Integrand size = 20, antiderivative size = 73 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {1851147 x}{390625}+\frac {129654 x^2}{15625}+\frac {2052 x^3}{3125}-\frac {181521 x^4}{12500}-\frac {51759 x^5}{3125}-\frac {729 x^6}{125}-\frac {11}{3906250 (3+5 x)^2}-\frac {229}{1953125 (3+5 x)}+\frac {2037 \log (3+5 x)}{1953125} \]
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Time = 0.03 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=-\frac {729 x^6}{125}-\frac {51759 x^5}{3125}-\frac {181521 x^4}{12500}+\frac {2052 x^3}{3125}+\frac {129654 x^2}{15625}+\frac {1851147 x}{390625}-\frac {229}{1953125 (5 x+3)}-\frac {11}{3906250 (5 x+3)^2}+\frac {2037 \log (5 x+3)}{1953125} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1851147}{390625}+\frac {259308 x}{15625}+\frac {6156 x^2}{3125}-\frac {181521 x^3}{3125}-\frac {51759 x^4}{625}-\frac {4374 x^5}{125}+\frac {11}{390625 (3+5 x)^3}+\frac {229}{390625 (3+5 x)^2}+\frac {2037}{390625 (3+5 x)}\right ) \, dx \\ & = \frac {1851147 x}{390625}+\frac {129654 x^2}{15625}+\frac {2052 x^3}{3125}-\frac {181521 x^4}{12500}-\frac {51759 x^5}{3125}-\frac {729 x^6}{125}-\frac {11}{3906250 (3+5 x)^2}-\frac {229}{1953125 (3+5 x)}+\frac {2037 \log (3+5 x)}{1953125} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.88 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {-\frac {5 \left (-12167374-107200136 x-372626040 x^2-583310700 x^3-150703875 x^4+887969250 x^5+1425650625 x^6+920362500 x^7+227812500 x^8\right )}{(3+5 x)^2}+8148 \log (-3 (3+5 x))}{7812500} \]
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Time = 2.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {729 x^{6}}{125}-\frac {51759 x^{5}}{3125}-\frac {181521 x^{4}}{12500}+\frac {2052 x^{3}}{3125}+\frac {129654 x^{2}}{15625}+\frac {1851147 x}{390625}+\frac {-\frac {229 x}{390625}-\frac {277}{781250}}{\left (3+5 x \right )^{2}}+\frac {2037 \ln \left (3+5 x \right )}{1953125}\) | \(52\) |
default | \(\frac {1851147 x}{390625}+\frac {129654 x^{2}}{15625}+\frac {2052 x^{3}}{3125}-\frac {181521 x^{4}}{12500}-\frac {51759 x^{5}}{3125}-\frac {729 x^{6}}{125}-\frac {11}{3906250 \left (3+5 x \right )^{2}}-\frac {229}{1953125 \left (3+5 x \right )}+\frac {2037 \ln \left (3+5 x \right )}{1953125}\) | \(56\) |
norman | \(\frac {\frac {49981667}{1171875} x +\frac {304945001}{1406250} x^{2}+\frac {5833107}{15625} x^{3}+\frac {1205631}{12500} x^{4}-\frac {3551877}{6250} x^{5}-\frac {2281041}{2500} x^{6}-\frac {73629}{125} x^{7}-\frac {729}{5} x^{8}}{\left (3+5 x \right )^{2}}+\frac {2037 \ln \left (3+5 x \right )}{1953125}\) | \(57\) |
parallelrisch | \(\frac {-10251562500 x^{8}-41416312500 x^{7}-64154278125 x^{6}-39958616250 x^{5}+6781674375 x^{4}+1833300 \ln \left (x +\frac {3}{5}\right ) x^{2}+26248981500 x^{3}+2199960 \ln \left (x +\frac {3}{5}\right ) x +15247250050 x^{2}+659988 \ln \left (x +\frac {3}{5}\right )+2998900020 x}{70312500 \left (3+5 x \right )^{2}}\) | \(71\) |
meijerg | \(\frac {64 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {544 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {112 x \left (15 x +6\right )}{15 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {2037 \ln \left (1+\frac {5 x}{3}\right )}{1953125}+\frac {756 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {2268 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {37422 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {59049 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{31250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {59049 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{125000 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {59049 x \left (-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{1953125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(247\) |
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Time = 0.22 (sec) , antiderivative size = 72, normalized size of antiderivative = 0.99 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=-\frac {1139062500 \, x^{8} + 4601812500 \, x^{7} + 7128253125 \, x^{6} + 4439846250 \, x^{5} - 753519375 \, x^{4} - 2916553500 \, x^{3} - 1694131200 \, x^{2} - 8148 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 333201880 \, x + 2770}{7812500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=- \frac {729 x^{6}}{125} - \frac {51759 x^{5}}{3125} - \frac {181521 x^{4}}{12500} + \frac {2052 x^{3}}{3125} + \frac {129654 x^{2}}{15625} + \frac {1851147 x}{390625} - \frac {458 x + 277}{19531250 x^{2} + 23437500 x + 7031250} + \frac {2037 \log {\left (5 x + 3 \right )}}{1953125} \]
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Time = 0.20 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.77 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=-\frac {729}{125} \, x^{6} - \frac {51759}{3125} \, x^{5} - \frac {181521}{12500} \, x^{4} + \frac {2052}{3125} \, x^{3} + \frac {129654}{15625} \, x^{2} + \frac {1851147}{390625} \, x - \frac {458 \, x + 277}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {2037}{1953125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=-\frac {729}{125} \, x^{6} - \frac {51759}{3125} \, x^{5} - \frac {181521}{12500} \, x^{4} + \frac {2052}{3125} \, x^{3} + \frac {129654}{15625} \, x^{2} + \frac {1851147}{390625} \, x - \frac {458 \, x + 277}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {2037}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.06 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {1851147\,x}{390625}+\frac {2037\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {\frac {229\,x}{9765625}+\frac {277}{19531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {129654\,x^2}{15625}+\frac {2052\,x^3}{3125}-\frac {181521\,x^4}{12500}-\frac {51759\,x^5}{3125}-\frac {729\,x^6}{125} \]
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