Optimal. Leaf size=15 \[ \frac {1}{2} e^{-32 x} \left (4+\log \left (\frac {16}{9}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2194} \begin {gather*} \frac {1}{2} e^{-32 x} \left (4+\log \left (\frac {16}{9}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (16 \left (4+\log \left (\frac {16}{9}\right )\right )\right ) \int e^{-32 x} \, dx\right )\\ &=\frac {1}{2} e^{-32 x} \left (4+\log \left (\frac {16}{9}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {1}{2} e^{-32 x} \left (4+\log \left (\frac {16}{9}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.03, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, {\left (\log \left (\frac {16}{9}\right ) + 4\right )} e^{\left (-32 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, {\left (\log \left (\frac {16}{9}\right ) + 4\right )} e^{\left (-32 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 0.87
method | result | size |
gosper | \(\frac {\left (\ln \left (\frac {16}{9}\right )+4\right ) {\mathrm e}^{-32 x}}{2}\) | \(13\) |
derivativedivides | \(-\left (-\frac {\ln \left (\frac {16}{9}\right )}{2}-2\right ) {\mathrm e}^{-32 x}\) | \(15\) |
default | \(-\frac {\left (-16 \ln \left (\frac {16}{9}\right )-64\right ) {\mathrm e}^{-32 x}}{32}\) | \(15\) |
norman | \(\left (2 \ln \relax (2)-\ln \relax (3)+2\right ) {\mathrm e}^{-32 x}\) | \(18\) |
meijerg | \(-\frac {\ln \left (\frac {16}{9}\right ) \left (1-{\mathrm e}^{-32 x}\right )}{2}-2+2 \,{\mathrm e}^{-32 x}\) | \(21\) |
risch | \(2 \,{\mathrm e}^{-32 x} \ln \relax (2)-{\mathrm e}^{-32 x} \ln \relax (3)+2 \,{\mathrm e}^{-32 x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, {\left (\log \left (\frac {16}{9}\right ) + 4\right )} e^{\left (-32 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.56, size = 9, normalized size = 0.60 \begin {gather*} {\mathrm {e}}^{-32\,x}\,\left (\ln \left (\frac {4}{3}\right )+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.93 \begin {gather*} \left (- \log {\relax (3 )} + 2 \log {\relax (2 )} + 2\right ) e^{- 32 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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