Optimal. Leaf size=12 \[ \frac{1}{20} \tan ^{-1}\left (\frac{x^5}{4}\right ) \]
[Out]
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Rubi [A] time = 0.0137458, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{20} \tan ^{-1}\left (\frac{x^5}{4}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^4/(16 + x^10),x]
[Out]
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Rubi in Sympy [A] time = 1.23571, size = 7, normalized size = 0.58 \[ \frac{\operatorname{atan}{\left (\frac{x^{5}}{4} \right )}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(x**10+16),x)
[Out]
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Mathematica [A] time = 0.00538723, size = 12, normalized size = 1. \[ \frac{1}{20} \tan ^{-1}\left (\frac{x^5}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(16 + x^10),x]
[Out]
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Maple [A] time = 0.002, size = 9, normalized size = 0.8 \[{\frac{1}{20}\arctan \left ({\frac{{x}^{5}}{4}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(x^10+16),x)
[Out]
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Maxima [A] time = 1.52469, size = 11, normalized size = 0.92 \[ \frac{1}{20} \, \arctan \left (\frac{1}{4} \, x^{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + 16),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228837, size = 11, normalized size = 0.92 \[ \frac{1}{20} \, \arctan \left (\frac{1}{4} \, x^{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + 16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.141754, size = 7, normalized size = 0.58 \[ \frac{\operatorname{atan}{\left (\frac{x^{5}}{4} \right )}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(x**10+16),x)
[Out]
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GIAC/XCAS [A] time = 0.214287, size = 11, normalized size = 0.92 \[ \frac{1}{20} \, \arctan \left (\frac{1}{4} \, x^{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + 16),x, algorithm="giac")
[Out]