Optimal. Leaf size=13 \[ -\frac{1}{2 \sqrt{x^4+1}} \]
[Out]
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Rubi [A] time = 0.00698683, 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 \[ -\frac{1}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Int[x^3/(1 + x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.61938, size = 12, normalized size = 0.92 \[ - \frac{1}{2 \sqrt{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**4+1)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00428745, size = 13, normalized size = 1. \[ -\frac{1}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(1 + x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 10, normalized size = 0.8 \[ -{\frac{1}{2}{\frac{1}{\sqrt{{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^4+1)^(3/2),x)
[Out]
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Maxima [A] time = 1.45428, 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/(x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258313, 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/(x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.34648, 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/(x**4+1)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227554, 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/(x^4 + 1)^(3/2),x, algorithm="giac")
[Out]