Optimal. Leaf size=26 \[ -\frac {1}{3} e^{-3 x}-\frac {e^{-2 x}}{2}-e^{-x} \]
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Rubi [A] time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2282, 14} \[ -\frac {1}{3} e^{-3 x}-\frac {e^{-2 x}}{2}-e^{-x} \]
Antiderivative was successfully verified.
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Rule 14
Rule 2282
Rubi steps
\begin {align*} \int e^{-4 x} \left (e^x+e^{2 x}+e^{3 x}\right ) \, dx &=\operatorname {Subst}\left (\int \frac {1+x+x^2}{x^4} \, dx,x,e^x\right )\\ &=\operatorname {Subst}\left (\int \left (\frac {1}{x^4}+\frac {1}{x^3}+\frac {1}{x^2}\right ) \, dx,x,e^x\right )\\ &=-\frac {1}{3} e^{-3 x}-\frac {e^{-2 x}}{2}-e^{-x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.88 \[ -\frac {1}{6} e^{-3 x} \left (3 e^x+6 e^{2 x}+2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 18, normalized size = 0.69 \[ -\frac {1}{6} \, {\left (6 \, e^{\left (2 \, x\right )} + 3 \, e^{x} + 2\right )} e^{\left (-3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 18, normalized size = 0.69 \[ -\frac {1}{6} \, {\left (6 \, e^{\left (2 \, x\right )} + 3 \, e^{x} + 2\right )} e^{\left (-3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.77 \[ -\frac {{\mathrm e}^{-3 x}}{3}-\frac {{\mathrm e}^{-2 x}}{2}-{\mathrm e}^{-x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 19, normalized size = 0.73 \[ -e^{\left (-x\right )} - \frac {1}{2} \, e^{\left (-2 \, x\right )} - \frac {1}{3} \, e^{\left (-3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 18, normalized size = 0.69 \[ -\frac {{\mathrm {e}}^{-3\,x}\,\left (6\,{\mathrm {e}}^{2\,x}+3\,{\mathrm {e}}^x+2\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.85 \[ - e^{- x} - \frac {e^{- 2 x}}{2} - \frac {e^{- 3 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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