Optimal. Leaf size=26 \[ -e^5+\left (-\frac {1}{2 x^2}+x-6 e^{-1+x} x\right ) \log (4) \]
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Rubi [A]
time = 0.25, antiderivative size = 35, normalized size of antiderivative = 1.35, number of steps
used = 5, number of rules used = 4, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6820, 12, 2207,
2225} \begin {gather*} -\frac {\log (4)}{2 x^2}+x \log (4)+6 e^{x-1} \log (4)-6 e^{x-1} (x+1) \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {1}{x^3}-6 e^{-1+x} (1+x)\right ) \log (4) \, dx\\ &=\log (4) \int \left (1+\frac {1}{x^3}-6 e^{-1+x} (1+x)\right ) \, dx\\ &=-\frac {\log (4)}{2 x^2}+x \log (4)-(6 \log (4)) \int e^{-1+x} (1+x) \, dx\\ &=-\frac {\log (4)}{2 x^2}+x \log (4)-6 e^{-1+x} (1+x) \log (4)+(6 \log (4)) \int e^{-1+x} \, dx\\ &=6 e^{-1+x} \log (4)-\frac {\log (4)}{2 x^2}+x \log (4)-6 e^{-1+x} (1+x) \log (4)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 20, normalized size = 0.77 \begin {gather*} \left (-\frac {1}{2 x^2}+x-6 e^{-1+x} x\right ) \log (4) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.46, size = 39, normalized size = 1.50
method | result | size |
risch | \(2 x \ln \left (2\right )-\frac {\ln \left (2\right )}{x^{2}}-12 x \ln \left (2\right ) {\mathrm e}^{x -1}\) | \(23\) |
derivativedivides | \(-\frac {\ln \left (2\right )}{x^{2}}-2 \left (1-x \right ) \ln \left (2\right )-12 \ln \left (2\right ) {\mathrm e}^{x -1}+12 \ln \left (2\right ) {\mathrm e}^{x -1} \left (1-x \right )\) | \(39\) |
default | \(-\frac {\ln \left (2\right )}{x^{2}}-2 \left (1-x \right ) \ln \left (2\right )-12 \ln \left (2\right ) {\mathrm e}^{x -1}+12 \ln \left (2\right ) {\mathrm e}^{x -1} \left (1-x \right )\) | \(39\) |
norman | \(\frac {\left (-12 x^{3} \ln \left (2\right )-\ln \left (2\right ) {\mathrm e}^{1-x}+2 x^{3} \ln \left (2\right ) {\mathrm e}^{1-x}\right ) {\mathrm e}^{x -1}}{x^{2}}\) | \(44\) |
meijerg | \(2 \ln \left (2\right ) {\mathrm e}^{x -2-{\mathrm e}^{-1} x} \left (1-{\mathrm e}\right )^{2} \left (\frac {{\mathrm e}^{2} \left (9 x^{2} {\mathrm e}^{-2} \left (1-{\mathrm e}\right )^{2}+12 x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )+6\right )}{12 x^{2} \left (1-{\mathrm e}\right )^{2}}-\frac {{\mathrm e}^{2+x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )} \left (3+3 x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )\right )}{6 x^{2} \left (1-{\mathrm e}\right )^{2}}-\frac {\ln \left (-x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )\right )}{2}-\frac {\expIntegral \left (1, -x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )\right )}{2}-\frac {5}{4}+\frac {\ln \left (x \right )}{2}+\frac {i \pi }{2}+\frac {\ln \left (1-{\mathrm e}\right )}{2}-\frac {{\mathrm e}^{2}}{2 x^{2} \left (1-{\mathrm e}\right )^{2}}-\frac {{\mathrm e}}{x \left (1-{\mathrm e}\right )}\right )-\frac {2 \ln \left (2\right ) {\mathrm e}^{x -{\mathrm e}^{-1} x +1} \left (1-{\mathrm e}^{x \,{\mathrm e}^{-1} \left (1-{\mathrm e}\right )}\right )}{1-{\mathrm e}}-12 \ln \left (2\right ) {\mathrm e}^{x -{\mathrm e}^{-1} x +1} \left (1-\frac {\left (2-2 \,{\mathrm e}^{-1} x \right ) {\mathrm e}^{{\mathrm e}^{-1} x}}{2}\right )+12 \ln \left (2\right ) {\mathrm e}^{x -{\mathrm e}^{-1} x} \left (1-{\mathrm e}^{{\mathrm e}^{-1} x}\right )\) | \(269\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 32, normalized size = 1.23 \begin {gather*} -12 \, {\left (x - 1\right )} e^{\left (x - 1\right )} \log \left (2\right ) + 2 \, x \log \left (2\right ) - 12 \, e^{\left (x - 1\right )} \log \left (2\right ) - \frac {\log \left (2\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 28, normalized size = 1.08 \begin {gather*} -\frac {12 \, x^{3} e^{\left (x - 1\right )} \log \left (2\right ) - {\left (2 \, x^{3} - 1\right )} \log \left (2\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 24, normalized size = 0.92 \begin {gather*} - 12 x e^{x - 1} \log {\left (2 \right )} + 2 x \log {\left (2 \right )} - \frac {\log {\left (2 \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 31, normalized size = 1.19 \begin {gather*} \frac {{\left (2 \, x^{3} e \log \left (2\right ) - 12 \, x^{3} e^{x} \log \left (2\right ) - e \log \left (2\right )\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 23, normalized size = 0.88 \begin {gather*} x\,{\mathrm {e}}^{-1}\,\ln \left (2\right )\,\left (2\,\mathrm {e}-12\,{\mathrm {e}}^x\right )-\frac {\ln \left (2\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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