Optimal. Leaf size=38 \[ 3 e^{\sqrt [3]{x}} x^{2/3}-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+6 e^{\sqrt [3]{x}} \]
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Rubi [A] time = 0.018782, 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, Rules used = {2207, 2176, 2194} \[ 3 e^{\sqrt [3]{x}} x^{2/3}-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+6 e^{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
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Rule 2207
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{\sqrt [3]{x}} \, dx &=3 \operatorname{Subst}\left (\int e^x x^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 e^{\sqrt [3]{x}} x^{2/3}-6 \operatorname{Subst}\left (\int e^x x \, dx,x,\sqrt [3]{x}\right )\\ &=-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+3 e^{\sqrt [3]{x}} x^{2/3}+6 \operatorname{Subst}\left (\int e^x \, dx,x,\sqrt [3]{x}\right )\\ &=6 e^{\sqrt [3]{x}}-6 e^{\sqrt [3]{x}} \sqrt [3]{x}+3 e^{\sqrt [3]{x}} x^{2/3}\\ \end{align*}
Mathematica [A] time = 0.0080055, 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.
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Maple [A] time = 0.002, size = 26, normalized size = 0.7 \begin{align*} 6\,{{\rm e}^{\sqrt [3]{x}}}-6\,{{\rm e}^{\sqrt [3]{x}}}\sqrt [3]{x}+3\,{{\rm e}^{\sqrt [3]{x}}}{x}^{2/3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936532, size = 22, normalized size = 0.58 \begin{align*} 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.19803, size = 55, normalized size = 1.45 \begin{align*} 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.318136, size = 34, normalized size = 0.89 \begin{align*} 3 x^{\frac{2}{3}} e^{\sqrt [3]{x}} - 6 \sqrt [3]{x} e^{\sqrt [3]{x}} + 6 e^{\sqrt [3]{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05636, size = 22, normalized size = 0.58 \begin{align*} 3 \,{\left (x^{\frac{2}{3}} - 2 \, x^{\frac{1}{3}} + 2\right )} e^{\left (x^{\frac{1}{3}}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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