Optimal. Leaf size=20 \[ -e^{-6+x}+2 e^x-\frac {5 \log (2)}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {14, 2194} \begin {gather*} \left (1-2 e^6\right ) \left (-e^{x-6}\right )-\frac {\log (32)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{-6+x} \left (-1+2 e^6\right )+\frac {\log (32)}{x^2}\right ) \, dx\\ &=-\frac {\log (32)}{x}+\left (-1+2 e^6\right ) \int e^{-6+x} \, dx\\ &=-e^{-6+x} \left (1-2 e^6\right )-\frac {\log (32)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 1.00 \begin {gather*} -e^{-6+x}+2 e^x-\frac {\log (32)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 25, normalized size = 1.25 \begin {gather*} \frac {{\left ({\left (2 \, x e^{6} - x\right )} e^{x} - 5 \, e^{6} \log \relax (2)\right )} e^{\left (-6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 25, normalized size = 1.25 \begin {gather*} \frac {{\left (2 \, x e^{\left (x + 6\right )} - x e^{x} - 5 \, e^{6} \log \relax (2)\right )} e^{\left (-6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.95
method | result | size |
default | \(-{\mathrm e}^{x} {\mathrm e}^{-6}-\frac {5 \ln \relax (2)}{x}+2 \,{\mathrm e}^{x}\) | \(19\) |
risch | \(-{\mathrm e}^{x} {\mathrm e}^{-6}-\frac {5 \ln \relax (2)}{x}+2 \,{\mathrm e}^{x}\) | \(19\) |
norman | \(\frac {\left (2 \,{\mathrm e}^{6}-1\right ) {\mathrm e}^{-6} x \,{\mathrm e}^{x}-5 \ln \relax (2)}{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 18, normalized size = 0.90 \begin {gather*} -\frac {5 \, \log \relax (2)}{x} - e^{\left (x - 6\right )} + 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.92, size = 16, normalized size = 0.80 \begin {gather*} -{\mathrm {e}}^x\,\left ({\mathrm {e}}^{-6}-2\right )-\frac {\ln \left (32\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 0.95 \begin {gather*} \frac {\left (-1 + 2 e^{6}\right ) e^{x}}{e^{6}} - \frac {5 \log {\relax (2 )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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