Integrand size = 22, antiderivative size = 97 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (2+3 x)}{823543}+\frac {78125}{11} \log (3+5 x) \]
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Time = 0.04 (sec) , antiderivative size = 97, 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 = {84} \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {167115051}{117649 (3 x+2)}+\frac {4774713}{33614 (3 x+2)^2}+\frac {45473}{2401 (3 x+2)^3}+\frac {3897}{1372 (3 x+2)^4}+\frac {111}{245 (3 x+2)^5}+\frac {1}{14 (3 x+2)^6}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (3 x+2)}{823543}+\frac {78125}{11} \log (5 x+3) \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {256}{9058973 (-1+2 x)}-\frac {9}{7 (2+3 x)^7}-\frac {333}{49 (2+3 x)^6}-\frac {11691}{343 (2+3 x)^5}-\frac {409257}{2401 (2+3 x)^4}-\frac {14324139}{16807 (2+3 x)^3}-\frac {501345153}{117649 (2+3 x)^2}-\frac {17547080931}{823543 (2+3 x)}+\frac {390625}{11 (3+5 x)}\right ) \, dx \\ & = \frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (2+3 x)}{823543}+\frac {78125}{11} \log (3+5 x) \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 97, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (4+6 x)}{823543}+\frac {78125}{11} \log (6+10 x) \]
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Time = 2.55 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.61
method | result | size |
norman | \(\frac {\frac {40608957393}{117649} x^{5}+\frac {184154098887}{117649} x^{3}+\frac {208981500498}{588245} x +\frac {273433644891}{235298} x^{4}+\frac {496223395263}{470596} x^{2}+\frac {56343426549}{1176490}}{\left (2+3 x \right )^{6}}-\frac {128 \ln \left (-1+2 x \right )}{9058973}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{11}\) | \(59\) |
risch | \(\frac {\frac {40608957393}{117649} x^{5}+\frac {184154098887}{117649} x^{3}+\frac {208981500498}{588245} x +\frac {273433644891}{235298} x^{4}+\frac {496223395263}{470596} x^{2}+\frac {56343426549}{1176490}}{\left (2+3 x \right )^{6}}-\frac {128 \ln \left (-1+2 x \right )}{9058973}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{11}\) | \(60\) |
default | \(\frac {78125 \ln \left (3+5 x \right )}{11}-\frac {128 \ln \left (-1+2 x \right )}{9058973}+\frac {1}{14 \left (2+3 x \right )^{6}}+\frac {111}{245 \left (2+3 x \right )^{5}}+\frac {3897}{1372 \left (2+3 x \right )^{4}}+\frac {45473}{2401 \left (2+3 x \right )^{3}}+\frac {4774713}{33614 \left (2+3 x \right )^{2}}+\frac {167115051}{117649 \left (2+3 x \right )}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}\) | \(80\) |
parallelrisch | \(-\frac {439221985392960 x -88942644000000000 \ln \left (x +\frac {3}{5}\right ) x^{2}+177885287646105600 \ln \left (\frac {2}{3}+x \right ) x^{3}-23718038400000000 \ln \left (x +\frac {3}{5}\right ) x +88942643823052800 \ln \left (\frac {2}{3}+x \right ) x^{2}+23718038352814080 \ln \left (\frac {2}{3}+x \right ) x +10649692829573028 x^{5}+3162725562475017 x^{6}+9666963414108000 x^{3}+14347432073052540 x^{4}+3257566473989520 x^{2}+398131200 \ln \left (x -\frac {1}{2}\right ) x^{4}+200120948601868800 \ln \left (\frac {2}{3}+x \right ) x^{4}+2635337594757120 \ln \left (\frac {2}{3}+x \right )+353894400 \ln \left (x -\frac {1}{2}\right ) x^{3}+176947200 \ln \left (x -\frac {1}{2}\right ) x^{2}+47185920 \ln \left (x -\frac {1}{2}\right ) x -2635337600000000 \ln \left (x +\frac {3}{5}\right )+120072569161121280 \ln \left (\frac {2}{3}+x \right ) x^{5}-177885288000000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-120072569400000000 \ln \left (x +\frac {3}{5}\right ) x^{5}-200120949000000000 \ln \left (x +\frac {3}{5}\right ) x^{4}+30018142290280320 \ln \left (\frac {2}{3}+x \right ) x^{6}-30018142350000000 \ln \left (x +\frac {3}{5}\right ) x^{6}+5242880 \ln \left (x -\frac {1}{2}\right )+59719680 \ln \left (x -\frac {1}{2}\right ) x^{6}+238878720 \ln \left (x -\frac {1}{2}\right ) x^{5}}{5797742720 \left (2+3 x \right )^{6}}\) | \(213\) |
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Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (79) = 158\).
Time = 0.24 (sec) , antiderivative size = 173, normalized size of antiderivative = 1.78 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {62537794385220 \, x^{5} + 210543906566070 \, x^{4} + 283597312285980 \, x^{3} + 191046007176255 \, x^{2} + 1286785937500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 1286785934940 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) - 2560 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 64366302153384 \, x + 8676887688546}{181179460 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
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Time = 0.12 (sec) , antiderivative size = 87, normalized size of antiderivative = 0.90 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=- \frac {- 812179147860 x^{5} - 2734336448910 x^{4} - 3683081977740 x^{3} - 2481116976315 x^{2} - 835926001992 x - 112686853098}{1715322420 x^{6} + 6861289680 x^{5} + 11435482800 x^{4} + 10164873600 x^{3} + 5082436800 x^{2} + 1355316480 x + 150590720} - \frac {128 \log {\left (x - \frac {1}{2} \right )}}{9058973} + \frac {78125 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {5849026977 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
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Time = 0.20 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {3 \, {\left (270726382620 \, x^{5} + 911445482970 \, x^{4} + 1227693992580 \, x^{3} + 827038992105 \, x^{2} + 278642000664 \, x + 37562284366\right )}}{2352980 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac {78125}{11} \, \log \left (5 \, x + 3\right ) - \frac {5849026977}{823543} \, \log \left (3 \, x + 2\right ) - \frac {128}{9058973} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.64 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {3 \, {\left (270726382620 \, x^{5} + 911445482970 \, x^{4} + 1227693992580 \, x^{3} + 827038992105 \, x^{2} + 278642000664 \, x + 37562284366\right )}}{2352980 \, {\left (3 \, x + 2\right )}^{6}} + \frac {78125}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5849026977}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {128}{9058973} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 1.42 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.77 \[ \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx=\frac {78125\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {5849026977\,\ln \left (x+\frac {2}{3}\right )}{823543}-\frac {128\,\ln \left (x-\frac {1}{2}\right )}{9058973}+\frac {\frac {55705017\,x^5}{117649}+\frac {1125241337\,x^4}{705894}+\frac {6820522181\,x^3}{3176523}+\frac {18378644269\,x^2}{12706092}+\frac {7740055574\,x}{15882615}+\frac {18781142183}{285887070}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}} \]
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