Optimal. Leaf size=20 \[ 259 e^{-\frac {x}{\log \left (\frac {16 x}{\frac {4}{3}+x}\right )}} \]
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Rubi [A] time = 0.53, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6706} \begin {gather*} 259 e^{-\frac {x}{\log \left (\frac {48 x}{3 x+4}\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=259 e^{-\frac {x}{\log \left (\frac {48 x}{4+3 x}\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 20, normalized size = 1.00 \begin {gather*} 259 e^{-\frac {x}{\log \left (\frac {48 x}{4+3 x}\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 19, normalized size = 0.95 \begin {gather*} 259 \, e^{\left (-\frac {x}{\log \left (\frac {48 \, x}{3 \, x + 4}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 19, normalized size = 0.95 \begin {gather*} 259 \, e^{\left (-\frac {x}{\log \left (\frac {48 \, x}{3 \, x + 4}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 20, normalized size = 1.00
method | result | size |
risch | \(259 \,{\mathrm e}^{-\frac {x}{\ln \left (\frac {48 x}{4+3 x}\right )}}\) | \(20\) |
norman | \(259 \,{\mathrm e}^{-\frac {x}{\ln \left (\frac {48 x}{4+3 x}\right )}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -259 \, \int \frac {{\left ({\left (3 \, x + 4\right )} \log \left (\frac {48 \, x}{3 \, x + 4}\right ) - 4\right )} e^{\left (-\frac {x}{\log \left (\frac {48 \, x}{3 \, x + 4}\right )}\right )}}{{\left (3 \, x + 4\right )} \log \left (\frac {48 \, x}{3 \, x + 4}\right )^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 19, normalized size = 0.95 \begin {gather*} 259\,{\mathrm {e}}^{-\frac {x}{\ln \left (\frac {48\,x}{3\,x+4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.46, size = 14, normalized size = 0.70 \begin {gather*} 259 e^{- \frac {x}{\log {\left (\frac {48 x}{3 x + 4} \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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