Optimal. Leaf size=21 \[ 83-x-2 \left (5+5 e^{-4-x} x^3\right ) \]
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Rubi [A] time = 0.15, antiderivative size = 16, normalized size of antiderivative = 0.76, number of steps used = 11, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {6688, 2196, 2176, 2194} \begin {gather*} -10 e^{-x-4} x^3-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2196
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+10 e^{-4-x} (-3+x) x^2\right ) \, dx\\ &=-x+10 \int e^{-4-x} (-3+x) x^2 \, dx\\ &=-x+10 \int \left (-3 e^{-4-x} x^2+e^{-4-x} x^3\right ) \, dx\\ &=-x+10 \int e^{-4-x} x^3 \, dx-30 \int e^{-4-x} x^2 \, dx\\ &=-x+30 e^{-4-x} x^2-10 e^{-4-x} x^3+30 \int e^{-4-x} x^2 \, dx-60 \int e^{-4-x} x \, dx\\ &=-x+60 e^{-4-x} x-10 e^{-4-x} x^3-60 \int e^{-4-x} \, dx+60 \int e^{-4-x} x \, dx\\ &=60 e^{-4-x}-x-10 e^{-4-x} x^3+60 \int e^{-4-x} \, dx\\ &=-x-10 e^{-4-x} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.76 \begin {gather*} -x-10 e^{-4-x} x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 20, normalized size = 0.95 \begin {gather*} -{\left (10 \, x^{3} + x e^{\left (x + 4\right )}\right )} e^{\left (-x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 18, normalized size = 0.86 \begin {gather*} -{\left (10 \, x^{3} e^{\left (-x\right )} + x e^{4}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 16, normalized size = 0.76
method | result | size |
risch | \(-x -10 \,{\mathrm e}^{-x -4} x^{3}\) | \(16\) |
norman | \(\left (-10 x^{3}-x \,{\mathrm e}^{4+x}\right ) {\mathrm e}^{-x -4}\) | \(21\) |
derivativedivides | \(-4-x +640 \,{\mathrm e}^{-x -4}-480 \,{\mathrm e}^{-x -4} \left (4+x \right )+120 \,{\mathrm e}^{-x -4} \left (4+x \right )^{2}-10 \,{\mathrm e}^{-x -4} \left (4+x \right )^{3}\) | \(51\) |
default | \(-4-x +640 \,{\mathrm e}^{-x -4}-480 \,{\mathrm e}^{-x -4} \left (4+x \right )+120 \,{\mathrm e}^{-x -4} \left (4+x \right )^{2}-10 \,{\mathrm e}^{-x -4} \left (4+x \right )^{3}\) | \(51\) |
meijerg | \(-\frac {{\mathrm e}^{-x +x \,{\mathrm e}^{-4}+4} \left (1-{\mathrm e}^{-x \,{\mathrm e}^{-4} \left (1-{\mathrm e}^{4}\right )}\right )}{1-{\mathrm e}^{4}}+10 \,{\mathrm e}^{12-x +x \,{\mathrm e}^{-4}} \left (6-\frac {\left (4 x^{3} {\mathrm e}^{-12}+12 x^{2} {\mathrm e}^{-8}+24 x \,{\mathrm e}^{-4}+24\right ) {\mathrm e}^{-x \,{\mathrm e}^{-4}}}{4}\right )-30 \,{\mathrm e}^{8-x +x \,{\mathrm e}^{-4}} \left (2-\frac {\left (3 x^{2} {\mathrm e}^{-8}+6 x \,{\mathrm e}^{-4}+6\right ) {\mathrm e}^{-x \,{\mathrm e}^{-4}}}{3}\right )\) | \(117\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.39, size = 41, normalized size = 1.95 \begin {gather*} -10 \, {\left (x^{3} + 3 \, x^{2} + 6 \, x + 6\right )} e^{\left (-x - 4\right )} + 30 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x - 4\right )} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 15, normalized size = 0.71 \begin {gather*} -x-10\,x^3\,{\mathrm {e}}^{-x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.67 \begin {gather*} - 10 x^{3} e^{- x - 4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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