Integrand size = 20, antiderivative size = 70 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {7}{15 (2+3 x)^5}+\frac {11}{4 (2+3 x)^4}+\frac {55}{3 (2+3 x)^3}+\frac {275}{2 (2+3 x)^2}+\frac {1375}{2+3 x}-6875 \log (2+3 x)+6875 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 70, 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} \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {1375}{3 x+2}+\frac {275}{2 (3 x+2)^2}+\frac {55}{3 (3 x+2)^3}+\frac {11}{4 (3 x+2)^4}+\frac {7}{15 (3 x+2)^5}-6875 \log (3 x+2)+6875 \log (5 x+3) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {7}{(2+3 x)^6}-\frac {33}{(2+3 x)^5}-\frac {165}{(2+3 x)^4}-\frac {825}{(2+3 x)^3}-\frac {4125}{(2+3 x)^2}-\frac {20625}{2+3 x}+\frac {34375}{3+5 x}\right ) \, dx \\ & = \frac {7}{15 (2+3 x)^5}+\frac {11}{4 (2+3 x)^4}+\frac {55}{3 (2+3 x)^3}+\frac {275}{2 (2+3 x)^2}+\frac {1375}{2+3 x}-6875 \log (2+3 x)+6875 \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.71 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {463586+2743565 x+6091800 x^2+6014250 x^3+2227500 x^4}{20 (2+3 x)^5}-6875 \log (2+3 x)+6875 \log (-3 (3+5 x)) \]
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Time = 0.73 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.66
method | result | size |
norman | \(\frac {111375 x^{4}+304590 x^{2}+\frac {548713}{4} x +\frac {601425}{2} x^{3}+\frac {231793}{10}}{\left (2+3 x \right )^{5}}-6875 \ln \left (2+3 x \right )+6875 \ln \left (3+5 x \right )\) | \(46\) |
risch | \(\frac {111375 x^{4}+304590 x^{2}+\frac {548713}{4} x +\frac {601425}{2} x^{3}+\frac {231793}{10}}{\left (2+3 x \right )^{5}}-6875 \ln \left (2+3 x \right )+6875 \ln \left (3+5 x \right )\) | \(47\) |
default | \(\frac {7}{15 \left (2+3 x \right )^{5}}+\frac {11}{4 \left (2+3 x \right )^{4}}+\frac {55}{3 \left (2+3 x \right )^{3}}+\frac {275}{2 \left (2+3 x \right )^{2}}+\frac {1375}{2+3 x}-6875 \ln \left (2+3 x \right )+6875 \ln \left (3+5 x \right )\) | \(63\) |
parallelrisch | \(-\frac {534600000 \ln \left (\frac {2}{3}+x \right ) x^{5}-534600000 \ln \left (x +\frac {3}{5}\right ) x^{5}+1782000000 \ln \left (\frac {2}{3}+x \right ) x^{4}-1782000000 \ln \left (x +\frac {3}{5}\right ) x^{4}+56325699 x^{5}+2376000000 \ln \left (\frac {2}{3}+x \right ) x^{3}-2376000000 \ln \left (x +\frac {3}{5}\right ) x^{3}+152112330 x^{4}+1584000000 \ln \left (\frac {2}{3}+x \right ) x^{2}-1584000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+154108440 x^{3}+528000000 \ln \left (\frac {2}{3}+x \right ) x -528000000 \ln \left (x +\frac {3}{5}\right ) x +69422160 x^{2}+70400000 \ln \left (\frac {2}{3}+x \right )-70400000 \ln \left (x +\frac {3}{5}\right )+11733280 x}{320 \left (2+3 x \right )^{5}}\) | \(132\) |
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Time = 0.22 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.64 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 137500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 137500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 2743565 \, x + 463586}{20 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.90 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=- \frac {- 2227500 x^{4} - 6014250 x^{3} - 6091800 x^{2} - 2743565 x - 463586}{4860 x^{5} + 16200 x^{4} + 21600 x^{3} + 14400 x^{2} + 4800 x + 640} + 6875 \log {\left (x + \frac {3}{5} \right )} - 6875 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.94 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 6875 \, \log \left (5 \, x + 3\right ) - 6875 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.69 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 2743565 \, x + 463586}{20 \, {\left (3 \, x + 2\right )}^{5}} + 6875 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6875 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.79 \[ \int \frac {1-2 x}{(2+3 x)^6 (3+5 x)} \, dx=\frac {\frac {1375\,x^4}{3}+\frac {2475\,x^3}{2}+\frac {101530\,x^2}{81}+\frac {548713\,x}{972}+\frac {231793}{2430}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}}-13750\,\mathrm {atanh}\left (30\,x+19\right ) \]
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