Optimal. Leaf size=25 \[ 2-\log \left (\frac {5}{4}\right )+x \left (-e^{-x} x^2-\log (4)\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 16, normalized size of antiderivative = 0.64, number of steps used = 9, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {6742, 2176, 2194} \begin {gather*} -e^{-x} x^3-x \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3 e^{-x} x^2+e^{-x} x^3-\log (4)\right ) \, dx\\ &=-x \log (4)-3 \int e^{-x} x^2 \, dx+\int e^{-x} x^3 \, dx\\ &=3 e^{-x} x^2-e^{-x} x^3-x \log (4)+3 \int e^{-x} x^2 \, dx-6 \int e^{-x} x \, dx\\ &=6 e^{-x} x-e^{-x} x^3-x \log (4)-6 \int e^{-x} \, dx+6 \int e^{-x} x \, dx\\ &=6 e^{-x}-e^{-x} x^3-x \log (4)+6 \int e^{-x} \, dx\\ &=-e^{-x} x^3-x \log (4)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 16, normalized size = 0.64 \begin {gather*} -e^{-x} x^3-x \log (4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 17, normalized size = 0.68 \begin {gather*} -{\left (x^{3} + 2 \, x e^{x} \log \relax (2)\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 15, normalized size = 0.60 \begin {gather*} -x^{3} e^{\left (-x\right )} - 2 \, x \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.64
method | result | size |
default | \(-x^{3} {\mathrm e}^{-x}-2 x \ln \relax (2)\) | \(16\) |
risch | \(-x^{3} {\mathrm e}^{-x}-2 x \ln \relax (2)\) | \(16\) |
norman | \(\left (-x^{3}-2 x \ln \relax (2) {\mathrm e}^{x}\right ) {\mathrm e}^{-x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 39, normalized size = 1.56 \begin {gather*} -{\left (x^{3} + 3 \, x^{2} + 6 \, x + 6\right )} e^{\left (-x\right )} + 3 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} - 2 \, x \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.33, size = 15, normalized size = 0.60 \begin {gather*} -2\,x\,\ln \relax (2)-x^3\,{\mathrm {e}}^{-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.56 \begin {gather*} - x^{3} e^{- x} - 2 x \log {\relax (2 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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