Optimal. Leaf size=26 \[ \frac{x^4}{4}+\frac{1}{4} \log \left (x^4+1\right )-\log \left (x^4+2\right ) \]
[Out]
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Rubi [A] time = 0.0448069, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{x^4}{4}+\frac{1}{4} \log \left (x^4+1\right )-\log \left (x^4+2\right ) \]
Antiderivative was successfully verified.
[In] Int[x^11/(2 + 3*x^4 + x^8),x]
[Out]
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Rubi in Sympy [A] time = 11.1046, size = 19, normalized size = 0.73 \[ \frac{x^{4}}{4} + \frac{\log{\left (x^{4} + 1 \right )}}{4} - \log{\left (x^{4} + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(x**8+3*x**4+2),x)
[Out]
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Mathematica [A] time = 0.00697979, size = 26, normalized size = 1. \[ \frac{x^4}{4}+\frac{1}{4} \log \left (x^4+1\right )-\log \left (x^4+2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(2 + 3*x^4 + x^8),x]
[Out]
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Maple [A] time = 0.008, size = 23, normalized size = 0.9 \[{\frac{{x}^{4}}{4}}+{\frac{\ln \left ({x}^{4}+1 \right ) }{4}}-\ln \left ({x}^{4}+2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(x^8+3*x^4+2),x)
[Out]
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Maxima [A] time = 0.744052, size = 30, normalized size = 1.15 \[ \frac{1}{4} \, x^{4} - \log \left (x^{4} + 2\right ) + \frac{1}{4} \, \log \left (x^{4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^8 + 3*x^4 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251848, size = 30, normalized size = 1.15 \[ \frac{1}{4} \, x^{4} - \log \left (x^{4} + 2\right ) + \frac{1}{4} \, \log \left (x^{4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^8 + 3*x^4 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.298764, size = 19, normalized size = 0.73 \[ \frac{x^{4}}{4} + \frac{\log{\left (x^{4} + 1 \right )}}{4} - \log{\left (x^{4} + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(x**8+3*x**4+2),x)
[Out]
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GIAC/XCAS [A] time = 0.281172, size = 30, normalized size = 1.15 \[ \frac{1}{4} \, x^{4} -{\rm ln}\left (x^{4} + 2\right ) + \frac{1}{4} \,{\rm ln}\left (x^{4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(x^8 + 3*x^4 + 2),x, algorithm="giac")
[Out]