Optimal. Leaf size=11 \[ -\frac{1}{4 \left (x^4+1\right )} \]
[Out]
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Rubi [A] time = 0.00693275, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{1}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Int[x^3/(1 + 2*x^4 + x^8),x]
[Out]
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Rubi in Sympy [A] time = 2.85374, size = 8, normalized size = 0.73 \[ - \frac{1}{4 \left (x^{4} + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**8+2*x**4+1),x)
[Out]
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Mathematica [A] time = 0.00306416, size = 11, normalized size = 1. \[ -\frac{1}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(1 + 2*x^4 + x^8),x]
[Out]
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Maple [A] time = 0.004, size = 10, normalized size = 0.9 \[ -{\frac{1}{4\,{x}^{4}+4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^8+2*x^4+1),x)
[Out]
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Maxima [A] time = 0.766338, size = 12, normalized size = 1.09 \[ -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^8 + 2*x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248724, size = 12, normalized size = 1.09 \[ -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^8 + 2*x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.227761, size = 8, normalized size = 0.73 \[ - \frac{1}{4 x^{4} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(x**8+2*x**4+1),x)
[Out]
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GIAC/XCAS [A] time = 0.261829, size = 12, normalized size = 1.09 \[ -\frac{1}{4 \,{\left (x^{4} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^8 + 2*x^4 + 1),x, algorithm="giac")
[Out]