Optimal. Leaf size=16 \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
[Out]
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Rubi [A] time = 0.0110394, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Int[x/(1 + x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.97324, size = 12, normalized size = 0.75 \[ \frac{x^{2}}{2 \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**4+1)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0086853, size = 16, normalized size = 1. \[ \frac{x^2}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 + x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \[{\frac{{x}^{2}}{2}{\frac{1}{\sqrt{{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^4+1)^(3/2),x)
[Out]
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Maxima [A] time = 1.41794, size = 16, normalized size = 1. \[ \frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262134, size = 28, normalized size = 1.75 \[ \frac{1}{2 \,{\left (x^{4} - \sqrt{x^{4} + 1} x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.57566, size = 12, normalized size = 0.75 \[ \frac{x^{2}}{2 \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**4+1)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228867, size = 16, normalized size = 1. \[ \frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1)^(3/2),x, algorithm="giac")
[Out]