Integrand size = 22, antiderivative size = 87 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {92582457 x}{9765625}+\frac {55559043 x^2}{3906250}-\frac {5350194 x^3}{390625}-\frac {1700919 x^4}{31250}-\frac {74601 x^5}{3125}+\frac {376407 x^6}{6250}+\frac {332424 x^7}{4375}+\frac {6561 x^8}{250}-\frac {121}{97656250 (3+5 x)^2}-\frac {572}{9765625 (3+5 x)}+\frac {5888 \log (3+5 x)}{9765625} \]
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Time = 0.03 (sec) , antiderivative size = 87, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {6561 x^8}{250}+\frac {332424 x^7}{4375}+\frac {376407 x^6}{6250}-\frac {74601 x^5}{3125}-\frac {1700919 x^4}{31250}-\frac {5350194 x^3}{390625}+\frac {55559043 x^2}{3906250}+\frac {92582457 x}{9765625}-\frac {572}{9765625 (5 x+3)}-\frac {121}{97656250 (5 x+3)^2}+\frac {5888 \log (5 x+3)}{9765625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {92582457}{9765625}+\frac {55559043 x}{1953125}-\frac {16050582 x^2}{390625}-\frac {3401838 x^3}{15625}-\frac {74601 x^4}{625}+\frac {1129221 x^5}{3125}+\frac {332424 x^6}{625}+\frac {26244 x^7}{125}+\frac {121}{9765625 (3+5 x)^3}+\frac {572}{1953125 (3+5 x)^2}+\frac {5888}{1953125 (3+5 x)}\right ) \, dx \\ & = \frac {92582457 x}{9765625}+\frac {55559043 x^2}{3906250}-\frac {5350194 x^3}{390625}-\frac {1700919 x^4}{31250}-\frac {74601 x^5}{3125}+\frac {376407 x^6}{6250}+\frac {332424 x^7}{4375}+\frac {6561 x^8}{250}-\frac {121}{97656250 (3+5 x)^2}-\frac {572}{9765625 (3+5 x)}+\frac {5888 \log (3+5 x)}{9765625} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 76, normalized size of antiderivative = 0.87 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {10358007077+92853841190 x+310701230325 x^2+369438720000 x^3-372682800000 x^4-1497169800000 x^5-1049233500000 x^6+1294582500000 x^7+2748937500000 x^8+1836738281250 x^9+448505859375 x^{10}+412160 (3+5 x)^2 \log (3+5 x)}{683593750 (3+5 x)^2} \]
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Time = 2.38 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {6561 x^{8}}{250}+\frac {332424 x^{7}}{4375}+\frac {376407 x^{6}}{6250}-\frac {74601 x^{5}}{3125}-\frac {1700919 x^{4}}{31250}-\frac {5350194 x^{3}}{390625}+\frac {55559043 x^{2}}{3906250}+\frac {92582457 x}{9765625}+\frac {-\frac {572 x}{1953125}-\frac {17281}{97656250}}{\left (3+5 x \right )^{2}}+\frac {5888 \ln \left (3+5 x \right )}{9765625}\) | \(62\) |
default | \(\frac {92582457 x}{9765625}+\frac {55559043 x^{2}}{3906250}-\frac {5350194 x^{3}}{390625}-\frac {1700919 x^{4}}{31250}-\frac {74601 x^{5}}{3125}+\frac {376407 x^{6}}{6250}+\frac {332424 x^{7}}{4375}+\frac {6561 x^{8}}{250}-\frac {121}{97656250 \left (3+5 x \right )^{2}}-\frac {572}{9765625 \left (3+5 x \right )}+\frac {5888 \ln \left (3+5 x \right )}{9765625}\) | \(66\) |
norman | \(\frac {\frac {499947008}{5859375} x +\frac {1449920512}{3515625} x^{2}+\frac {42221568}{78125} x^{3}-\frac {8518464}{15625} x^{4}-\frac {34221024}{15625} x^{5}-\frac {4796496}{3125} x^{6}+\frac {8285328}{4375} x^{7}+\frac {703728}{175} x^{8}+\frac {94041}{35} x^{9}+\frac {6561}{10} x^{10}}{\left (3+5 x \right )^{2}}+\frac {5888 \ln \left (3+5 x \right )}{9765625}\) | \(67\) |
parallelrisch | \(\frac {807310546875 x^{10}+3306128906250 x^{9}+4948087500000 x^{8}+2330248500000 x^{7}-1888620300000 x^{6}-2694905640000 x^{5}-670829040000 x^{4}+18547200 \ln \left (x +\frac {3}{5}\right ) x^{2}+664989696000 x^{3}+22256640 \ln \left (x +\frac {3}{5}\right ) x +507472179200 x^{2}+6676992 \ln \left (x +\frac {3}{5}\right )+104988871680 x}{1230468750 \left (3+5 x \right )^{2}}\) | \(81\) |
meijerg | \(\frac {41452398 x \left (\frac {3906250}{6561} x^{8}-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{68359375 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {5888 \ln \left (1+\frac {5 x}{3}\right )}{9765625}-\frac {14348907 x \left (-\frac {150390625}{19683} x^{9}+\frac {42968750}{6561} x^{8}-\frac {4296875}{729} x^{7}+\frac {1375000}{243} x^{6}-\frac {481250}{81} x^{5}+\frac {192500}{27} x^{4}-\frac {96250}{9} x^{3}+\frac {77000}{3} x^{2}+69300 x +27720\right )}{1503906250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {1043199 x \left (-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{781250 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {128 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2432 x \left (15 x +6\right )}{225 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {8748 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{15625 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1456542 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{390625 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {192 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{25 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1024 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {57456 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {18144 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(352\) |
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Time = 0.22 (sec) , antiderivative size = 82, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {448505859375 \, x^{10} + 1836738281250 \, x^{9} + 2748937500000 \, x^{8} + 1294582500000 \, x^{7} - 1049233500000 \, x^{6} - 1497169800000 \, x^{5} - 372682800000 \, x^{4} + 369438720000 \, x^{3} + 281928652425 \, x^{2} + 412160 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 58326747710 \, x - 120967}{683593750 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 78, normalized size of antiderivative = 0.90 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {6561 x^{8}}{250} + \frac {332424 x^{7}}{4375} + \frac {376407 x^{6}}{6250} - \frac {74601 x^{5}}{3125} - \frac {1700919 x^{4}}{31250} - \frac {5350194 x^{3}}{390625} + \frac {55559043 x^{2}}{3906250} + \frac {92582457 x}{9765625} + \frac {- 28600 x - 17281}{2441406250 x^{2} + 2929687500 x + 878906250} + \frac {5888 \log {\left (5 x + 3 \right )}}{9765625} \]
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Time = 0.20 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.76 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {6561}{250} \, x^{8} + \frac {332424}{4375} \, x^{7} + \frac {376407}{6250} \, x^{6} - \frac {74601}{3125} \, x^{5} - \frac {1700919}{31250} \, x^{4} - \frac {5350194}{390625} \, x^{3} + \frac {55559043}{3906250} \, x^{2} + \frac {92582457}{9765625} \, x - \frac {11 \, {\left (2600 \, x + 1571\right )}}{97656250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {5888}{9765625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.30 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {6561}{250} \, x^{8} + \frac {332424}{4375} \, x^{7} + \frac {376407}{6250} \, x^{6} - \frac {74601}{3125} \, x^{5} - \frac {1700919}{31250} \, x^{4} - \frac {5350194}{390625} \, x^{3} + \frac {55559043}{3906250} \, x^{2} + \frac {92582457}{9765625} \, x - \frac {11 \, {\left (2600 \, x + 1571\right )}}{97656250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {5888}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 1.19 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^8}{(3+5 x)^3} \, dx=\frac {92582457\,x}{9765625}+\frac {5888\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {\frac {572\,x}{48828125}+\frac {17281}{2441406250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {55559043\,x^2}{3906250}-\frac {5350194\,x^3}{390625}-\frac {1700919\,x^4}{31250}-\frac {74601\,x^5}{3125}+\frac {376407\,x^6}{6250}+\frac {332424\,x^7}{4375}+\frac {6561\,x^8}{250} \]
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