Optimal. Leaf size=32 \[ \frac {x (5+x) \left (-e^{-5+x}+x\right ) \left (x-x^2 (5+x)\right )}{6-\log (4)} \]
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Rubi [B] time = 0.26, antiderivative size = 124, normalized size of antiderivative = 3.88, number of steps used = 24, number of rules used = 4, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {12, 2196, 2176, 2194} \begin {gather*} -\frac {x^6}{6-\log (4)}+\frac {e^{x-5} x^5}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {10 e^{x-5} x^4}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {24 e^{x-5} x^3}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}-\frac {5 e^{x-5} x^2}{6-\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-15 x^2+96 x^3+50 x^4+6 x^5+e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right )\right ) \, dx}{-6+\log (4)}\\ &=\frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {\int e^{-5+x} \left (10 x-67 x^2-64 x^3-15 x^4-x^5\right ) \, dx}{-6+\log (4)}\\ &=\frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {\int \left (10 e^{-5+x} x-67 e^{-5+x} x^2-64 e^{-5+x} x^3-15 e^{-5+x} x^4-e^{-5+x} x^5\right ) \, dx}{-6+\log (4)}\\ &=\frac {5 x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {10 \int e^{-5+x} x \, dx}{6-\log (4)}+\frac {15 \int e^{-5+x} x^4 \, dx}{6-\log (4)}+\frac {64 \int e^{-5+x} x^3 \, dx}{6-\log (4)}+\frac {67 \int e^{-5+x} x^2 \, dx}{6-\log (4)}-\frac {\int e^{-5+x} x^5 \, dx}{-6+\log (4)}\\ &=-\frac {10 e^{-5+x} x}{6-\log (4)}+\frac {67 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {64 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {15 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {5 \int e^{-5+x} x^4 \, dx}{6-\log (4)}+\frac {10 \int e^{-5+x} \, dx}{6-\log (4)}-\frac {60 \int e^{-5+x} x^3 \, dx}{6-\log (4)}-\frac {134 \int e^{-5+x} x \, dx}{6-\log (4)}-\frac {192 \int e^{-5+x} x^2 \, dx}{6-\log (4)}\\ &=\frac {10 e^{-5+x}}{6-\log (4)}-\frac {144 e^{-5+x} x}{6-\log (4)}-\frac {125 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {4 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {20 \int e^{-5+x} x^3 \, dx}{6-\log (4)}+\frac {134 \int e^{-5+x} \, dx}{6-\log (4)}+\frac {180 \int e^{-5+x} x^2 \, dx}{6-\log (4)}+\frac {384 \int e^{-5+x} x \, dx}{6-\log (4)}\\ &=\frac {144 e^{-5+x}}{6-\log (4)}+\frac {240 e^{-5+x} x}{6-\log (4)}+\frac {55 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {60 \int e^{-5+x} x^2 \, dx}{6-\log (4)}-\frac {360 \int e^{-5+x} x \, dx}{6-\log (4)}-\frac {384 \int e^{-5+x} \, dx}{6-\log (4)}\\ &=-\frac {240 e^{-5+x}}{6-\log (4)}-\frac {120 e^{-5+x} x}{6-\log (4)}-\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}+\frac {120 \int e^{-5+x} x \, dx}{6-\log (4)}+\frac {360 \int e^{-5+x} \, dx}{6-\log (4)}\\ &=\frac {120 e^{-5+x}}{6-\log (4)}-\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}-\frac {120 \int e^{-5+x} \, dx}{6-\log (4)}\\ &=-\frac {5 e^{-5+x} x^2}{6-\log (4)}+\frac {5 x^3}{6-\log (4)}+\frac {24 e^{-5+x} x^3}{6-\log (4)}-\frac {24 x^4}{6-\log (4)}+\frac {10 e^{-5+x} x^4}{6-\log (4)}-\frac {10 x^5}{6-\log (4)}+\frac {e^{-5+x} x^5}{6-\log (4)}-\frac {x^6}{6-\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 37, normalized size = 1.16 \begin {gather*} \frac {x^2 \left (-e^x+e^5 x\right ) \left (-5+24 x+10 x^2+x^3\right )}{e^5 (-6+\log (4))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 52, normalized size = 1.62 \begin {gather*} \frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \relax (2) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 52, normalized size = 1.62 \begin {gather*} \frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \relax (2) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 87, normalized size = 2.72
method | result | size |
derivativedivides | \(\frac {-9875 \,{\mathrm e}^{x -5} \left (x -5\right )-12250 \,{\mathrm e}^{x -5}-3105 \,{\mathrm e}^{x -5} \left (x -5\right )^{2}-474 \,{\mathrm e}^{x -5} \left (x -5\right )^{3}-35 \,{\mathrm e}^{x -5} \left (x -5\right )^{4}-{\mathrm e}^{x -5} \left (x -5\right )^{5}-5 x^{3}+24 x^{4}+10 x^{5}+x^{6}}{2 \ln \relax (2)-6}\) | \(87\) |
default | \(\frac {-9875 \,{\mathrm e}^{x -5} \left (x -5\right )-12250 \,{\mathrm e}^{x -5}-3105 \,{\mathrm e}^{x -5} \left (x -5\right )^{2}-474 \,{\mathrm e}^{x -5} \left (x -5\right )^{3}-35 \,{\mathrm e}^{x -5} \left (x -5\right )^{4}-{\mathrm e}^{x -5} \left (x -5\right )^{5}-5 x^{3}+24 x^{4}+10 x^{5}+x^{6}}{2 \ln \relax (2)-6}\) | \(87\) |
risch | \(\frac {x^{6}}{2 \ln \relax (2)-6}+\frac {10 x^{5}}{2 \ln \relax (2)-6}+\frac {24 x^{4}}{2 \ln \relax (2)-6}-\frac {5 x^{3}}{2 \ln \relax (2)-6}+\frac {\left (-x^{5}-10 x^{4}-24 x^{3}+5 x^{2}\right ) {\mathrm e}^{x -5}}{2 \ln \relax (2)-6}\) | \(87\) |
norman | \(-\frac {5 x^{3}}{2 \left (\ln \relax (2)-3\right )}+\frac {12 x^{4}}{\ln \relax (2)-3}+\frac {5 x^{5}}{\ln \relax (2)-3}+\frac {x^{6}}{2 \ln \relax (2)-6}+\frac {5 x^{2} {\mathrm e}^{x -5}}{2 \left (\ln \relax (2)-3\right )}-\frac {12 x^{3} {\mathrm e}^{x -5}}{\ln \relax (2)-3}-\frac {5 x^{4} {\mathrm e}^{x -5}}{\ln \relax (2)-3}-\frac {x^{5} {\mathrm e}^{x -5}}{2 \left (\ln \relax (2)-3\right )}\) | \(106\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 52, normalized size = 1.62 \begin {gather*} \frac {x^{6} + 10 \, x^{5} + 24 \, x^{4} - 5 \, x^{3} - {\left (x^{5} + 10 \, x^{4} + 24 \, x^{3} - 5 \, x^{2}\right )} e^{\left (x - 5\right )}}{2 \, {\left (\log \relax (2) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 62, normalized size = 1.94 \begin {gather*} \frac {5\,x^2\,{\mathrm {e}}^{x-5}-24\,x^3\,{\mathrm {e}}^{x-5}-10\,x^4\,{\mathrm {e}}^{x-5}-x^5\,{\mathrm {e}}^{x-5}-5\,x^3+24\,x^4+10\,x^5+x^6}{\ln \relax (4)-6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 71, normalized size = 2.22 \begin {gather*} \frac {x^{6}}{-6 + 2 \log {\relax (2 )}} + \frac {5 x^{5}}{-3 + \log {\relax (2 )}} + \frac {12 x^{4}}{-3 + \log {\relax (2 )}} - \frac {5 x^{3}}{-6 + 2 \log {\relax (2 )}} + \frac {\left (- x^{5} - 10 x^{4} - 24 x^{3} + 5 x^{2}\right ) e^{x - 5}}{-6 + 2 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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