Optimal. Leaf size=28 \[ \frac {x \log (9)}{x+\frac {x}{1+4 e^3-\frac {x}{4 \log (2)}}} \]
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Rubi [A]
time = 0.02, antiderivative size = 21, normalized size of antiderivative = 0.75, number of steps
used = 4, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 2006, 27,
32} \begin {gather*} \frac {4 \log (2) \log (9)}{x-8 \left (1+2 e^3\right ) \log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 2006
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((4 \log (2) \log (9)) \int \frac {1}{x^2+\left (-16 x-32 e^3 x\right ) \log (2)+\left (64+256 e^3+256 e^6\right ) \log ^2(2)} \, dx\right )\\ &=-\left ((4 \log (2) \log (9)) \int \frac {1}{x^2-16 \left (1+2 e^3\right ) x \log (2)+64 \left (\log (2)+e^3 \log (4)\right )^2} \, dx\right )\\ &=-\left ((4 \log (2) \log (9)) \int \frac {1}{\left (x-8 \left (1+2 e^3\right ) \log (2)\right )^2} \, dx\right )\\ &=\frac {4 \log (2) \log (9)}{x-8 \left (1+2 e^3\right ) \log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 0.75 \begin {gather*} \frac {4 \log (2) \log (9)}{x-8 \left (\log (2)+e^3 \log (4)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.46, size = 22, normalized size = 0.79
method | result | size |
risch | \(-\frac {\ln \left (2\right ) \ln \left (3\right )}{2 \left ({\mathrm e}^{3} \ln \left (2\right )+\frac {\ln \left (2\right )}{2}-\frac {x}{16}\right )}\) | \(22\) |
gosper | \(-\frac {8 \ln \left (3\right ) \ln \left (2\right )}{16 \,{\mathrm e}^{3} \ln \left (2\right )+8 \ln \left (2\right )-x}\) | \(23\) |
norman | \(-\frac {8 \ln \left (3\right ) \ln \left (2\right )}{16 \,{\mathrm e}^{3} \ln \left (2\right )+8 \ln \left (2\right )-x}\) | \(23\) |
meijerg | \(\frac {\ln \left (2\right ) \ln \left (3\right ) x}{\left (-16 \,{\mathrm e}^{3} \ln \left (2\right )-8 \ln \left (2\right )\right ) \left (2 \,{\mathrm e}^{3} \ln \left (2\right )+\ln \left (2\right )\right ) \left (1-\frac {x}{8 \left (2 \,{\mathrm e}^{3} \ln \left (2\right )+\ln \left (2\right )\right )}\right )}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 22, normalized size = 0.79 \begin {gather*} -\frac {8 \, \log \left (3\right ) \log \left (2\right )}{8 \, {\left (2 \, e^{3} + 1\right )} \log \left (2\right ) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 22, normalized size = 0.79 \begin {gather*} -\frac {8 \, \log \left (3\right ) \log \left (2\right )}{8 \, {\left (2 \, e^{3} + 1\right )} \log \left (2\right ) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 22, normalized size = 0.79 \begin {gather*} \frac {8 \log {\left (2 \right )} \log {\left (3 \right )}}{x - 16 e^{3} \log {\left (2 \right )} - 8 \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 22, normalized size = 0.79 \begin {gather*} -\frac {8 \, \log \left (3\right ) \log \left (2\right )}{16 \, e^{3} \log \left (2\right ) - x + 8 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.20, size = 22, normalized size = 0.79 \begin {gather*} -\frac {8\,\ln \left (2\right )\,\ln \left (3\right )}{8\,\ln \left (2\right )-x+16\,{\mathrm {e}}^3\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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