Optimal. Leaf size=13 \[ \frac{\sqrt{x^4+1}}{2} \]
[Out]
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Rubi [A] time = 0.00693403, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\sqrt{x^4+1}}{2} \]
Antiderivative was successfully verified.
[In] Int[x^3/Sqrt[1 + x^4],x]
[Out]
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Rubi in Sympy [A] time = 1.62751, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{4} + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00453576, size = 13, normalized size = 1. \[ \frac{\sqrt{x^4+1}}{2} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/Sqrt[1 + x^4],x]
[Out]
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Maple [A] time = 0.006, size = 10, normalized size = 0.8 \[{\frac{1}{2}\sqrt{{x}^{4}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^4+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.43518, size = 12, normalized size = 0.92 \[ \frac{1}{2} \, \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261994, size = 12, normalized size = 0.92 \[ \frac{1}{2} \, \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.378164, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{4} + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210733, size = 12, normalized size = 0.92 \[ \frac{1}{2} \, \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/sqrt(x^4 + 1),x, algorithm="giac")
[Out]