Integrand size = 22, antiderivative size = 72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {83333293 x}{1953125}+\frac {80555569 x^2}{781250}+\frac {1327159 x^3}{78125}-\frac {20577159 x^4}{62500}-\frac {7315947 x^5}{15625}+\frac {130383 x^6}{1250}+\frac {672867 x^7}{875}+\frac {16767 x^8}{25}+\frac {972 x^9}{5}+\frac {121 \log (3+5 x)}{9765625} \]
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Time = 0.02 (sec) , antiderivative size = 72, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972 x^9}{5}+\frac {16767 x^8}{25}+\frac {672867 x^7}{875}+\frac {130383 x^6}{1250}-\frac {7315947 x^5}{15625}-\frac {20577159 x^4}{62500}+\frac {1327159 x^3}{78125}+\frac {80555569 x^2}{781250}+\frac {83333293 x}{1953125}+\frac {121 \log (5 x+3)}{9765625} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {83333293}{1953125}+\frac {80555569 x}{390625}+\frac {3981477 x^2}{78125}-\frac {20577159 x^3}{15625}-\frac {7315947 x^4}{3125}+\frac {391149 x^5}{625}+\frac {672867 x^6}{125}+\frac {134136 x^7}{25}+\frac {8748 x^8}{5}+\frac {121}{1953125 (3+5 x)}\right ) \, dx \\ & = \frac {83333293 x}{1953125}+\frac {80555569 x^2}{781250}+\frac {1327159 x^3}{78125}-\frac {20577159 x^4}{62500}-\frac {7315947 x^5}{15625}+\frac {130383 x^6}{1250}+\frac {672867 x^7}{875}+\frac {16767 x^8}{25}+\frac {972 x^9}{5}+\frac {121 \log (3+5 x)}{9765625} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {7880238537+58333305100 x+140972245750 x^2+23225282500 x^3-450125353125 x^4-640145362500 x^5+142606406250 x^6+1051354687500 x^7+916945312500 x^8+265781250000 x^9+16940 \log (3+5 x)}{1367187500} \]
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Time = 2.35 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(\frac {972 x^{9}}{5}+\frac {16767 x^{8}}{25}+\frac {672867 x^{7}}{875}+\frac {130383 x^{6}}{1250}-\frac {7315947 x^{5}}{15625}-\frac {20577159 x^{4}}{62500}+\frac {1327159 x^{3}}{78125}+\frac {80555569 x^{2}}{781250}+\frac {83333293 x}{1953125}+\frac {121 \ln \left (x +\frac {3}{5}\right )}{9765625}\) | \(51\) |
default | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
norman | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
risch | \(\frac {83333293 x}{1953125}+\frac {80555569 x^{2}}{781250}+\frac {1327159 x^{3}}{78125}-\frac {20577159 x^{4}}{62500}-\frac {7315947 x^{5}}{15625}+\frac {130383 x^{6}}{1250}+\frac {672867 x^{7}}{875}+\frac {16767 x^{8}}{25}+\frac {972 x^{9}}{5}+\frac {121 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{9765625}+\frac {832 x}{5}-\frac {592 x \left (-5 x +6\right )}{25}-\frac {2772 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}+\frac {30618 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}-\frac {66339 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}-\frac {111537 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{156250}+\frac {10451673 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{21875000}-\frac {1948617 x \left (-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{27343750}+\frac {1594323 x \left (\frac {109375000}{6561} x^{8}-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{136718750}\) | \(217\) |
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Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.05 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972 x^{9}}{5} + \frac {16767 x^{8}}{25} + \frac {672867 x^{7}}{875} + \frac {130383 x^{6}}{1250} - \frac {7315947 x^{5}}{15625} - \frac {20577159 x^{4}}{62500} + \frac {1327159 x^{3}}{78125} + \frac {80555569 x^{2}}{781250} + \frac {83333293 x}{1953125} + \frac {121 \log {\left (5 x + 3 \right )}}{9765625} \]
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Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx=\frac {83333293\,x}{1953125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{9765625}+\frac {80555569\,x^2}{781250}+\frac {1327159\,x^3}{78125}-\frac {20577159\,x^4}{62500}-\frac {7315947\,x^5}{15625}+\frac {130383\,x^6}{1250}+\frac {672867\,x^7}{875}+\frac {16767\,x^8}{25}+\frac {972\,x^9}{5} \]
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