Integrand size = 20, antiderivative size = 57 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {21}{2 (2+3 x)^2}+\frac {309}{2+3 x}-\frac {55}{2 (3+5 x)^2}+\frac {505}{3+5 x}-3060 \log (2+3 x)+3060 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 57, 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} \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {309}{3 x+2}+\frac {505}{5 x+3}+\frac {21}{2 (3 x+2)^2}-\frac {55}{2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (5 x+3) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {63}{(2+3 x)^3}-\frac {927}{(2+3 x)^2}-\frac {9180}{2+3 x}+\frac {275}{(3+5 x)^3}-\frac {2525}{(3+5 x)^2}+\frac {15300}{3+5 x}\right ) \, dx \\ & = \frac {21}{2 (2+3 x)^2}+\frac {309}{2+3 x}-\frac {55}{2 (3+5 x)^2}+\frac {505}{3+5 x}-3060 \log (2+3 x)+3060 \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.04 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {21}{2 (2+3 x)^2}+\frac {309}{2+3 x}-\frac {55}{2 (3+5 x)^2}+\frac {505}{3+5 x}-3060 \log (2+3 x)+3060 \log (-3 (3+5 x)) \]
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Time = 2.25 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84
method | result | size |
norman | \(\frac {45900 x^{3}+55148 x +87210 x^{2}+\frac {23213}{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-3060 \ln \left (2+3 x \right )+3060 \ln \left (3+5 x \right )\) | \(48\) |
risch | \(\frac {45900 x^{3}+55148 x +87210 x^{2}+\frac {23213}{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}-3060 \ln \left (2+3 x \right )+3060 \ln \left (3+5 x \right )\) | \(49\) |
default | \(\frac {21}{2 \left (2+3 x \right )^{2}}+\frac {309}{2+3 x}-\frac {55}{2 \left (3+5 x \right )^{2}}+\frac {505}{3+5 x}-3060 \ln \left (2+3 x \right )+3060 \ln \left (3+5 x \right )\) | \(54\) |
parallelrisch | \(-\frac {49572000 \ln \left (\frac {2}{3}+x \right ) x^{4}-49572000 \ln \left (x +\frac {3}{5}\right ) x^{4}+125582400 \ln \left (\frac {2}{3}+x \right ) x^{3}-125582400 \ln \left (x +\frac {3}{5}\right ) x^{3}+5222925 x^{4}+119193120 \ln \left (\frac {2}{3}+x \right ) x^{2}-119193120 \ln \left (x +\frac {3}{5}\right ) x^{2}+9926610 x^{3}+50232960 \ln \left (\frac {2}{3}+x \right ) x -50232960 \ln \left (x +\frac {3}{5}\right ) x +6279113 x^{2}+7931520 \ln \left (\frac {2}{3}+x \right )-7931520 \ln \left (x +\frac {3}{5}\right )+1321908 x}{72 \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}\) | \(116\) |
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Time = 0.23 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.67 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {91800 \, x^{3} + 174420 \, x^{2} + 6120 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 6120 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 110296 \, x + 23213}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.93 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=- \frac {- 91800 x^{3} - 174420 x^{2} - 110296 x - 23213}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 3060 \log {\left (x + \frac {3}{5} \right )} - 3060 \log {\left (x + \frac {2}{3} \right )} \]
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Time = 0.20 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.98 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {91800 \, x^{3} + 174420 \, x^{2} + 110296 \, x + 23213}{2 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 3060 \, \log \left (5 \, x + 3\right ) - 3060 \, \log \left (3 \, x + 2\right ) \]
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Time = 0.29 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.84 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {91800 \, x^{3} + 174420 \, x^{2} + 110296 \, x + 23213}{2 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 3060 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 3060 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.79 \[ \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx=\frac {204\,x^3+\frac {1938\,x^2}{5}+\frac {55148\,x}{225}+\frac {23213}{450}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}}-6120\,\mathrm {atanh}\left (30\,x+19\right ) \]
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