Optimal. Leaf size=21 \[ \frac {1}{-8+3^{5/x}-x-\log (x \log (x))} \]
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Rubi [A]
time = 0.29, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps
used = 2, number of rules used = 2, integrand size = 116, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6820, 6818}
\begin {gather*} -\frac {1}{x-243^{\frac {1}{x}}+\log (x \log (x))+8} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x+\left (x+x^2+5\ 243^{\frac {1}{x}} \log (3)\right ) \log (x)}{x^2 \log (x) \left (8-243^{\frac {1}{x}}+x+\log (x \log (x))\right )^2} \, dx\\ &=-\frac {1}{8-243^{\frac {1}{x}}+x+\log (x \log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 19, normalized size = 0.90 \begin {gather*} -\frac {1}{8-243^{\frac {1}{x}}+x+\log (x \log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.32, size = 98, normalized size = 4.67
method | result | size |
risch | \(-\frac {2 i}{\pi \,\mathrm {csgn}\left (i \ln \left (x \right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \ln \left (x \right )\right )-\pi \,\mathrm {csgn}\left (i \ln \left (x \right )\right ) \mathrm {csgn}\left (i x \ln \left (x \right )\right )^{2}-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \ln \left (x \right )\right )^{2}+\pi \mathrm {csgn}\left (i x \ln \left (x \right )\right )^{3}+2 i x -2 i 243^{\frac {1}{x}}+2 i \ln \left (x \right )+2 i \ln \left (\ln \left (x \right )\right )+16 i}\) | \(98\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 23, normalized size = 1.10 \begin {gather*} \frac {1}{3^{\frac {5}{x}} - x - \log \left (x\right ) - \log \left (\log \left (x\right )\right ) - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 1.00 \begin {gather*} \frac {1}{3^{\frac {5}{x}} - x - \log \left (x \log \left (x\right )\right ) - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 19, normalized size = 0.90 \begin {gather*} \frac {1}{- x + e^{\frac {5 \log {\left (3 \right )}}{x}} - \log {\left (x \log {\left (x \right )} \right )} - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.68, size = 21, normalized size = 1.00 \begin {gather*} -\frac {1}{x+\ln \left (x\,\ln \left (x\right )\right )-3^{5/x}+8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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