Optimal. Leaf size=17 \[ \frac {9 e^{-x}}{2 \log \left (\frac {4 x}{21}\right )} \]
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Rubi [A] time = 0.33, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {12, 6741, 2202} \begin {gather*} \frac {9 e^{-x}}{2 \log \left (\frac {4 x}{21}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2202
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {-9 e^{-x}-9 e^{-x} x \log \left (\frac {4 x}{21}\right )}{x \log ^2\left (\frac {4 x}{21}\right )} \, dx\\ &=\frac {1}{2} \int \frac {9 e^{-x} \left (-1-x \log \left (\frac {4 x}{21}\right )\right )}{x \log ^2\left (\frac {4 x}{21}\right )} \, dx\\ &=\frac {9}{2} \int \frac {e^{-x} \left (-1-x \log \left (\frac {4 x}{21}\right )\right )}{x \log ^2\left (\frac {4 x}{21}\right )} \, dx\\ &=\frac {9 e^{-x}}{2 \log \left (\frac {4 x}{21}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {9 e^{-x}}{2 \log \left (\frac {4 x}{21}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 \, e^{\left (-x + \log \relax (3)\right )}}{2 \, \log \left (\frac {4}{21} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 12, normalized size = 0.71 \begin {gather*} \frac {9 \, e^{\left (-x\right )}}{2 \, \log \left (\frac {4}{21} \, 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 = 0.76
method | result | size |
risch | \(\frac {9 \,{\mathrm e}^{-x}}{2 \ln \left (\frac {4 x}{21}\right )}\) | \(13\) |
norman | \(\frac {3 \,{\mathrm e}^{\ln \relax (3)-x}}{2 \ln \left (\frac {4 x}{21}\right )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 21, normalized size = 1.24 \begin {gather*} -\frac {9 \, e^{\left (-x\right )}}{2 \, {\left (\log \relax (7) + \log \relax (3) - 2 \, \log \relax (2) - \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.83, size = 12, normalized size = 0.71 \begin {gather*} \frac {9\,{\mathrm {e}}^{-x}}{2\,\ln \left (\frac {4\,x}{21}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 12, normalized size = 0.71 \begin {gather*} \frac {9 e^{- x}}{2 \log {\left (\frac {4 x}{21} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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