Optimal. Leaf size=22 \[ \log \left (\frac {1}{x^2}\right )-\frac {3}{25 \left (4-\frac {6}{x \log (x)}\right )} \]
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Rubi [F]
time = 0.30, 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 {-900+9 x+1209 x \log (x)-400 x^2 \log ^2(x)}{450 x-600 x^2 \log (x)+200 x^3 \log ^2(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 {-900+9 x+1209 x \log (x)-400 x^2 \log ^2(x)}{50 x (3-2 x \log (x))^2} \, dx\\ &=\frac {1}{50} \int \frac {-900+9 x+1209 x \log (x)-400 x^2 \log ^2(x)}{x (3-2 x \log (x))^2} \, dx\\ &=\frac {1}{50} \int \left (-\frac {100}{x}+\frac {9 (3+2 x)}{2 x (-3+2 x \log (x))^2}+\frac {9}{2 x (-3+2 x \log (x))}\right ) \, dx\\ &=-2 \log (x)+\frac {9}{100} \int \frac {3+2 x}{x (-3+2 x \log (x))^2} \, dx+\frac {9}{100} \int \frac {1}{x (-3+2 x \log (x))} \, dx\\ &=-2 \log (x)+\frac {9}{100} \int \frac {1}{x (-3+2 x \log (x))} \, dx+\frac {9}{100} \int \left (\frac {2}{(-3+2 x \log (x))^2}+\frac {3}{x (-3+2 x \log (x))^2}\right ) \, dx\\ &=-2 \log (x)+\frac {9}{100} \int \frac {1}{x (-3+2 x \log (x))} \, dx+\frac {9}{50} \int \frac {1}{(-3+2 x \log (x))^2} \, dx+\frac {27}{100} \int \frac {1}{x (-3+2 x \log (x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 22, normalized size = 1.00 \begin {gather*} \frac {1}{50} \left (-100 \log (x)+\frac {9}{2 (3-2 x \log (x))}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.32, size = 25, normalized size = 1.14
method | result | size |
norman | \(-\frac {9}{100 \left (2 x \ln \left (x \right )-3\right )}-2 \ln \left (x \right )\) | \(17\) |
risch | \(-\frac {9}{100 \left (2 x \ln \left (x \right )-3\right )}-2 \ln \left (x \right )\) | \(17\) |
default | \(-\frac {-300 \ln \left (x \right )+200 x \ln \left (x \right )^{2}+\frac {9}{2}}{50 \left (2 x \ln \left (x \right )-3\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 16, normalized size = 0.73 \begin {gather*} -\frac {9}{100 \, {\left (2 \, x \log \left (x\right ) - 3\right )}} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 24, normalized size = 1.09 \begin {gather*} -\frac {400 \, x \log \left (x\right )^{2} - 600 \, \log \left (x\right ) + 9}{100 \, {\left (2 \, x \log \left (x\right ) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 15, normalized size = 0.68 \begin {gather*} - 2 \log {\left (x \right )} - \frac {9}{200 x \log {\left (x \right )} - 300} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 16, normalized size = 0.73 \begin {gather*} -\frac {9}{100 \, {\left (2 \, x \log \left (x\right ) - 3\right )}} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.24, size = 16, normalized size = 0.73 \begin {gather*} -2\,\ln \left (x\right )-\frac {9}{100\,\left (2\,x\,\ln \left (x\right )-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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