x^2}\right )+\frac{x^2}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^7*(1 + 2*x^4 + x^8)),x]
[Out]
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Maple [A] time = 0.017, size = 28, normalized size = 0.8 \[{\frac{{x}^{2}}{4\,{x}^{4}+4}}+{\frac{5\,\arctan \left ({x}^{2} \right ) }{4}}-{\frac{1}{6\,{x}^{6}}}+{x}^{-2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(x^8+2*x^4+1),x)
[Out]
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Maxima [A] time = 0.860928, size = 41, normalized size = 1.11 \[ \frac{15 \, x^{8} + 10 \, x^{4} - 2}{12 \,{\left (x^{10} + x^{6}\right )}} + \frac{5}{4} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 2*x^4 + 1)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.245721, size = 49, normalized size = 1.32 \[ \frac{15 \, x^{8} + 10 \, x^{4} + 15 \,{\left (x^{10} + x^{6}\right )} \arctan \left (x^{2}\right ) - 2}{12 \,{\left (x^{10} + x^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 2*x^4 + 1)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.515027, size = 29, normalized size = 0.78 \[ \frac{5 \operatorname{atan}{\left (x^{2} \right )}}{4} + \frac{15 x^{8} + 10 x^{4} - 2}{12 x^{10} + 12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(x**8+2*x**4+1),x)
[Out]
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GIAC/XCAS [A] time = 0.271181, size = 42, normalized size = 1.14 \[ \frac{x^{2}}{4 \,{\left (x^{4} + 1\right )}} + \frac{6 \, x^{4} - 1}{6 \, x^{6}} + \frac{5}{4} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 2*x^4 + 1)*x^7),x, algorithm="giac")
[Out]