Integrand size = 22, antiderivative size = 86 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {32}{456533 (1-2 x)}+\frac {81}{98 (2+3 x)^2}+\frac {8829}{343 (2+3 x)}-\frac {625}{242 (3+5 x)^2}+\frac {59375}{1331 (3+5 x)}-\frac {6528 \log (1-2 x)}{35153041}-\frac {630342 \log (2+3 x)}{2401}+\frac {3843750 \log (3+5 x)}{14641} \]
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Time = 0.03 (sec) , antiderivative size = 86, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {32}{456533 (1-2 x)}+\frac {8829}{343 (3 x+2)}+\frac {59375}{1331 (5 x+3)}+\frac {81}{98 (3 x+2)^2}-\frac {625}{242 (5 x+3)^2}-\frac {6528 \log (1-2 x)}{35153041}-\frac {630342 \log (3 x+2)}{2401}+\frac {3843750 \log (5 x+3)}{14641} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {64}{456533 (-1+2 x)^2}-\frac {13056}{35153041 (-1+2 x)}-\frac {243}{49 (2+3 x)^3}-\frac {26487}{343 (2+3 x)^2}-\frac {1891026}{2401 (2+3 x)}+\frac {3125}{121 (3+5 x)^3}-\frac {296875}{1331 (3+5 x)^2}+\frac {19218750}{14641 (3+5 x)}\right ) \, dx \\ & = \frac {32}{456533 (1-2 x)}+\frac {81}{98 (2+3 x)^2}+\frac {8829}{343 (2+3 x)}-\frac {625}{242 (3+5 x)^2}+\frac {59375}{1331 (3+5 x)}-\frac {6528 \log (1-2 x)}{35153041}-\frac {630342 \log (2+3 x)}{2401}+\frac {3843750 \log (3+5 x)}{14641} \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 79, normalized size of antiderivative = 0.92 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {2 \left (\frac {77}{4} \left (\frac {64}{1-2 x}+\frac {754677}{(2+3 x)^2}+\frac {23502798}{2+3 x}-\frac {2358125}{(3+5 x)^2}+\frac {40731250}{3+5 x}\right )-3264 \log (1-2 x)-4614418611 \log (4+6 x)+4614421875 \log (6+10 x)\right )}{35153041} \]
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Time = 0.89 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.79
method | result | size |
norman | \(\frac {-\frac {1250840457}{456533} x +\frac {904191789}{456533} x^{2}+\frac {3595608900}{456533} x^{4}+\frac {5033827980}{456533} x^{3}-\frac {909187261}{913066}}{\left (-1+2 x \right ) \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {6528 \ln \left (-1+2 x \right )}{35153041}-\frac {630342 \ln \left (2+3 x \right )}{2401}+\frac {3843750 \ln \left (3+5 x \right )}{14641}\) | \(68\) |
risch | \(\frac {-\frac {1250840457}{456533} x +\frac {904191789}{456533} x^{2}+\frac {3595608900}{456533} x^{4}+\frac {5033827980}{456533} x^{3}-\frac {909187261}{913066}}{\left (-1+2 x \right ) \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {6528 \ln \left (-1+2 x \right )}{35153041}-\frac {630342 \ln \left (2+3 x \right )}{2401}+\frac {3843750 \ln \left (3+5 x \right )}{14641}\) | \(69\) |
default | \(-\frac {625}{242 \left (3+5 x \right )^{2}}+\frac {59375}{1331 \left (3+5 x \right )}+\frac {3843750 \ln \left (3+5 x \right )}{14641}-\frac {32}{456533 \left (-1+2 x \right )}-\frac {6528 \ln \left (-1+2 x \right )}{35153041}+\frac {81}{98 \left (2+3 x \right )^{2}}+\frac {8829}{343 \left (2+3 x \right )}-\frac {630342 \ln \left (2+3 x \right )}{2401}\) | \(71\) |
parallelrisch | \(-\frac {-3986497885524 x +56480523750000 \ln \left (x +\frac {3}{5}\right ) x^{2}+340211855351808 \ln \left (\frac {2}{3}+x \right ) x^{3}+103658373000000 \ln \left (x +\frac {3}{5}\right ) x -56480483798640 \ln \left (\frac {2}{3}+x \right ) x^{2}-103658299677504 \ln \left (\frac {2}{3}+x \right ) x +31503338593650 x^{5}+7936256256544 x^{3}+44122732732155 x^{4}-10963469901461 x^{2}+430064640 \ln \left (x -\frac {1}{2}\right ) x^{4}+607995796185360 \ln \left (\frac {2}{3}+x \right ) x^{4}-23921146079424 \ln \left (\frac {2}{3}+x \right )+240648192 \ln \left (x -\frac {1}{2}\right ) x^{3}-39951360 \ln \left (x -\frac {1}{2}\right ) x^{2}-73322496 \ln \left (x -\frac {1}{2}\right ) x +23921163000000 \ln \left (x +\frac {3}{5}\right )+299014325992800 \ln \left (\frac {2}{3}+x \right ) x^{5}-340212096000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-299014537500000 \ln \left (x +\frac {3}{5}\right ) x^{5}-607996226250000 \ln \left (x +\frac {3}{5}\right ) x^{4}-16920576 \ln \left (x -\frac {1}{2}\right )+211507200 \ln \left (x -\frac {1}{2}\right ) x^{5}}{2531018952 \left (-1+2 x \right ) \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}\) | \(195\) |
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Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (70) = 140\).
Time = 0.22 (sec) , antiderivative size = 148, normalized size of antiderivative = 1.72 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {553723770600 \, x^{4} + 775209508920 \, x^{3} + 139245535506 \, x^{2} + 18457687500 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (5 \, x + 3\right ) - 18457674444 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (3 \, x + 2\right ) - 13056 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \log \left (2 \, x - 1\right ) - 192629430378 \, x - 70007419097}{70306082 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {7191217800 x^{4} + 10067655960 x^{3} + 1808383578 x^{2} - 2501680914 x - 909187261}{410879700 x^{5} + 835455390 x^{4} + 467489792 x^{3} - 77610610 x^{2} - 142438296 x - 32870376} - \frac {6528 \log {\left (x - \frac {1}{2} \right )}}{35153041} + \frac {3843750 \log {\left (x + \frac {3}{5} \right )}}{14641} - \frac {630342 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
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Time = 0.19 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.86 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {7191217800 \, x^{4} + 10067655960 \, x^{3} + 1808383578 \, x^{2} - 2501680914 \, x - 909187261}{913066 \, {\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )}} + \frac {3843750}{14641} \, \log \left (5 \, x + 3\right ) - \frac {630342}{2401} \, \log \left (3 \, x + 2\right ) - \frac {6528}{35153041} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 97, normalized size of antiderivative = 1.13 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=-\frac {32}{456533 \, {\left (2 \, x - 1\right )}} - \frac {4 \, {\left (\frac {207724651275}{2 \, x - 1} + \frac {470659858850}{{\left (2 \, x - 1\right )}^{2}} + \frac {355299675423}{{\left (2 \, x - 1\right )}^{3}} + 30544881750\right )}}{35153041 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2} {\left (\frac {7}{2 \, x - 1} + 3\right )}^{2}} - \frac {630342}{2401} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) + \frac {3843750}{14641} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
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Time = 1.19 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.79 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^3} \, dx=\frac {3843750\,\ln \left (x+\frac {3}{5}\right )}{14641}-\frac {630342\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {6528\,\ln \left (x-\frac {1}{2}\right )}{35153041}-\frac {\frac {7990242\,x^4}{456533}+\frac {55931422\,x^3}{2282665}+\frac {301397263\,x^2}{68479950}-\frac {138982273\,x}{22826650}-\frac {909187261}{410879700}}{-x^5-\frac {61\,x^4}{30}-\frac {256\,x^3}{225}+\frac {17\,x^2}{90}+\frac {26\,x}{75}+\frac {2}{25}} \]
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