Optimal. Leaf size=29 \[ \frac {-13+\frac {-3+\frac {3}{x \left (-\frac {2}{x}+\log (9 x)\right )}}{x}}{x} \]
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Rubi [F]
time = 0.42, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {36+49 x+\left (-33 x-52 x^2\right ) \log (9 x)+\left (6 x^2+13 x^3\right ) \log ^2(9 x)}{4 x^3-4 x^4 \log (9 x)+x^5 \log ^2(9 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {36+49 x-x (33+52 x) \log (9 x)+x^2 (6+13 x) \log ^2(9 x)}{x^3 (2-x \log (9 x))^2} \, dx\\ &=\int \left (\frac {6+13 x}{x^3}-\frac {3 (2+x)}{x^3 (-2+x \log (9 x))^2}-\frac {9}{x^3 (-2+x \log (9 x))}\right ) \, dx\\ &=-\left (3 \int \frac {2+x}{x^3 (-2+x \log (9 x))^2} \, dx\right )-9 \int \frac {1}{x^3 (-2+x \log (9 x))} \, dx+\int \frac {6+13 x}{x^3} \, dx\\ &=-\frac {(6+13 x)^2}{12 x^2}-3 \int \left (\frac {2}{x^3 (-2+x \log (9 x))^2}+\frac {1}{x^2 (-2+x \log (9 x))^2}\right ) \, dx-9 \int \frac {1}{x^3 (-2+x \log (9 x))} \, dx\\ &=-\frac {(6+13 x)^2}{12 x^2}-3 \int \frac {1}{x^2 (-2+x \log (9 x))^2} \, dx-6 \int \frac {1}{x^3 (-2+x \log (9 x))^2} \, dx-9 \int \frac {1}{x^3 (-2+x \log (9 x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 21, normalized size = 0.72 \begin {gather*} \frac {-3-13 x+\frac {3}{-2+x \log (9 x)}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.74, size = 38, normalized size = 1.31
method | result | size |
risch | \(-\frac {13 x +3}{x^{2}}+\frac {3}{x^{2} \left (x \ln \left (9 x \right )-2\right )}\) | \(27\) |
norman | \(\frac {9-13 x^{2} \ln \left (9 x \right )+26 x -3 x \ln \left (9 x \right )}{x^{2} \left (x \ln \left (9 x \right )-2\right )}\) | \(36\) |
derivativedivides | \(\frac {729-243 x \ln \left (9 x \right )-1053 x^{2} \ln \left (9 x \right )+2106 x}{9 x^{2} \left (9 x \ln \left (9 x \right )-18\right )}\) | \(38\) |
default | \(\frac {729-243 x \ln \left (9 x \right )-1053 x^{2} \ln \left (9 x \right )+2106 x}{9 x^{2} \left (9 x \ln \left (9 x \right )-18\right )}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 53, normalized size = 1.83 \begin {gather*} -\frac {26 \, x^{2} \log \left (3\right ) + 2 \, x {\left (3 \, \log \left (3\right ) - 13\right )} + {\left (13 \, x^{2} + 3 \, x\right )} \log \left (x\right ) - 9}{2 \, x^{3} \log \left (3\right ) + x^{3} \log \left (x\right ) - 2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 37, normalized size = 1.28 \begin {gather*} -\frac {{\left (13 \, x^{2} + 3 \, x\right )} \log \left (9 \, x\right ) - 26 \, x - 9}{x^{3} \log \left (9 \, x\right ) - 2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 24, normalized size = 0.83 \begin {gather*} \frac {3}{x^{3} \log {\left (9 x \right )} - 2 x^{2}} + \frac {- 13 x - 3}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 29, normalized size = 1.00 \begin {gather*} \frac {3}{x^{3} \log \left (9 \, x\right ) - 2 \, x^{2}} - \frac {13 \, x + 3}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.24, size = 35, normalized size = 1.21 \begin {gather*} \frac {26\,x-3\,x\,\ln \left (9\,x\right )-13\,x^2\,\ln \left (9\,x\right )+9}{x^2\,\left (x\,\ln \left (9\,x\right )-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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