Optimal. Leaf size=46 \[ -e^{-x} x^4-4 e^{-x} x^3-12 e^{-x} x^2-24 e^{-x} x-24 e^{-x} \]
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Rubi [A] time = 0.04, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2176, 2194} \[ -e^{-x} x^4-4 e^{-x} x^3-12 e^{-x} x^2-24 e^{-x} x-24 e^{-x} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {align*} \int e^{-x} x^4 \, dx &=-e^{-x} x^4+4 \int e^{-x} x^3 \, dx\\ &=-4 e^{-x} x^3-e^{-x} x^4+12 \int e^{-x} x^2 \, dx\\ &=-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4+24 \int e^{-x} x \, dx\\ &=-24 e^{-x} x-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4+24 \int e^{-x} \, dx\\ &=-24 e^{-x}-24 e^{-x} x-12 e^{-x} x^2-4 e^{-x} x^3-e^{-x} x^4\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.57 \[ e^{-x} \left (-x^4-4 x^3-12 x^2-24 x-24\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 24, normalized size = 0.52 \[ -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 24, normalized size = 0.52 \[ -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.54 \[ -\left (x^{4}+4 x^{3}+12 x^{2}+24 x +24\right ) {\mathrm e}^{-x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 24, normalized size = 0.52 \[ -{\left (x^{4} + 4 \, x^{3} + 12 \, x^{2} + 24 \, x + 24\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.52 \[ -{\mathrm {e}}^{-x}\,\left (x^4+4\,x^3+12\,x^2+24\,x+24\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 22, normalized size = 0.48 \[ \left (- x^{4} - 4 x^{3} - 12 x^{2} - 24 x - 24\right ) e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
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