Integrand size = 22, antiderivative size = 76 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=\frac {13880997 x}{1953125}-\frac {461623 x^2}{390625}-\frac {1836723 x^3}{78125}-\frac {5643 x^4}{3125}+\frac {774981 x^5}{15625}+\frac {12231 x^6}{625}-\frac {37908 x^7}{875}-\frac {729 x^8}{25}-\frac {1331}{9765625 (3+5 x)}+\frac {23232 \log (3+5 x)}{9765625} \]
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Time = 0.03 (sec) , antiderivative size = 76, 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} \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=-\frac {729 x^8}{25}-\frac {37908 x^7}{875}+\frac {12231 x^6}{625}+\frac {774981 x^5}{15625}-\frac {5643 x^4}{3125}-\frac {1836723 x^3}{78125}-\frac {461623 x^2}{390625}+\frac {13880997 x}{1953125}-\frac {1331}{9765625 (5 x+3)}+\frac {23232 \log (5 x+3)}{9765625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {13880997}{1953125}-\frac {923246 x}{390625}-\frac {5510169 x^2}{78125}-\frac {22572 x^3}{3125}+\frac {774981 x^4}{3125}+\frac {73386 x^5}{625}-\frac {37908 x^6}{125}-\frac {5832 x^7}{25}+\frac {1331}{1953125 (3+5 x)^2}+\frac {23232}{1953125 (3+5 x)}\right ) \, dx \\ & = \frac {13880997 x}{1953125}-\frac {461623 x^2}{390625}-\frac {1836723 x^3}{78125}-\frac {5643 x^4}{3125}+\frac {774981 x^5}{15625}+\frac {12231 x^6}{625}-\frac {37908 x^7}{875}-\frac {729 x^8}{25}-\frac {1331}{9765625 (3+5 x)}+\frac {23232 \log (3+5 x)}{9765625} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=\frac {2118706028+10818777780 x+10934112000 x^2-26126590000 x^3-42029925000 x^4+47772112500 x^5+104830031250 x^6-10979296875 x^7-103939453125 x^8-49833984375 x^9+813120 (3+5 x) \log (6 (3+5 x))}{341796875 (3+5 x)} \]
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Time = 2.47 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.72
method | result | size |
risch | \(-\frac {729 x^{8}}{25}-\frac {37908 x^{7}}{875}+\frac {12231 x^{6}}{625}+\frac {774981 x^{5}}{15625}-\frac {5643 x^{4}}{3125}-\frac {1836723 x^{3}}{78125}-\frac {461623 x^{2}}{390625}+\frac {13880997 x}{1953125}-\frac {1331}{48828125 \left (x +\frac {3}{5}\right )}+\frac {23232 \ln \left (3+5 x \right )}{9765625}\) | \(55\) |
default | \(\frac {13880997 x}{1953125}-\frac {461623 x^{2}}{390625}-\frac {1836723 x^{3}}{78125}-\frac {5643 x^{4}}{3125}+\frac {774981 x^{5}}{15625}+\frac {12231 x^{6}}{625}-\frac {37908 x^{7}}{875}-\frac {729 x^{8}}{25}-\frac {1331}{9765625 \left (3+5 x \right )}+\frac {23232 \ln \left (3+5 x \right )}{9765625}\) | \(57\) |
norman | \(\frac {\frac {124930304}{5859375} x +\frac {12496128}{390625} x^{2}-\frac {5971792}{78125} x^{3}-\frac {1921368}{15625} x^{4}+\frac {2183868}{15625} x^{5}+\frac {958446}{3125} x^{6}-\frac {28107}{875} x^{7}-\frac {53217}{175} x^{8}-\frac {729}{5} x^{9}}{3+5 x}+\frac {23232 \ln \left (3+5 x \right )}{9765625}\) | \(62\) |
parallelrisch | \(\frac {-29900390625 x^{9}-62363671875 x^{8}-6587578125 x^{7}+62898018750 x^{6}+28663267500 x^{5}-25217955000 x^{4}-15675954000 x^{3}+2439360 \ln \left (x +\frac {3}{5}\right ) x +6560467200 x^{2}+1463616 \ln \left (x +\frac {3}{5}\right )+4372560640 x}{615234375+1025390625 x}\) | \(67\) |
meijerg | \(\frac {1594323 x \left (-\frac {13671875}{6561} x^{8}+\frac {390625}{243} x^{7}-\frac {312500}{243} x^{6}+\frac {87500}{81} x^{5}-\frac {8750}{9} x^{4}+\frac {8750}{9} x^{3}-\frac {3500}{3} x^{2}+2100 x +2520\right )}{68359375 \left (1+\frac {5 x}{3}\right )}+\frac {23232 \ln \left (1+\frac {5 x}{3}\right )}{9765625}+\frac {334611 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{1562500 \left (1+\frac {5 x}{3}\right )}-\frac {236196 x \left (\frac {390625}{243} x^{7}-\frac {312500}{243} x^{6}+\frac {87500}{81} x^{5}-\frac {8750}{9} x^{4}+\frac {8750}{9} x^{3}-\frac {3500}{3} x^{2}+2100 x +2520\right )}{2734375 \left (1+\frac {5 x}{3}\right )}+\frac {80919 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{156250 \left (1+\frac {5 x}{3}\right )}-\frac {256 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {756 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {18711 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {176 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}+\frac {336 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{25 \left (1+\frac {5 x}{3}\right )}\) | \(280\) |
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Time = 0.22 (sec) , antiderivative size = 67, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=-\frac {9966796875 \, x^{9} + 20787890625 \, x^{8} + 2195859375 \, x^{7} - 20966006250 \, x^{6} - 9554422500 \, x^{5} + 8405985000 \, x^{4} + 5225318000 \, x^{3} - 2186822400 \, x^{2} - 162624 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1457504685 \, x + 9317}{68359375 \, {\left (5 \, x + 3\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.89 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=- \frac {729 x^{8}}{25} - \frac {37908 x^{7}}{875} + \frac {12231 x^{6}}{625} + \frac {774981 x^{5}}{15625} - \frac {5643 x^{4}}{3125} - \frac {1836723 x^{3}}{78125} - \frac {461623 x^{2}}{390625} + \frac {13880997 x}{1953125} + \frac {23232 \log {\left (5 x + 3 \right )}}{9765625} - \frac {1331}{48828125 x + 29296875} \]
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Time = 0.24 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=-\frac {729}{25} \, x^{8} - \frac {37908}{875} \, x^{7} + \frac {12231}{625} \, x^{6} + \frac {774981}{15625} \, x^{5} - \frac {5643}{3125} \, x^{4} - \frac {1836723}{78125} \, x^{3} - \frac {461623}{390625} \, x^{2} + \frac {13880997}{1953125} \, x - \frac {1331}{9765625 \, {\left (5 \, x + 3\right )}} + \frac {23232}{9765625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 102, normalized size of antiderivative = 1.34 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=\frac {1}{341796875} \, {\left (5 \, x + 3\right )}^{8} {\left (\frac {422820}{5 \, x + 3} - \frac {2021355}{{\left (5 \, x + 3\right )}^{2}} + \frac {474957}{{\left (5 \, x + 3\right )}^{3}} + \frac {9876195}{{\left (5 \, x + 3\right )}^{4}} + \frac {14499345}{{\left (5 \, x + 3\right )}^{5}} + \frac {10904215}{{\left (5 \, x + 3\right )}^{6}} + \frac {5836215}{{\left (5 \, x + 3\right )}^{7}} - 25515\right )} - \frac {1331}{9765625 \, {\left (5 \, x + 3\right )}} - \frac {23232}{9765625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (2+3 x)^6}{(3+5 x)^2} \, dx=\frac {13880997\,x}{1953125}+\frac {23232\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {1331}{48828125\,\left (x+\frac {3}{5}\right )}-\frac {461623\,x^2}{390625}-\frac {1836723\,x^3}{78125}-\frac {5643\,x^4}{3125}+\frac {774981\,x^5}{15625}+\frac {12231\,x^6}{625}-\frac {37908\,x^7}{875}-\frac {729\,x^8}{25} \]
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