Integrand size = 22, antiderivative size = 65 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=\frac {1331}{2401 (1-2 x)}+\frac {1}{1323 (2+3 x)^3}-\frac {101}{6174 (2+3 x)^2}+\frac {363}{2401 (2+3 x)}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (2+3 x)}{16807} \]
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Time = 0.02 (sec) , antiderivative size = 65, 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} \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=\frac {1331}{2401 (1-2 x)}+\frac {363}{2401 (3 x+2)}-\frac {101}{6174 (3 x+2)^2}+\frac {1}{1323 (3 x+2)^3}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (3 x+2)}{16807} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2662}{2401 (-1+2 x)^2}-\frac {6534}{16807 (-1+2 x)}-\frac {1}{147 (2+3 x)^4}+\frac {101}{1029 (2+3 x)^3}-\frac {1089}{2401 (2+3 x)^2}+\frac {9801}{16807 (2+3 x)}\right ) \, dx \\ & = \frac {1331}{2401 (1-2 x)}+\frac {1}{1323 (2+3 x)^3}-\frac {101}{6174 (2+3 x)^2}+\frac {363}{2401 (2+3 x)}-\frac {3267 \log (1-2 x)}{16807}+\frac {3267 \log (2+3 x)}{16807} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.95 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=\frac {\frac {7}{2} \left (\frac {71874}{1-2 x}+\frac {98}{(2+3 x)^3}-\frac {2121}{(2+3 x)^2}+\frac {19602}{2+3 x}\right )-88209 \log (1-2 x)+88209 \log (4+6 x)}{453789} \]
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Time = 2.67 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74
method | result | size |
norman | \(\frac {-\frac {2667797}{129654} x -\frac {199994}{7203} x^{2}-\frac {29403}{2401} x^{3}-\frac {324628}{64827}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(48\) |
risch | \(\frac {-\frac {2667797}{129654} x -\frac {199994}{7203} x^{2}-\frac {29403}{2401} x^{3}-\frac {324628}{64827}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(49\) |
default | \(-\frac {1331}{2401 \left (-1+2 x \right )}-\frac {3267 \ln \left (-1+2 x \right )}{16807}+\frac {1}{1323 \left (2+3 x \right )^{3}}-\frac {101}{6174 \left (2+3 x \right )^{2}}+\frac {363}{2401 \left (2+3 x \right )}+\frac {3267 \ln \left (2+3 x \right )}{16807}\) | \(54\) |
parallelrisch | \(-\frac {1411344 \ln \left (x -\frac {1}{2}\right ) x^{4}-1411344 \ln \left (\frac {2}{3}+x \right ) x^{4}+2117016 \ln \left (x -\frac {1}{2}\right ) x^{3}-2117016 \ln \left (\frac {2}{3}+x \right ) x^{3}+4544792 x^{4}+470448 \ln \left (x -\frac {1}{2}\right ) x^{2}-470448 \ln \left (\frac {2}{3}+x \right ) x^{2}+8463756 x^{3}-522720 \ln \left (x -\frac {1}{2}\right ) x +522720 \ln \left (\frac {2}{3}+x \right ) x +5248152 x^{2}-209088 \ln \left (x -\frac {1}{2}\right )+209088 \ln \left (\frac {2}{3}+x \right )+1083348 x}{134456 \left (-1+2 x \right ) \left (2+3 x \right )^{3}}\) | \(116\) |
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Time = 0.22 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.46 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=-\frac {11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 176418 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 18674579 \, x + 4544792}{907578 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.86 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=\frac {- 1587762 x^{3} - 3599892 x^{2} - 2667797 x - 649256}{7001316 x^{4} + 10501974 x^{3} + 2333772 x^{2} - 2593080 x - 1037232} - \frac {3267 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {3267 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
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Time = 0.22 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.86 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=-\frac {1587762 \, x^{3} + 3599892 \, x^{2} + 2667797 \, x + 649256}{129654 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac {3267}{16807} \, \log \left (3 \, x + 2\right ) - \frac {3267}{16807} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.92 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=-\frac {1331}{2401 \, {\left (2 \, x - 1\right )}} - \frac {2 \, {\left (\frac {43645}{2 \, x - 1} + \frac {50127}{{\left (2 \, x - 1\right )}^{2}} + 9502\right )}}{16807 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{3}} + \frac {3267}{16807} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
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Time = 1.43 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71 \[ \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^4} \, dx=\frac {6534\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}-\frac {\frac {1089\,x^3}{4802}+\frac {99997\,x^2}{194481}+\frac {2667797\,x}{7001316}+\frac {162314}{1750329}}{x^4+\frac {3\,x^3}{2}+\frac {x^2}{3}-\frac {10\,x}{27}-\frac {4}{27}} \]
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