Optimal. Leaf size=24 \[ 5+\frac {\left (x-\frac {3}{\log (x)}+\log (x)\right )^2}{\left (-\frac {14}{3}-x\right )^2} \]
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Rubi [F]
time = 0.62, 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 {-2268-486 x+\left (270 x+162 x^2\right ) \log (x)+\left (-756 x+162 x^2\right ) \log ^2(x)+\left (576 x+306 x^2\right ) \log ^3(x)+\left (252+306 x-54 x^2\right ) \log ^4(x)-54 x \log ^5(x)}{\left (2744 x+1764 x^2+378 x^3+27 x^4\right ) \log ^3(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 {-2268-486 x+\left (270 x+162 x^2\right ) \log (x)+\left (-756 x+162 x^2\right ) \log ^2(x)+\left (576 x+306 x^2\right ) \log ^3(x)+\left (252+306 x-54 x^2\right ) \log ^4(x)-54 x \log ^5(x)}{x \left (2744+1764 x+378 x^2+27 x^3\right ) \log ^3(x)} \, dx\\ &=\int \left (\frac {18 (32+17 x)}{(14+3 x)^3}-\frac {162}{x (14+3 x)^2 \log ^3(x)}+\frac {54 (5+3 x)}{(14+3 x)^3 \log ^2(x)}+\frac {54 (-14+3 x)}{(14+3 x)^3 \log (x)}-\frac {18 \left (-14-17 x+3 x^2\right ) \log (x)}{x (14+3 x)^3}-\frac {54 \log ^2(x)}{(14+3 x)^3}\right ) \, dx\\ &=18 \int \frac {32+17 x}{(14+3 x)^3} \, dx-18 \int \frac {\left (-14-17 x+3 x^2\right ) \log (x)}{x (14+3 x)^3} \, dx+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx-54 \int \frac {\log ^2(x)}{(14+3 x)^3} \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx\\ &=\frac {9 (32+17 x)^2}{142 (14+3 x)^2}+\frac {9 \log ^2(x)}{(14+3 x)^2}-18 \int \frac {\log (x)}{x (14+3 x)^2} \, dx-18 \int \left (-\frac {\log (x)}{196 x}-\frac {28 \log (x)}{(14+3 x)^3}+\frac {17 \log (x)}{14 (14+3 x)^2}+\frac {3 \log (x)}{196 (14+3 x)}\right ) \, dx+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx\\ &=\frac {9 (32+17 x)^2}{142 (14+3 x)^2}+\frac {9 \log ^2(x)}{(14+3 x)^2}+\frac {9}{98} \int \frac {\log (x)}{x} \, dx-\frac {27}{98} \int \frac {\log (x)}{14+3 x} \, dx-\frac {9}{7} \int \frac {\log (x)}{x (14+3 x)} \, dx+\frac {27}{7} \int \frac {\log (x)}{(14+3 x)^2} \, dx-\frac {153}{7} \int \frac {\log (x)}{(14+3 x)^2} \, dx+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx+504 \int \frac {\log (x)}{(14+3 x)^3} \, dx\\ &=\frac {9 (32+17 x)^2}{142 (14+3 x)^2}-\frac {84 \log (x)}{(14+3 x)^2}-\frac {9 x \log (x)}{7 (14+3 x)}-\frac {9}{98} \log \left (1+\frac {3 x}{14}\right ) \log (x)+\frac {9 \log ^2(x)}{196}+\frac {9 \log ^2(x)}{(14+3 x)^2}+\frac {9}{98} \int \frac {\log \left (1+\frac {3 x}{14}\right )}{x} \, dx-\frac {9}{98} \int \frac {\log (x)}{x} \, dx-\frac {27}{98} \int \frac {1}{14+3 x} \, dx+\frac {27}{98} \int \frac {\log (x)}{14+3 x} \, dx+\frac {153}{98} \int \frac {1}{14+3 x} \, dx+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx+84 \int \frac {1}{x (14+3 x)^2} \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx\\ &=\frac {9 (32+17 x)^2}{142 (14+3 x)^2}-\frac {84 \log (x)}{(14+3 x)^2}-\frac {9 x \log (x)}{7 (14+3 x)}+\frac {9 \log ^2(x)}{(14+3 x)^2}+\frac {3}{7} \log (14+3 x)-\frac {9}{98} \text {Li}_2\left (-\frac {3 x}{14}\right )-\frac {9}{98} \int \frac {\log \left (1+\frac {3 x}{14}\right )}{x} \, dx+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx+84 \int \left (\frac {1}{196 x}-\frac {3}{14 (14+3 x)^2}-\frac {3}{196 (14+3 x)}\right ) \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx\\ &=\frac {6}{14+3 x}+\frac {9 (32+17 x)^2}{142 (14+3 x)^2}+\frac {3 \log (x)}{7}-\frac {84 \log (x)}{(14+3 x)^2}-\frac {9 x \log (x)}{7 (14+3 x)}+\frac {9 \log ^2(x)}{(14+3 x)^2}+54 \int \frac {5+3 x}{(14+3 x)^3 \log ^2(x)} \, dx+54 \int \frac {-14+3 x}{(14+3 x)^3 \log (x)} \, dx-162 \int \frac {1}{x (14+3 x)^2 \log ^3(x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 41, normalized size = 1.71 \begin {gather*} \frac {\left (-9-14 \log (x)+3 \log ^2(x)\right ) \left (-9+2 (7+3 x) \log (x)+3 \log ^2(x)\right )}{(14+3 x)^2 \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs.
\(2(22)=44\).
time = 2.68, size = 46, normalized size = 1.92
method | result | size |
default | \(\frac {81-250 \ln \left (x \right )^{2}-84 x \ln \left (x \right )^{2}+9 \ln \left (x \right )^{4}-54 x \ln \left (x \right )+18 x \ln \left (x \right )^{3}}{\left (3 x +14\right )^{2} \ln \left (x \right )^{2}}\) | \(46\) |
risch | \(\frac {9 \ln \left (x \right )^{2}}{9 x^{2}+84 x +196}+\frac {18 x \ln \left (x \right )}{9 x^{2}+84 x +196}-\frac {2 \left (42 x +125\right )}{9 x^{2}+84 x +196}-\frac {27 \left (2 x \ln \left (x \right )-3\right )}{\left (9 x^{2}+84 x +196\right ) \ln \left (x \right )^{2}}\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (23) = 46\).
time = 0.30, size = 48, normalized size = 2.00 \begin {gather*} \frac {18 \, x \log \left (x\right )^{3} + 9 \, \log \left (x\right )^{4} - 2 \, {\left (42 \, x + 125\right )} \log \left (x\right )^{2} - 54 \, x \log \left (x\right ) + 81}{{\left (9 \, x^{2} + 84 \, x + 196\right )} \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (23) = 46\).
time = 0.42, size = 48, normalized size = 2.00 \begin {gather*} \frac {18 \, x \log \left (x\right )^{3} + 9 \, \log \left (x\right )^{4} - 2 \, {\left (42 \, x + 125\right )} \log \left (x\right )^{2} - 54 \, x \log \left (x\right ) + 81}{{\left (9 \, x^{2} + 84 \, x + 196\right )} \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (20) = 40\).
time = 0.15, size = 73, normalized size = 3.04 \begin {gather*} \frac {18 x \log {\left (x \right )}}{9 x^{2} + 84 x + 196} + \frac {- 84 x - 250}{9 x^{2} + 84 x + 196} + \frac {- 54 x \log {\left (x \right )} + 81}{\left (9 x^{2} + 84 x + 196\right ) \log {\left (x \right )}^{2}} + \frac {9 \log {\left (x \right )}^{2}}{9 x^{2} + 84 x + 196} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 89 vs.
\(2 (23) = 46\).
time = 0.41, size = 89, normalized size = 3.71 \begin {gather*} \frac {18 \, x \log \left (x\right )}{9 \, x^{2} + 84 \, x + 196} + \frac {9 \, \log \left (x\right )^{2}}{9 \, x^{2} + 84 \, x + 196} - \frac {27 \, {\left (2 \, x \log \left (x\right ) - 3\right )}}{9 \, x^{2} \log \left (x\right )^{2} + 84 \, x \log \left (x\right )^{2} + 196 \, \log \left (x\right )^{2}} - \frac {2 \, {\left (42 \, x + 125\right )}}{9 \, x^{2} + 84 \, x + 196} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.39, size = 49, normalized size = 2.04 \begin {gather*} \frac {9\,\left (125\,x^2\,{\ln \left (x\right )}^2+196\,x\,{\ln \left (x\right )}^3+252\,x\,{\ln \left (x\right )}^2-588\,x\,\ln \left (x\right )+98\,{\ln \left (x\right )}^4+882\right )}{98\,{\ln \left (x\right )}^2\,{\left (3\,x+14\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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