Optimal. Leaf size=86 \[ \frac {2672}{2033647 (1-2 x)}+\frac {39393}{16807 (3 x+2)}+\frac {8}{26411 (1-2 x)^2}+\frac {1107}{4802 (3 x+2)^2}+\frac {9}{343 (3 x+2)^3}-\frac {267760 \log (1-2 x)}{156590819}-\frac {1380915 \log (3 x+2)}{117649}+\frac {15625 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.05, 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 = {88} \[ \frac {2672}{2033647 (1-2 x)}+\frac {39393}{16807 (3 x+2)}+\frac {8}{26411 (1-2 x)^2}+\frac {1107}{4802 (3 x+2)^2}+\frac {9}{343 (3 x+2)^3}-\frac {267760 \log (1-2 x)}{156590819}-\frac {1380915 \log (3 x+2)}{117649}+\frac {15625 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x)^4 (3+5 x)} \, dx &=\int \left (-\frac {32}{26411 (-1+2 x)^3}+\frac {5344}{2033647 (-1+2 x)^2}-\frac {535520}{156590819 (-1+2 x)}-\frac {81}{343 (2+3 x)^4}-\frac {3321}{2401 (2+3 x)^3}-\frac {118179}{16807 (2+3 x)^2}-\frac {4142745}{117649 (2+3 x)}+\frac {78125}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {8}{26411 (1-2 x)^2}+\frac {2672}{2033647 (1-2 x)}+\frac {9}{343 (2+3 x)^3}+\frac {1107}{4802 (2+3 x)^2}+\frac {39393}{16807 (2+3 x)}-\frac {267760 \log (1-2 x)}{156590819}-\frac {1380915 \log (2+3 x)}{117649}+\frac {15625 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 69, normalized size = 0.80 \[ \frac {5 \left (\frac {77 \left (342903240 x^4+125249220 x^3-222614730 x^2-43096225 x+40167012\right )}{5 (1-2 x)^2 (3 x+2)^3}-107104 \log (5-10 x)-735199146 \log (5 (3 x+2))+735306250 \log (5 x+3)\right )}{313181638} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.57, size = 148, normalized size = 1.72 \[ \frac {26403549480 \, x^{4} + 9644189940 \, x^{3} - 17141334210 \, x^{2} + 3676531250 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 3675995730 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 535520 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 3318409325 \, x + 3092859924}{313181638 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 64, normalized size = 0.74 \[ \frac {342903240 \, x^{4} + 125249220 \, x^{3} - 222614730 \, x^{2} - 43096225 \, x + 40167012}{4067294 \, {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {15625}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1380915}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {267760}{156590819} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {267760 \ln \left (2 x -1\right )}{156590819}-\frac {1380915 \ln \left (3 x +2\right )}{117649}+\frac {15625 \ln \left (5 x +3\right )}{1331}+\frac {9}{343 \left (3 x +2\right )^{3}}+\frac {1107}{4802 \left (3 x +2\right )^{2}}+\frac {39393}{16807 \left (3 x +2\right )}+\frac {8}{26411 \left (2 x -1\right )^{2}}-\frac {2672}{2033647 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 74, normalized size = 0.86 \[ \frac {342903240 \, x^{4} + 125249220 \, x^{3} - 222614730 \, x^{2} - 43096225 \, x + 40167012}{4067294 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac {15625}{1331} \, \log \left (5 \, x + 3\right ) - \frac {1380915}{117649} \, \log \left (3 \, x + 2\right ) - \frac {267760}{156590819} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 63, normalized size = 0.73 \[ \frac {15625\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {1380915\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {267760\,\ln \left (x-\frac {1}{2}\right )}{156590819}+\frac {\frac {1587515\,x^4}{2033647}+\frac {1159715\,x^3}{4067294}-\frac {4122495\,x^2}{8134588}-\frac {43096225\,x}{439267752}+\frac {3347251}{36605646}}{x^5+x^4-\frac {5\,x^3}{12}-\frac {29\,x^2}{54}+\frac {x}{27}+\frac {2}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 75, normalized size = 0.87 \[ - \frac {- 342903240 x^{4} - 125249220 x^{3} + 222614730 x^{2} + 43096225 x - 40167012}{439267752 x^{5} + 439267752 x^{4} - 183028230 x^{3} - 235903052 x^{2} + 16269176 x + 32538352} - \frac {267760 \log {\left (x - \frac {1}{2} \right )}}{156590819} + \frac {15625 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {1380915 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
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