Optimal. Leaf size=13 \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
[Out]
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Rubi [A] time = 0.00689211, 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 \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
[In] Int[x^3/(1 + x^4)^(4/3),x]
[Out]
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Rubi in Sympy [A] time = 1.6376, size = 12, normalized size = 0.92 \[ - \frac{3}{4 \sqrt [3]{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(x**4+1)**(4/3),x)
[Out]
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Mathematica [A] time = 0.00550883, size = 13, normalized size = 1. \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(1 + x^4)^(4/3),x]
[Out]
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Maple [A] time = 0.005, size = 10, normalized size = 0.8 \[ -{\frac{3}{4}{\frac{1}{\sqrt [3]{{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(x^4+1)^(4/3),x)
[Out]
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Maxima [A] time = 1.41986, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251176, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.54353, size = 12, normalized size = 0.92 \[ - \frac{3}{4 \sqrt [3]{x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(x**4+1)**(4/3),x)
[Out]
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GIAC/XCAS [A] time = 0.214483, size = 12, normalized size = 0.92 \[ -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(x^4 + 1)^(4/3),x, algorithm="giac")
[Out]