Optimal. Leaf size=22 \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]
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Rubi [A] time = 0.0277052, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {2282, 14} \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]
Antiderivative was successfully verified.
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Rule 2282
Rule 14
Rubi steps
\begin{align*} \int e^x \left (-e^{-x}+e^x\right )^2 \, dx &=\operatorname{Subst}\left (\int \frac{\frac{1}{x}-2 x+x^3}{x} \, dx,x,e^x\right )\\ &=\operatorname{Subst}\left (\int \left (-2+\frac{1}{x^2}+x^2\right ) \, dx,x,e^x\right )\\ &=-e^{-x}-2 e^x+\frac{e^{3 x}}{3}\\ \end{align*}
Mathematica [A] time = 0.007386, size = 22, normalized size = 1. \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.023, size = 18, normalized size = 0.8 \begin{align*}{\frac{ \left ({{\rm e}^{x}} \right ) ^{3}}{3}}-2\,{{\rm e}^{x}}- \left ({{\rm e}^{x}} \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967162, size = 28, normalized size = 1.27 \begin{align*} -\frac{1}{3} \,{\left (6 \, e^{\left (-2 \, x\right )} - 1\right )} e^{\left (3 \, x\right )} - e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.842875, size = 51, normalized size = 2.32 \begin{align*} \frac{1}{3} \,{\left (e^{\left (4 \, x\right )} - 6 \, e^{\left (2 \, x\right )} - 3\right )} e^{\left (-x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.110703, size = 15, normalized size = 0.68 \begin{align*} \frac{e^{3 x}}{3} - 2 e^{x} - e^{- x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30317, size = 23, normalized size = 1.05 \begin{align*} \frac{1}{3} \, e^{\left (3 \, x\right )} - e^{\left (-x\right )} - 2 \, e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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