Integrand size = 22, antiderivative size = 86 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {32}{184877 (1-2 x)}+\frac {9}{196 (2+3 x)^4}+\frac {117}{343 (2+3 x)^3}+\frac {12393}{4802 (2+3 x)^2}+\frac {434043}{16807 (2+3 x)}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (2+3 x)}{117649}+\frac {15625}{121} \log (3+5 x) \]
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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} \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {32}{184877 (1-2 x)}+\frac {434043}{16807 (3 x+2)}+\frac {12393}{4802 (3 x+2)^2}+\frac {117}{343 (3 x+2)^3}+\frac {9}{196 (3 x+2)^4}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (3 x+2)}{117649}+\frac {15625}{121} \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {64}{184877 (-1+2 x)^2}-\frac {12800}{14235529 (-1+2 x)}-\frac {27}{49 (2+3 x)^5}-\frac {1053}{343 (2+3 x)^4}-\frac {37179}{2401 (2+3 x)^3}-\frac {1302129}{16807 (2+3 x)^2}-\frac {45576675}{117649 (2+3 x)}+\frac {78125}{121 (3+5 x)}\right ) \, dx \\ & = \frac {32}{184877 (1-2 x)}+\frac {9}{196 (2+3 x)^4}+\frac {117}{343 (2+3 x)^3}+\frac {12393}{4802 (2+3 x)^2}+\frac {434043}{16807 (2+3 x)}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (2+3 x)}{117649}+\frac {15625}{121} \log (3+5 x) \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 81, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {5 \left (\frac {77}{5} \left (\frac {128}{1-2 x}+\frac {33957}{(2+3 x)^4}+\frac {252252}{(2+3 x)^3}+\frac {1908522}{(2+3 x)^2}+\frac {19097892}{2+3 x}\right )-5120 \log (5-10 x)-1470607380 \log (5 (2+3 x))+1470612500 \log (3+5 x)\right )}{56942116} \]
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Time = 2.70 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.71
method | result | size |
norman | \(\frac {-\frac {194642025}{369754} x +\frac {186937875}{369754} x^{2}+\frac {257818950}{184877} x^{4}+\frac {395313750}{184877} x^{3}-\frac {160957733}{739508}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {6400 \ln \left (-1+2 x \right )}{14235529}-\frac {15192225 \ln \left (2+3 x \right )}{117649}+\frac {15625 \ln \left (3+5 x \right )}{121}\) | \(61\) |
risch | \(\frac {-\frac {194642025}{369754} x +\frac {186937875}{369754} x^{2}+\frac {257818950}{184877} x^{4}+\frac {395313750}{184877} x^{3}-\frac {160957733}{739508}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {6400 \ln \left (-1+2 x \right )}{14235529}-\frac {15192225 \ln \left (2+3 x \right )}{117649}+\frac {15625 \ln \left (3+5 x \right )}{121}\) | \(62\) |
default | \(\frac {15625 \ln \left (3+5 x \right )}{121}-\frac {32}{184877 \left (-1+2 x \right )}-\frac {6400 \ln \left (-1+2 x \right )}{14235529}+\frac {9}{196 \left (2+3 x \right )^{4}}+\frac {117}{343 \left (2+3 x \right )^{3}}+\frac {12393}{4802 \left (2+3 x \right )^{2}}+\frac {434043}{16807 \left (2+3 x \right )}-\frac {15192225 \ln \left (2+3 x \right )}{117649}\) | \(71\) |
parallelrisch | \(-\frac {-313601758624 x +2823576000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+25412095526400 \ln \left (\frac {2}{3}+x \right ) x^{3}+7529536000000 \ln \left (x +\frac {3}{5}\right ) x -2823566169600 \ln \left (\frac {2}{3}+x \right ) x^{2}-7529509785600 \ln \left (\frac {2}{3}+x \right ) x +2007786761442 x^{5}+728942855256 x^{3}+3079672864191 x^{4}-758064814584 x^{2}+143769600 \ln \left (x -\frac {1}{2}\right ) x^{4}+41294655230400 \ln \left (\frac {2}{3}+x \right ) x^{4}-1882377446400 \ln \left (\frac {2}{3}+x \right )+88473600 \ln \left (x -\frac {1}{2}\right ) x^{3}-9830400 \ln \left (x -\frac {1}{2}\right ) x^{2}-26214400 \ln \left (x -\frac {1}{2}\right ) x +1882384000000 \ln \left (x +\frac {3}{5}\right )+19059071644800 \ln \left (\frac {2}{3}+x \right ) x^{5}-25412184000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-19059138000000 \ln \left (x +\frac {3}{5}\right ) x^{5}-41294799000000 \ln \left (x +\frac {3}{5}\right ) x^{4}-6553600 \ln \left (x -\frac {1}{2}\right )+66355200 \ln \left (x -\frac {1}{2}\right ) x^{5}}{911073856 \left (-1+2 x \right ) \left (2+3 x \right )^{4}}\) | \(188\) |
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Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (70) = 140\).
Time = 0.23 (sec) , antiderivative size = 148, normalized size of antiderivative = 1.72 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {79408236600 \, x^{4} + 121756635000 \, x^{3} + 28788432750 \, x^{2} + 7353062500 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (5 \, x + 3\right ) - 7353036900 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) - 25600 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) - 29974871850 \, x - 12393745441}{56942116 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {1031275800 x^{4} + 1581255000 x^{3} + 373875750 x^{2} - 389284050 x - 160957733}{119800296 x^{5} + 259567308 x^{4} + 159733728 x^{3} - 17748192 x^{2} - 47328512 x - 11832128} - \frac {6400 \log {\left (x - \frac {1}{2} \right )}}{14235529} + \frac {15625 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {15192225 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
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Time = 0.21 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.86 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {1031275800 \, x^{4} + 1581255000 \, x^{3} + 373875750 \, x^{2} - 389284050 \, x - 160957733}{739508 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac {15625}{121} \, \log \left (5 \, x + 3\right ) - \frac {15192225}{117649} \, \log \left (3 \, x + 2\right ) - \frac {6400}{14235529} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 82, normalized size of antiderivative = 0.95 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {434043}{16807 \, {\left (3 \, x + 2\right )}} + \frac {192}{1294139 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} + \frac {12393}{4802 \, {\left (3 \, x + 2\right )}^{2}} + \frac {117}{343 \, {\left (3 \, x + 2\right )}^{3}} + \frac {9}{196 \, {\left (3 \, x + 2\right )}^{4}} + \frac {15625}{121} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {6400}{14235529} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
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Time = 1.35 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.79 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx=\frac {15625\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {15192225\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {6400\,\ln \left (x-\frac {1}{2}\right )}{14235529}-\frac {\frac {1591475\,x^4}{184877}+\frac {7320625\,x^3}{554631}+\frac {2307875\,x^2}{739508}-\frac {64880675\,x}{19966716}-\frac {160957733}{119800296}}{-x^5-\frac {13\,x^4}{6}-\frac {4\,x^3}{3}+\frac {4\,x^2}{27}+\frac {32\,x}{81}+\frac {8}{81}} \]
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