Optimal. Leaf size=23 \[ \frac{2 \tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
[Out]
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Rubi [A] time = 0.0448043, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{2 \tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[x^4/(2 + x^5 + x^10),x]
[Out]
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Rubi in Sympy [A] time = 5.20041, size = 24, normalized size = 1.04 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\sqrt{7} \left (\frac{2 x^{5}}{7} + \frac{1}{7}\right ) \right )}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(x**10+x**5+2),x)
[Out]
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Mathematica [A] time = 0.00923215, size = 23, normalized size = 1. \[ \frac{2 \tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(2 + x^5 + x^10),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 0.8 \[{\frac{2\,\sqrt{7}}{35}\arctan \left ({\frac{ \left ( 2\,{x}^{5}+1 \right ) \sqrt{7}}{7}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(x^10+x^5+2),x)
[Out]
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Maxima [A] time = 0.820614, size = 24, normalized size = 1.04 \[ \frac{2}{35} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + x^5 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.260471, size = 24, normalized size = 1.04 \[ \frac{2}{35} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + x^5 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.323585, size = 27, normalized size = 1.17 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\frac{2 \sqrt{7} x^{5}}{7} + \frac{\sqrt{7}}{7} \right )}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(x**10+x**5+2),x)
[Out]
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GIAC/XCAS [A] time = 0.295419, size = 24, normalized size = 1.04 \[ \frac{2}{35} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(x^10 + x^5 + 2),x, algorithm="giac")
[Out]