Optimal. Leaf size=22 \[ -e^{-x}-2 e^x+\frac {e^{3 x}}{3} \]
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Rubi [A] time = 0.03, antiderivative size = 22, normalized size of antiderivative = 1.00, 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 14
Rule 2282
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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ -e^{-x}-2 e^x+\frac {e^{3 x}}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 18, normalized size = 0.82 \[ \frac {1}{3} \, {\left (e^{\left (4 \, x\right )} - 6 \, e^{\left (2 \, x\right )} - 3\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 17, normalized size = 0.77 \[ \frac {1}{3} \, e^{\left (3 \, x\right )} - e^{\left (-x\right )} - 2 \, e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 18, normalized size = 0.82 \[ -2 \,{\mathrm e}^{x}-{\mathrm e}^{-x}+\frac {{\mathrm e}^{3 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 21, normalized size = 0.95 \[ -\frac {1}{3} \, {\left (6 \, e^{\left (-2 \, x\right )} - 1\right )} e^{\left (3 \, x\right )} - e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 17, normalized size = 0.77 \[ \frac {{\mathrm {e}}^{3\,x}}{3}-{\mathrm {e}}^{-x}-2\,{\mathrm {e}}^x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.68 \[ \frac {e^{3 x}}{3} - 2 e^{x} - e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
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