Integrand size = 39, antiderivative size = 19 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=\frac {(-1+3 x) (3-\log (6-x))}{x^9} \]
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Time = 0.17 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.68, number of steps used = 9, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {1607, 6874, 907, 45, 2461, 12, 78} \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=-\frac {3}{x^9}+\frac {\log (6-x)}{x^9}+\frac {9}{x^8}-\frac {3 \log (6-x)}{x^8} \]
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Rule 12
Rule 45
Rule 78
Rule 907
Rule 1607
Rule 2461
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{(-6+x) x^{10}} \, dx \\ & = \int \left (\frac {-162+460 x-75 x^2}{(-6+x) x^{10}}+\frac {3 (-3+8 x) \log (6-x)}{x^{10}}\right ) \, dx \\ & = 3 \int \frac {(-3+8 x) \log (6-x)}{x^{10}} \, dx+\int \frac {-162+460 x-75 x^2}{(-6+x) x^{10}} \, dx \\ & = \frac {\log (6-x)}{x^9}-\frac {3 \log (6-x)}{x^8}+3 \int \frac {1-3 x}{3 (6-x) x^9} \, dx+\int \left (-\frac {17}{10077696 (-6+x)}+\frac {27}{x^{10}}-\frac {433}{6 x^9}+\frac {17}{36 x^8}+\frac {17}{216 x^7}+\frac {17}{1296 x^6}+\frac {17}{7776 x^5}+\frac {17}{46656 x^4}+\frac {17}{279936 x^3}+\frac {17}{1679616 x^2}+\frac {17}{10077696 x}\right ) \, dx \\ & = -\frac {3}{x^9}+\frac {433}{48 x^8}-\frac {17}{252 x^7}-\frac {17}{1296 x^6}-\frac {17}{6480 x^5}-\frac {17}{31104 x^4}-\frac {17}{139968 x^3}-\frac {17}{559872 x^2}-\frac {17}{1679616 x}-\frac {17 \log (6-x)}{10077696}+\frac {\log (6-x)}{x^9}-\frac {3 \log (6-x)}{x^8}+\frac {17 \log (x)}{10077696}+\int \frac {1-3 x}{(6-x) x^9} \, dx \\ & = -\frac {3}{x^9}+\frac {433}{48 x^8}-\frac {17}{252 x^7}-\frac {17}{1296 x^6}-\frac {17}{6480 x^5}-\frac {17}{31104 x^4}-\frac {17}{139968 x^3}-\frac {17}{559872 x^2}-\frac {17}{1679616 x}-\frac {17 \log (6-x)}{10077696}+\frac {\log (6-x)}{x^9}-\frac {3 \log (6-x)}{x^8}+\frac {17 \log (x)}{10077696}+\int \left (\frac {17}{10077696 (-6+x)}+\frac {1}{6 x^9}-\frac {17}{36 x^8}-\frac {17}{216 x^7}-\frac {17}{1296 x^6}-\frac {17}{7776 x^5}-\frac {17}{46656 x^4}-\frac {17}{279936 x^3}-\frac {17}{1679616 x^2}-\frac {17}{10077696 x}\right ) \, dx \\ & = -\frac {3}{x^9}+\frac {9}{x^8}+\frac {\log (6-x)}{x^9}-\frac {3 \log (6-x)}{x^8} \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.68 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=-\frac {3}{x^9}+\frac {9}{x^8}+\frac {\log (6-x)}{x^9}-\frac {3 \log (6-x)}{x^8} \]
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Time = 0.56 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32
method | result | size |
norman | \(\frac {-3+9 x -3 \ln \left (-x +6\right ) x +\ln \left (-x +6\right )}{x^{9}}\) | \(25\) |
risch | \(-\frac {\left (-1+3 x \right ) \ln \left (-x +6\right )}{x^{9}}+\frac {9 x -3}{x^{9}}\) | \(28\) |
parallelrisch | \(-\frac {36+36 \ln \left (-x +6\right ) x -108 x -12 \ln \left (-x +6\right )}{12 x^{9}}\) | \(28\) |
derivativedivides | \(-\frac {3}{x^{9}}+\frac {9}{x^{8}}-\frac {17 \ln \left (-x +6\right )}{10077696}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{7}-48 \left (-x +6\right )^{6}+1008 \left (-x +6\right )^{5}-12096 \left (-x +6\right )^{4}+90720 \left (-x +6\right )^{3}-435456 \left (-x +6\right )^{2}-1306368 x +5598720\right )}{559872 x^{8}}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{8}-54 \left (-x +6\right )^{7}+1296 \left (-x +6\right )^{6}-18144 \left (-x +6\right )^{5}+163296 \left (-x +6\right )^{4}-979776 \left (-x +6\right )^{3}+3919104 \left (-x +6\right )^{2}+10077696 x -45349632\right )}{10077696 x^{9}}\) | \(175\) |
default | \(-\frac {3}{x^{9}}+\frac {9}{x^{8}}-\frac {17 \ln \left (-x +6\right )}{10077696}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{7}-48 \left (-x +6\right )^{6}+1008 \left (-x +6\right )^{5}-12096 \left (-x +6\right )^{4}+90720 \left (-x +6\right )^{3}-435456 \left (-x +6\right )^{2}-1306368 x +5598720\right )}{559872 x^{8}}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{8}-54 \left (-x +6\right )^{7}+1296 \left (-x +6\right )^{6}-18144 \left (-x +6\right )^{5}+163296 \left (-x +6\right )^{4}-979776 \left (-x +6\right )^{3}+3919104 \left (-x +6\right )^{2}+10077696 x -45349632\right )}{10077696 x^{9}}\) | \(175\) |
parts | \(-\frac {17 \ln \left (-x \right )}{10077696}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{7}-48 \left (-x +6\right )^{6}+1008 \left (-x +6\right )^{5}-12096 \left (-x +6\right )^{4}+90720 \left (-x +6\right )^{3}-435456 \left (-x +6\right )^{2}-1306368 x +5598720\right )}{559872 x^{8}}+\frac {9}{x^{8}}+\frac {\ln \left (-x +6\right ) \left (-x +6\right ) \left (\left (-x +6\right )^{8}-54 \left (-x +6\right )^{7}+1296 \left (-x +6\right )^{6}-18144 \left (-x +6\right )^{5}+163296 \left (-x +6\right )^{4}-979776 \left (-x +6\right )^{3}+3919104 \left (-x +6\right )^{2}+10077696 x -45349632\right )}{10077696 x^{9}}-\frac {3}{x^{9}}+\frac {17 \ln \left (x \right )}{10077696}-\frac {17 \ln \left (-6+x \right )}{10077696}\) | \(183\) |
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Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=-\frac {{\left (3 \, x - 1\right )} \log \left (-x + 6\right ) - 9 \, x + 3}{x^{9}} \]
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Time = 0.11 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=\frac {\left (1 - 3 x\right ) \log {\left (6 - x \right )}}{x^{9}} - \frac {3 - 9 x}{x^{9}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (18) = 36\).
Time = 0.24 (sec) , antiderivative size = 112, normalized size of antiderivative = 5.89 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=\frac {210 \, x^{8} + 630 \, x^{7} + 2520 \, x^{6} + 11340 \, x^{5} + 54432 \, x^{4} + 272160 \, x^{3} + 1399680 \, x^{2} + 35 \, {\left (x^{9} - 1119744 \, x + 373248\right )} \log \left (-x + 6\right ) + 124921440 \, x}{13063680 \, x^{9}} - \frac {35 \, x^{8} + 105 \, x^{7} + 420 \, x^{6} + 1890 \, x^{5} + 9072 \, x^{4} + 45360 \, x^{3} + 233280 \, x^{2} + 1224720 \, x + 6531840}{2177280 \, x^{9}} - \frac {1}{373248} \, \log \left (x - 6\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (18) = 36\).
Time = 0.27 (sec) , antiderivative size = 143, normalized size of antiderivative = 7.53 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=-\frac {{\left (3 \, x - 1\right )} \log \left (-x + 6\right )}{{\left (x - 6\right )}^{9} + 54 \, {\left (x - 6\right )}^{8} + 1296 \, {\left (x - 6\right )}^{7} + 18144 \, {\left (x - 6\right )}^{6} + 163296 \, {\left (x - 6\right )}^{5} + 979776 \, {\left (x - 6\right )}^{4} + 3919104 \, {\left (x - 6\right )}^{3} + 10077696 \, {\left (x - 6\right )}^{2} + 15116544 \, x - 80621568} + \frac {3 \, {\left (3 \, x - 1\right )}}{{\left (x - 6\right )}^{9} + 54 \, {\left (x - 6\right )}^{8} + 1296 \, {\left (x - 6\right )}^{7} + 18144 \, {\left (x - 6\right )}^{6} + 163296 \, {\left (x - 6\right )}^{5} + 979776 \, {\left (x - 6\right )}^{4} + 3919104 \, {\left (x - 6\right )}^{3} + 10077696 \, {\left (x - 6\right )}^{2} + 15116544 \, x - 80621568} \]
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Time = 11.65 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {-162+460 x-75 x^2+\left (54-153 x+24 x^2\right ) \log (6-x)}{-6 x^{10}+x^{11}} \, dx=-\frac {\left (\ln \left (6-x\right )-3\right )\,\left (3\,x-1\right )}{x^9} \]
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