Integrand size = 20, antiderivative size = 66 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {3060}{3 x+2}+\frac {3350}{5 x+3}+\frac {309}{2 (3 x+2)^2}-\frac {275}{2 (5 x+3)^2}+\frac {7}{(3 x+2)^3}-25350 \log (3 x+2)+25350 \log (5 x+3) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {63}{(2+3 x)^4}-\frac {927}{(2+3 x)^3}-\frac {9180}{(2+3 x)^2}-\frac {76050}{2+3 x}+\frac {1375}{(3+5 x)^3}-\frac {16750}{(3+5 x)^2}+\frac {126750}{3+5 x}\right ) \, dx \\ & = \frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 68, normalized size of antiderivative = 1.03 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {7}{(2+3 x)^3}+\frac {309}{2 (2+3 x)^2}+\frac {3060}{2+3 x}-\frac {275}{2 (3+5 x)^2}+\frac {3350}{3+5 x}-25350 \log (2+3 x)+25350 \log (-3 (3+5 x)) \]
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Time = 2.23 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.80
method | result | size |
norman | \(\frac {1140750 x^{4}+2815540 x^{2}+2927925 x^{3}+\frac {2404363}{2} x +192304}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(53\) |
risch | \(\frac {1140750 x^{4}+2815540 x^{2}+2927925 x^{3}+\frac {2404363}{2} x +192304}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(54\) |
default | \(\frac {7}{\left (2+3 x \right )^{3}}+\frac {309}{2 \left (2+3 x \right )^{2}}+\frac {3060}{2+3 x}-\frac {275}{2 \left (3+5 x \right )^{2}}+\frac {3350}{3+5 x}-25350 \ln \left (2+3 x \right )+25350 \ln \left (3+5 x \right )\) | \(63\) |
parallelrisch | \(-\frac {1232010000 \ln \left (\frac {2}{3}+x \right ) x^{5}-1232010000 \ln \left (x +\frac {3}{5}\right ) x^{5}+3942432000 \ln \left (\frac {2}{3}+x \right ) x^{4}-3942432000 \ln \left (x +\frac {3}{5}\right ) x^{4}+129805200 x^{5}+5043027600 \ln \left (\frac {2}{3}+x \right ) x^{3}-5043027600 \ln \left (x +\frac {3}{5}\right ) x^{3}+333242640 x^{4}+3223303200 \ln \left (\frac {2}{3}+x \right ) x^{2}-3223303200 \ln \left (x +\frac {3}{5}\right ) x^{2}+320525352 x^{3}+1029412800 \ln \left (\frac {2}{3}+x \right ) x -1029412800 \ln \left (x +\frac {3}{5}\right ) x +136889984 x^{2}+131414400 \ln \left (\frac {2}{3}+x \right )-131414400 \ln \left (x +\frac {3}{5}\right )+21902388 x}{72 \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}\) | \(139\) |
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Time = 0.23 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.74 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 50700 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 50700 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 2404363 \, x + 384608}{2 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.95 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=- \frac {- 2281500 x^{4} - 5855850 x^{3} - 5631080 x^{2} - 2404363 x - 384608}{1350 x^{5} + 4320 x^{4} + 5526 x^{3} + 3532 x^{2} + 1128 x + 144} + 25350 \log {\left (x + \frac {3}{5} \right )} - 25350 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.22 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.00 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 2404363 \, x + 384608}{2 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 25350 \, \log \left (5 \, x + 3\right ) - 25350 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.29 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.83 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 2404363 \, x + 384608}{2 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3}} + 25350 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 25350 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.83 \[ \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {1690\,x^4+\frac {13013\,x^3}{3}+\frac {563108\,x^2}{135}+\frac {2404363\,x}{1350}+\frac {192304}{675}}{x^5+\frac {16\,x^4}{5}+\frac {307\,x^3}{75}+\frac {1766\,x^2}{675}+\frac {188\,x}{225}+\frac {8}{75}}-50700\,\mathrm {atanh}\left (30\,x+19\right ) \]
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