Optimal. Leaf size=38 \[ 3 e^{\sqrt [3]{x}} x^{2/3}-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+6 e^{\sqrt [3]{x}} \]
[Out]
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Rubi [A] time = 0.0325605, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.429 \[ 3 e^{\sqrt [3]{x}} x^{2/3}-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+6 e^{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
[In] Int[E^x^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.94994, size = 34, normalized size = 0.89 \[ 3 x^{\frac{2}{3}} e^{\sqrt [3]{x}} - 6 \sqrt [3]{x} e^{\sqrt [3]{x}} + 6 e^{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.00603552, size = 24, normalized size = 0.63 \[ e^{\sqrt [3]{x}} \left (3 x^{2/3}-6 \sqrt [3]{x}+6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^x^(1/3),x]
[Out]
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Maple [A] time = 0.003, size = 26, normalized size = 0.7 \[ 6\,{{\rm e}^{\sqrt [3]{x}}}-6\,{{\rm e}^{\sqrt [3]{x}}}\sqrt [3]{x}+3\,{{\rm e}^{\sqrt [3]{x}}}{x}^{2/3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^(1/3)),x)
[Out]
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Maxima [A] time = 1.37396, size = 22, normalized size = 0.58 \[ 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231071, size = 22, normalized size = 0.58 \[ 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^(1/3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.438435, size = 34, normalized size = 0.89 \[ 3 x^{\frac{2}{3}} e^{\sqrt [3]{x}} - 6 \sqrt [3]{x} e^{\sqrt [3]{x}} + 6 e^{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.213582, size = 22, normalized size = 0.58 \[ 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^(1/3)),x, algorithm="giac")
[Out]