Integrand size = 22, antiderivative size = 66 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {17796 x}{15625}-\frac {5301 x^2}{6250}-\frac {5499 x^3}{3125}+\frac {648 x^4}{625}+\frac {972 x^5}{625}-\frac {121}{781250 (3+5 x)^2}-\frac {1771}{390625 (3+5 x)}+\frac {10234 \log (3+5 x)}{390625} \]
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Time = 0.03 (sec) , antiderivative size = 66, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {972 x^5}{625}+\frac {648 x^4}{625}-\frac {5499 x^3}{3125}-\frac {5301 x^2}{6250}+\frac {17796 x}{15625}-\frac {1771}{390625 (5 x+3)}-\frac {121}{781250 (5 x+3)^2}+\frac {10234 \log (5 x+3)}{390625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {17796}{15625}-\frac {5301 x}{3125}-\frac {16497 x^2}{3125}+\frac {2592 x^3}{625}+\frac {972 x^4}{125}+\frac {121}{78125 (3+5 x)^3}+\frac {1771}{78125 (3+5 x)^2}+\frac {10234}{78125 (3+5 x)}\right ) \, dx \\ & = \frac {17796 x}{15625}-\frac {5301 x^2}{6250}-\frac {5499 x^3}{3125}+\frac {648 x^4}{625}+\frac {972 x^5}{625}-\frac {121}{781250 (3+5 x)^2}-\frac {1771}{390625 (3+5 x)}+\frac {10234 \log (3+5 x)}{390625} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {20870428+109699660 x+161774550 x^2-50032500 x^3-252590625 x^4+4331250 x^5+283500000 x^6+151875000 x^7+102340 (3+5 x)^2 \log (6 (3+5 x))}{3906250 (3+5 x)^2} \]
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Time = 0.78 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {972 x^{5}}{625}+\frac {648 x^{4}}{625}-\frac {5499 x^{3}}{3125}-\frac {5301 x^{2}}{6250}+\frac {17796 x}{15625}+\frac {-\frac {1771 x}{78125}-\frac {10747}{781250}}{\left (3+5 x \right )^{2}}+\frac {10234 \ln \left (3+5 x \right )}{390625}\) | \(47\) |
default | \(\frac {17796 x}{15625}-\frac {5301 x^{2}}{6250}-\frac {5499 x^{3}}{3125}+\frac {648 x^{4}}{625}+\frac {972 x^{5}}{625}-\frac {121}{781250 \left (3+5 x \right )^{2}}-\frac {1771}{390625 \left (3+5 x \right )}+\frac {10234 \ln \left (3+5 x \right )}{390625}\) | \(51\) |
norman | \(\frac {\frac {2407894}{234375} x +\frac {3736841}{140625} x^{2}-\frac {40026}{3125} x^{3}-\frac {80829}{1250} x^{4}+\frac {693}{625} x^{5}+\frac {9072}{125} x^{6}+\frac {972}{25} x^{7}}{\left (3+5 x \right )^{2}}+\frac {10234 \ln \left (3+5 x \right )}{390625}\) | \(52\) |
parallelrisch | \(\frac {273375000 x^{7}+510300000 x^{6}+7796250 x^{5}-454663125 x^{4}+4605300 \ln \left (x +\frac {3}{5}\right ) x^{2}-90058500 x^{3}+5526360 \ln \left (x +\frac {3}{5}\right ) x +186842050 x^{2}+1657908 \ln \left (x +\frac {3}{5}\right )+72236820 x}{7031250 \left (3+5 x \right )^{2}}\) | \(66\) |
meijerg | \(\frac {16 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {56 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {56 x \left (15 x +6\right )}{225 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {10234 \ln \left (1+\frac {5 x}{3}\right )}{390625}-\frac {42 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{25 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {189 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {3969 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{6250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2187 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{15625 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {19683 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{781250 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(202\) |
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Time = 0.21 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {30375000 \, x^{7} + 56700000 \, x^{6} + 866250 \, x^{5} - 50518125 \, x^{4} - 10006500 \, x^{3} + 20730375 \, x^{2} + 20468 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 7990490 \, x - 10747}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {972 x^{5}}{625} + \frac {648 x^{4}}{625} - \frac {5499 x^{3}}{3125} - \frac {5301 x^{2}}{6250} + \frac {17796 x}{15625} + \frac {- 17710 x - 10747}{19531250 x^{2} + 23437500 x + 7031250} + \frac {10234 \log {\left (5 x + 3 \right )}}{390625} \]
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Time = 0.22 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.77 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {972}{625} \, x^{5} + \frac {648}{625} \, x^{4} - \frac {5499}{3125} \, x^{3} - \frac {5301}{6250} \, x^{2} + \frac {17796}{15625} \, x - \frac {11 \, {\left (1610 \, x + 977\right )}}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {10234}{390625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.30 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {972}{625} \, x^{5} + \frac {648}{625} \, x^{4} - \frac {5499}{3125} \, x^{3} - \frac {5301}{6250} \, x^{2} + \frac {17796}{15625} \, x - \frac {11 \, {\left (1610 \, x + 977\right )}}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {10234}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx=\frac {17796\,x}{15625}+\frac {10234\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {\frac {1771\,x}{1953125}+\frac {10747}{19531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {5301\,x^2}{6250}-\frac {5499\,x^3}{3125}+\frac {648\,x^4}{625}+\frac {972\,x^5}{625} \]
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