Optimal. Leaf size=86 \[ \frac {4774713}{16807 (3 x+2)}+\frac {136419}{4802 (3 x+2)^2}+\frac {1299}{343 (3 x+2)^3}+\frac {111}{196 (3 x+2)^4}+\frac {3}{35 (3 x+2)^5}-\frac {64 \log (1-2 x)}{1294139}-\frac {167115051 \log (3 x+2)}{117649}+\frac {15625}{11} \log (5 x+3) \]
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Rubi [A] time = 0.04, antiderivative size = 86, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {72} \[ \frac {4774713}{16807 (3 x+2)}+\frac {136419}{4802 (3 x+2)^2}+\frac {1299}{343 (3 x+2)^3}+\frac {111}{196 (3 x+2)^4}+\frac {3}{35 (3 x+2)^5}-\frac {64 \log (1-2 x)}{1294139}-\frac {167115051 \log (3 x+2)}{117649}+\frac {15625}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^6 (3+5 x)} \, dx &=\int \left (-\frac {128}{1294139 (-1+2 x)}-\frac {9}{7 (2+3 x)^6}-\frac {333}{49 (2+3 x)^5}-\frac {11691}{343 (2+3 x)^4}-\frac {409257}{2401 (2+3 x)^3}-\frac {14324139}{16807 (2+3 x)^2}-\frac {501345153}{117649 (2+3 x)}+\frac {78125}{11 (3+5 x)}\right ) \, dx\\ &=\frac {3}{35 (2+3 x)^5}+\frac {111}{196 (2+3 x)^4}+\frac {1299}{343 (2+3 x)^3}+\frac {136419}{4802 (2+3 x)^2}+\frac {4774713}{16807 (2+3 x)}-\frac {64 \log (1-2 x)}{1294139}-\frac {167115051 \log (2+3 x)}{117649}+\frac {15625}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.11, size = 60, normalized size = 0.70 \[ \frac {\frac {2079 \left (286482780 x^4+773503410 x^3+783477080 x^2+352854525 x+59622386\right )}{4 (3 x+2)^5}-320 \log (1-2 x)-9191327805 \log (6 x+4)+9191328125 \log (10 x+6)}{6470695} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.83, size = 148, normalized size = 1.72 \[ \frac {595597699620 \, x^{4} + 1608113589390 \, x^{3} + 1628848849320 \, x^{2} + 36765312500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 36765311220 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) - 1280 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 733584557475 \, x + 123954940494}{25882780 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 57, normalized size = 0.66 \[ \frac {27 \, {\left (286482780 \, x^{4} + 773503410 \, x^{3} + 783477080 \, x^{2} + 352854525 \, x + 59622386\right )}}{336140 \, {\left (3 \, x + 2\right )}^{5}} + \frac {15625}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {167115051}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {64}{1294139} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 71, normalized size = 0.83 \[ -\frac {64 \ln \left (2 x -1\right )}{1294139}-\frac {167115051 \ln \left (3 x +2\right )}{117649}+\frac {15625 \ln \left (5 x +3\right )}{11}+\frac {3}{35 \left (3 x +2\right )^{5}}+\frac {111}{196 \left (3 x +2\right )^{4}}+\frac {1299}{343 \left (3 x +2\right )^{3}}+\frac {136419}{4802 \left (3 x +2\right )^{2}}+\frac {4774713}{16807 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 74, normalized size = 0.86 \[ \frac {27 \, {\left (286482780 \, x^{4} + 773503410 \, x^{3} + 783477080 \, x^{2} + 352854525 \, x + 59622386\right )}}{336140 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {15625}{11} \, \log \left (5 \, x + 3\right ) - \frac {167115051}{117649} \, \log \left (3 \, x + 2\right ) - \frac {64}{1294139} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 65, normalized size = 0.76 \[ \frac {15625\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {167115051\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {64\,\ln \left (x-\frac {1}{2}\right )}{1294139}+\frac {\frac {1591571\,x^4}{16807}+\frac {25783447\,x^3}{100842}+\frac {39173854\,x^2}{151263}+\frac {23523635\,x}{201684}+\frac {29811193}{1512630}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 76, normalized size = 0.88 \[ - \frac {- 7735035060 x^{4} - 20884592070 x^{3} - 21153881160 x^{2} - 9527072175 x - 1609804422}{81682020 x^{5} + 272273400 x^{4} + 363031200 x^{3} + 242020800 x^{2} + 80673600 x + 10756480} - \frac {64 \log {\left (x - \frac {1}{2} \right )}}{1294139} + \frac {15625 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {167115051 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
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