Integrand size = 108, antiderivative size = 28 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\frac {\left (-3-x+\frac {3 x^3}{\log ^2(5) \log ^2(x)}\right ) (-2+\log (3+x))}{x} \]
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\[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^3(x)} \, dx}{\log ^2(5)} \\ & = \frac {\int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{x^2 (3+x) \log ^3(x)} \, dx}{\log ^2(5)} \\ & = \frac {\int \left (-\frac {\log ^2(5) (6+x-3 \log (3+x))}{x^2}-\frac {6 x (-2+\log (3+x))}{\log ^3(x)}+\frac {-9 x (4+x)+6 x (3+x) \log (3+x)}{(3+x) \log ^2(x)}\right ) \, dx}{\log ^2(5)} \\ & = \frac {\int \frac {-9 x (4+x)+6 x (3+x) \log (3+x)}{(3+x) \log ^2(x)} \, dx}{\log ^2(5)}-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}-\int \frac {6+x-3 \log (3+x)}{x^2} \, dx \\ & = \frac {\int \left (-\frac {9 x (4+x)}{(3+x) \log ^2(x)}+\frac {6 x \log (3+x)}{\log ^2(x)}\right ) \, dx}{\log ^2(5)}-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}-\int \left (\frac {6+x}{x^2}-\frac {3 \log (3+x)}{x^2}\right ) \, dx \\ & = 3 \int \frac {\log (3+x)}{x^2} \, dx-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}+\frac {6 \int \frac {x \log (3+x)}{\log ^2(x)} \, dx}{\log ^2(5)}-\frac {9 \int \frac {x (4+x)}{(3+x) \log ^2(x)} \, dx}{\log ^2(5)}-\int \frac {6+x}{x^2} \, dx \\ & = -\frac {3 \log (3+x)}{x}+3 \int \frac {1}{x (3+x)} \, dx-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}+\frac {6 \int \frac {x \log (3+x)}{\log ^2(x)} \, dx}{\log ^2(5)}-\frac {9 \int \frac {x (4+x)}{(3+x) \log ^2(x)} \, dx}{\log ^2(5)}-\int \left (\frac {6}{x^2}+\frac {1}{x}\right ) \, dx \\ & = \frac {6}{x}-\log (x)-\frac {3 \log (3+x)}{x}-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}+\frac {6 \int \frac {x \log (3+x)}{\log ^2(x)} \, dx}{\log ^2(5)}-\frac {9 \int \frac {x (4+x)}{(3+x) \log ^2(x)} \, dx}{\log ^2(5)}+\int \frac {1}{x} \, dx-\int \frac {1}{3+x} \, dx \\ & = \frac {6}{x}-\log (3+x)-\frac {3 \log (3+x)}{x}-\frac {6 \int \frac {x (-2+\log (3+x))}{\log ^3(x)} \, dx}{\log ^2(5)}+\frac {6 \int \frac {x \log (3+x)}{\log ^2(x)} \, dx}{\log ^2(5)}-\frac {9 \int \frac {x (4+x)}{(3+x) \log ^2(x)} \, dx}{\log ^2(5)} \\ \end{align*}
Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\frac {6+\frac {3 x^3 (-2+\log (3+x))}{\log ^2(5) \log ^2(x)}-(3+x) \log (3+x)}{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(66\) vs. \(2(28)=56\).
Time = 1.26 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.39
method | result | size |
parallelrisch | \(-\frac {\ln \left (5\right )^{2} \ln \left (3+x \right ) x \ln \left (x \right )^{2}+3 \ln \left (5\right )^{2} \ln \left (3+x \right ) \ln \left (x \right )^{2}-6 \ln \left (5\right )^{2} \ln \left (x \right )^{2}-3 \ln \left (3+x \right ) x^{3}+6 x^{3}}{\ln \left (5\right )^{2} x \ln \left (x \right )^{2}}\) | \(67\) |
risch | \(-\frac {3 \left (\ln \left (5\right )^{2} \ln \left (x \right )^{2}-x^{3}\right ) \ln \left (3+x \right )}{\ln \left (5\right )^{2} x \ln \left (x \right )^{2}}-\frac {\ln \left (5\right )^{2} \ln \left (3+x \right ) x \ln \left (x \right )^{2}-6 \ln \left (5\right )^{2} \ln \left (x \right )^{2}+6 x^{3}}{\ln \left (5\right )^{2} x \ln \left (x \right )^{2}}\) | \(77\) |
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Time = 0.24 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\frac {6 \, \log \left (5\right )^{2} \log \left (x\right )^{2} - 6 \, x^{3} - {\left ({\left (x + 3\right )} \log \left (5\right )^{2} \log \left (x\right )^{2} - 3 \, x^{3}\right )} \log \left (x + 3\right )}{x \log \left (5\right )^{2} \log \left (x\right )^{2}} \]
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Exception generated. \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\frac {6 \, \log \left (5\right )^{2} \log \left (x\right )^{2} - 6 \, x^{3} + {\left (3 \, x^{3} - {\left (x \log \left (5\right )^{2} + 3 \, \log \left (5\right )^{2}\right )} \log \left (x\right )^{2}\right )} \log \left (x + 3\right )}{x \log \left (5\right )^{2} \log \left (x\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (27) = 54\).
Time = 0.28 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=-\frac {\log \left (5\right )^{2} \log \left (x + 3\right ) + 3 \, {\left (\frac {\log \left (5\right )^{2}}{x} - \frac {x^{2}}{\log \left (x\right )^{2}}\right )} \log \left (x + 3\right ) - \frac {6 \, \log \left (5\right )^{2}}{x} + \frac {6 \, x^{2}}{\log \left (x\right )^{2}}}{\log \left (5\right )^{2}} \]
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Time = 13.92 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx=\frac {6}{x}-\frac {3\,\ln \left (x+3\right )}{x}-\ln \left (x+3\right )-\frac {6\,x^2}{{\ln \left (5\right )}^2\,{\ln \left (x\right )}^2}+\frac {3\,x^2\,\ln \left (x+3\right )}{{\ln \left (5\right )}^2\,{\ln \left (x\right )}^2} \]
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