Optimal. Leaf size=15 \[ \frac{3}{4} \sqrt [3]{x^4-4 x} \]
[Out]
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Rubi [A] time = 0.00760728, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{3}{4} \sqrt [3]{x^4-4 x} \]
Antiderivative was successfully verified.
[In] Int[(-1 + x^3)/(-4*x + x^4)^(2/3),x]
[Out]
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Rubi in Sympy [A] time = 1.29084, size = 12, normalized size = 0.8 \[ \frac{3 \sqrt [3]{x^{4} - 4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-1)/(x**4-4*x)**(2/3),x)
[Out]
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Mathematica [A] time = 0.01844, size = 15, normalized size = 1. \[ \frac{3}{4} \sqrt [3]{x \left (x^3-4\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + x^3)/(-4*x + x^4)^(2/3),x]
[Out]
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Maple [A] time = 0.01, size = 18, normalized size = 1.2 \[{\frac{3\,x \left ({x}^{3}-4 \right ) }{4} \left ({x}^{4}-4\,x \right ) ^{-{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-1)/(x^4-4*x)^(2/3),x)
[Out]
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Maxima [A] time = 0.724625, size = 15, normalized size = 1. \[ \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x^4 - 4*x)^(2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259559, size = 15, normalized size = 1. \[ \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x^4 - 4*x)^(2/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.518973, size = 12, normalized size = 0.8 \[ \frac{3 \sqrt [3]{x^{4} - 4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-1)/(x**4-4*x)**(2/3),x)
[Out]
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GIAC/XCAS [A] time = 0.284484, size = 15, normalized size = 1. \[ \frac{3}{4} \,{\left (x^{4} - 4 \, x\right )}^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x^4 - 4*x)^(2/3),x, algorithm="giac")
[Out]