Optimal. Leaf size=18 \[ e^x+x \log \left (4+\frac {1}{e^{166}}\right ) \log \left (\frac {4}{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2194, 2295} \begin {gather*} e^x+x \log \left (4+\frac {1}{e^{166}}\right ) \log \left (\frac {4}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (4+\frac {1}{e^{166}}\right ) \int \left (-1+\log \left (\frac {4}{x}\right )\right ) \, dx+\int e^x \, dx\\ &=e^x-x \log \left (4+\frac {1}{e^{166}}\right )+\log \left (4+\frac {1}{e^{166}}\right ) \int \log \left (\frac {4}{x}\right ) \, dx\\ &=e^x+x \log \left (4+\frac {1}{e^{166}}\right ) \log \left (\frac {4}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} e^x+x \log \left (4+\frac {1}{e^{166}}\right ) \log \left (\frac {4}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 21, normalized size = 1.17 \begin {gather*} x \log \left ({\left (4 \, e^{166} + 1\right )} e^{\left (-166\right )}\right ) \log \left (\frac {4}{x}\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 21, normalized size = 1.17 \begin {gather*} x \log \left ({\left (4 \, e^{166} + 1\right )} e^{\left (-166\right )}\right ) \log \left (\frac {4}{x}\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 1.17
method | result | size |
norman | \(\left (\ln \left (4 \,{\mathrm e}^{166}+1\right )-166\right ) x \ln \left (\frac {4}{x}\right )+{\mathrm e}^{x}\) | \(21\) |
risch | \(\left (\ln \left (4 \,{\mathrm e}^{166}+1\right )-166\right ) x \ln \left (\frac {4}{x}\right )+{\mathrm e}^{x}\) | \(21\) |
default | \(\ln \left (\left (4 \,{\mathrm e}^{166}+1\right ) {\mathrm e}^{-166}\right ) \ln \left (\frac {4}{x}\right ) x +{\mathrm e}^{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 21, normalized size = 1.17 \begin {gather*} x \log \left ({\left (4 \, e^{166} + 1\right )} e^{\left (-166\right )}\right ) \log \left (\frac {4}{x}\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 20, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^x+x\,\ln \left (\frac {4}{x}\right )\,\left (\ln \left (4\,{\mathrm {e}}^{166}+1\right )-166\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 20, normalized size = 1.11 \begin {gather*} \left (- 166 x + x \log {\left (1 + 4 e^{166} \right )}\right ) \log {\left (\frac {4}{x} \right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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