Integrand size = 22, antiderivative size = 76 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=\frac {1}{945 (2+3 x)^5}-\frac {103}{5292 (2+3 x)^4}+\frac {3469}{27783 (2+3 x)^3}-\frac {1331}{4802 (2+3 x)^2}-\frac {2662}{16807 (2+3 x)}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (2+3 x)}{117649} \]
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Time = 0.02 (sec) , antiderivative size = 76, 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} \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=-\frac {2662}{16807 (3 x+2)}-\frac {1331}{4802 (3 x+2)^2}+\frac {3469}{27783 (3 x+2)^3}-\frac {103}{5292 (3 x+2)^4}+\frac {1}{945 (3 x+2)^5}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (3 x+2)}{117649} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {10648}{117649 (-1+2 x)}-\frac {1}{63 (2+3 x)^6}+\frac {103}{441 (2+3 x)^5}-\frac {3469}{3087 (2+3 x)^4}+\frac {3993}{2401 (2+3 x)^3}+\frac {7986}{16807 (2+3 x)^2}+\frac {15972}{117649 (2+3 x)}\right ) \, dx \\ & = \frac {1}{945 (2+3 x)^5}-\frac {103}{5292 (2+3 x)^4}+\frac {3469}{27783 (2+3 x)^3}-\frac {1331}{4802 (2+3 x)^2}-\frac {2662}{16807 (2+3 x)}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (2+3 x)}{117649} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.68 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=\frac {2 \left (-\frac {7 \left (116805778+646472325 x+1308416040 x^2+1135249830 x^3+349307640 x^4\right )}{8 (2+3 x)^5}-1078110 \log (1-2 x)+1078110 \log (4+6 x)\right )}{47647845} \]
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Time = 2.54 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.61
method | result | size |
norman | \(\frac {-\frac {43098155}{1815156} x -\frac {7268978}{151263} x^{2}-\frac {1401543}{33614} x^{3}-\frac {215622}{16807} x^{4}-\frac {58402889}{13613670}}{\left (2+3 x \right )^{5}}-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(46\) |
risch | \(\frac {-\frac {43098155}{1815156} x -\frac {7268978}{151263} x^{2}-\frac {1401543}{33614} x^{3}-\frac {215622}{16807} x^{4}-\frac {58402889}{13613670}}{\left (2+3 x \right )^{5}}-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(47\) |
default | \(-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {1}{945 \left (2+3 x \right )^{5}}-\frac {103}{5292 \left (2+3 x \right )^{4}}+\frac {3469}{27783 \left (2+3 x \right )^{3}}-\frac {1331}{4802 \left (2+3 x \right )^{2}}-\frac {2662}{16807 \left (2+3 x \right )}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
parallelrisch | \(\frac {1241982720 \ln \left (\frac {2}{3}+x \right ) x^{5}-1241982720 \ln \left (x -\frac {1}{2}\right ) x^{5}+4139942400 \ln \left (\frac {2}{3}+x \right ) x^{4}-4139942400 \ln \left (x -\frac {1}{2}\right ) x^{4}+3679382007 x^{5}+5519923200 \ln \left (\frac {2}{3}+x \right ) x^{3}-5519923200 \ln \left (x -\frac {1}{2}\right ) x^{3}+10815626850 x^{4}+3679948800 \ln \left (\frac {2}{3}+x \right ) x^{2}-3679948800 \ln \left (x -\frac {1}{2}\right ) x^{2}+11643624440 x^{3}+1226649600 \ln \left (\frac {2}{3}+x \right ) x -1226649600 \ln \left (x -\frac {1}{2}\right ) x +5474369040 x^{2}+163553280 \ln \left (\frac {2}{3}+x \right )-163553280 \ln \left (x -\frac {1}{2}\right )+952294560 x}{112943040 \left (2+3 x \right )^{5}}\) | \(132\) |
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Time = 0.22 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.51 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=-\frac {2445153480 \, x^{4} + 7946748810 \, x^{3} + 9158912280 \, x^{2} - 8624880 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 8624880 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 4525306275 \, x + 817640446}{190591380 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.86 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=- \frac {349307640 x^{4} + 1135249830 x^{3} + 1308416040 x^{2} + 646472325 x + 116805778}{6616243620 x^{5} + 22054145400 x^{4} + 29405527200 x^{3} + 19603684800 x^{2} + 6534561600 x + 871274880} - \frac {5324 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {5324 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
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Time = 0.19 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.87 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=-\frac {349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {5324}{117649} \, \log \left (3 \, x + 2\right ) - \frac {5324}{117649} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.63 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=-\frac {349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \, {\left (3 \, x + 2\right )}^{5}} + \frac {5324}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {5324}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.74 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx=\frac {10648\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}-\frac {\frac {2662\,x^4}{50421}+\frac {17303\,x^3}{100842}+\frac {7268978\,x^2}{36756909}+\frac {43098155\,x}{441082908}+\frac {58402889}{3308121810}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
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