Optimal. Leaf size=86 \[ \frac {8}{26411 (1-2 x)^2}+\frac {2672}{2033647 (1-2 x)}+\frac {9}{343 (2+3 x)^3}+\frac {1107}{4802 (2+3 x)^2}+\frac {39393}{16807 (2+3 x)}-\frac {267760 \log (1-2 x)}{156590819}-\frac {1380915 \log (2+3 x)}{117649}+\frac {15625 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.03, 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 = {90}
\begin {gather*} \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} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.07, size = 69, normalized size = 0.80 \begin {gather*} \frac {5 \left (\frac {77 \left (40167012-43096225 x-222614730 x^2+125249220 x^3+342903240 x^4\right )}{5 (1-2 x)^2 (2+3 x)^3}-107104 \log (5-10 x)-735199146 \log (5 (2+3 x))+735306250 \log (3+5 x)\right )}{313181638} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 71, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {171451620}{2033647} x^{4}+\frac {62624610}{2033647} x^{3}-\frac {111307365}{2033647} x^{2}-\frac {43096225}{4067294} x +\frac {20083506}{2033647}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3}}-\frac {267760 \ln \left (-1+2 x \right )}{156590819}-\frac {1380915 \ln \left (2+3 x \right )}{117649}+\frac {15625 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
norman | \(\frac {\frac {136954665}{369754} x^{4}+\frac {1163598075}{4067294} x^{5}-\frac {1438333245}{16269176} x^{3}-\frac {1695019985}{8134588} x^{2}+\frac {63179731}{2033647}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3}}-\frac {267760 \ln \left (-1+2 x \right )}{156590819}-\frac {1380915 \ln \left (2+3 x \right )}{117649}+\frac {15625 \ln \left (3+5 x \right )}{1331}\) | \(63\) |
default | \(\frac {8}{26411 \left (-1+2 x \right )^{2}}-\frac {2672}{2033647 \left (-1+2 x \right )}-\frac {267760 \ln \left (-1+2 x \right )}{156590819}+\frac {9}{343 \left (2+3 x \right )^{3}}+\frac {1107}{4802 \left (2+3 x \right )^{2}}+\frac {39393}{16807 \left (2+3 x \right )}-\frac {1380915 \ln \left (2+3 x \right )}{117649}+\frac {15625 \ln \left (3+5 x \right )}{1331}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 74, normalized size = 0.86 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs.
\(2 (70) = 140\).
time = 0.65, size = 148, normalized size = 1.72 \begin {gather*} \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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 75, normalized size = 0.87 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.08, size = 64, normalized size = 0.74 \begin {gather*} \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 ) \end {gather*}
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 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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