Optimal. Leaf size=20 \[ \frac {16 e^{8-x} (3+\log (2))^2}{7 x^2} \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 2197} \begin {gather*} \frac {16 e^{8-x} (3+\log (2))^2}{7 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{7} \int \frac {e^{-x} \left (e^8 (-288-144 x)+e^8 (-192-96 x) \log (2)+e^8 (-32-16 x) \log ^2(2)\right )}{x^3} \, dx\\ &=\frac {16 e^{8-x} (3+\log (2))^2}{7 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {16 e^{8-x} (3+\log (2))^2}{7 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 27, normalized size = 1.35 \begin {gather*} \frac {16 \, {\left (e^{8} \log \relax (2)^{2} + 6 \, e^{8} \log \relax (2) + 9 \, e^{8}\right )} e^{\left (-x\right )}}{7 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 35, normalized size = 1.75 \begin {gather*} \frac {16 \, {\left (e^{\left (-x + 8\right )} \log \relax (2)^{2} + 6 \, e^{\left (-x + 8\right )} \log \relax (2) + 9 \, e^{\left (-x + 8\right )}\right )}}{7 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 1.10
method | result | size |
risch | \(\frac {16 \left (\ln \relax (2)^{2}+6 \ln \relax (2)+9\right ) {\mathrm e}^{8-x}}{7 x^{2}}\) | \(22\) |
gosper | \(\frac {16 \,{\mathrm e}^{8} \left (\ln \relax (2)^{2}+6 \ln \relax (2)+9\right ) {\mathrm e}^{-x}}{7 x^{2}}\) | \(24\) |
norman | \(\frac {\left (\frac {16 \,{\mathrm e}^{8} \ln \relax (2)^{2}}{7}+\frac {96 \,{\mathrm e}^{8} \ln \relax (2)}{7}+\frac {144 \,{\mathrm e}^{8}}{7}\right ) {\mathrm e}^{-x}}{x^{2}}\) | \(34\) |
default | \(-\frac {288 \,{\mathrm e}^{8} \left (-\frac {{\mathrm e}^{-x}}{2 x^{2}}+\frac {{\mathrm e}^{-x}}{2 x}-\frac {\expIntegralEi \left (1, x\right )}{2}\right )}{7}-\frac {144 \,{\mathrm e}^{8} \left (-\frac {{\mathrm e}^{-x}}{x}+\expIntegralEi \left (1, x\right )\right )}{7}+\frac {96 \,{\mathrm e}^{-x} {\mathrm e}^{8} \ln \relax (2)}{7 x^{2}}+\frac {16 \,{\mathrm e}^{-x} {\mathrm e}^{8} \ln \relax (2)^{2}}{7 x^{2}}\) | \(83\) |
meijerg | \(\frac {\left (-16 \,{\mathrm e}^{8} \ln \relax (2)^{2}-96 \,{\mathrm e}^{8} \ln \relax (2)-144 \,{\mathrm e}^{8}\right ) \left (-\frac {1}{x}+1+\frac {-2 x +2}{2 x}-\frac {{\mathrm e}^{-x}}{x}+\expIntegralEi \left (1, x\right )\right )}{7}-\frac {32 \,{\mathrm e}^{8} \ln \relax (2)^{2} \left (-\frac {1}{2 x^{2}}+\frac {1}{x}-\frac {3}{4}+\frac {9 x^{2}-12 x +6}{12 x^{2}}-\frac {\left (-3 x +3\right ) {\mathrm e}^{-x}}{6 x^{2}}-\frac {\expIntegralEi \left (1, x\right )}{2}\right )}{7}-\frac {192 \,{\mathrm e}^{8} \ln \relax (2) \left (-\frac {1}{2 x^{2}}+\frac {1}{x}-\frac {3}{4}+\frac {9 x^{2}-12 x +6}{12 x^{2}}-\frac {\left (-3 x +3\right ) {\mathrm e}^{-x}}{6 x^{2}}-\frac {\expIntegralEi \left (1, x\right )}{2}\right )}{7}-\frac {288 \,{\mathrm e}^{8} \left (-\frac {1}{2 x^{2}}+\frac {1}{x}-\frac {3}{4}+\frac {9 x^{2}-12 x +6}{12 x^{2}}-\frac {\left (-3 x +3\right ) {\mathrm e}^{-x}}{6 x^{2}}-\frac {\expIntegralEi \left (1, x\right )}{2}\right )}{7}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.41, size = 55, normalized size = 2.75 \begin {gather*} \frac {16}{7} \, e^{8} \Gamma \left (-1, x\right ) \log \relax (2)^{2} + \frac {32}{7} \, e^{8} \Gamma \left (-2, x\right ) \log \relax (2)^{2} + \frac {96}{7} \, e^{8} \Gamma \left (-1, x\right ) \log \relax (2) + \frac {192}{7} \, e^{8} \Gamma \left (-2, x\right ) \log \relax (2) + \frac {144}{7} \, e^{8} \Gamma \left (-1, x\right ) + \frac {288}{7} \, e^{8} \Gamma \left (-2, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 17, normalized size = 0.85 \begin {gather*} \frac {16\,{\mathrm {e}}^{8-x}\,{\left (\ln \relax (2)+3\right )}^2}{7\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 31, normalized size = 1.55 \begin {gather*} \frac {\left (16 e^{8} \log {\relax (2 )}^{2} + 96 e^{8} \log {\relax (2 )} + 144 e^{8}\right ) e^{- x}}{7 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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