Optimal. Leaf size=16 \[ -\frac{1}{4 x^4}-\frac{1}{4} \tan ^{-1}\left (x^4\right ) \]
[Out]
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Rubi [A] time = 0.0243344, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ -\frac{1}{4 x^4}-\frac{1}{4} \tan ^{-1}\left (x^4\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(1 + x^8)),x]
[Out]
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Rubi in Sympy [A] time = 4.72229, size = 14, normalized size = 0.88 \[ - \frac{\operatorname{atan}{\left (x^{4} \right )}}{4} - \frac{1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(x**8+1),x)
[Out]
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Mathematica [A] time = 0.00776439, size = 16, normalized size = 1. \[ \frac{1}{4} \tan ^{-1}\left (\frac{1}{x^4}\right )-\frac{1}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(1 + x^8)),x]
[Out]
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Maple [A] time = 0.008, size = 13, normalized size = 0.8 \[ -{\frac{1}{4\,{x}^{4}}}-{\frac{\arctan \left ({x}^{4} \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(x^8+1),x)
[Out]
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Maxima [A] time = 1.56746, size = 16, normalized size = 1. \[ -\frac{1}{4 \, x^{4}} - \frac{1}{4} \, \arctan \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 1)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215091, size = 20, normalized size = 1.25 \[ -\frac{x^{4} \arctan \left (x^{4}\right ) + 1}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 1)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.370067, size = 14, normalized size = 0.88 \[ - \frac{\operatorname{atan}{\left (x^{4} \right )}}{4} - \frac{1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(x**8+1),x)
[Out]
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GIAC/XCAS [A] time = 0.233213, size = 16, normalized size = 1. \[ -\frac{1}{4 \, x^{4}} - \frac{1}{4} \, \arctan \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^8 + 1)*x^5),x, algorithm="giac")
[Out]