Optimal. Leaf size=86 \[ \frac{2704}{3195731 (1-2 x)}-\frac{6156}{2401 (3 x+2)}-\frac{3125}{1331 (5 x+3)}+\frac{8}{41503 (1-2 x)^2}-\frac{81}{686 (3 x+2)^2}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641} \]
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Rubi [A] time = 0.0459781, antiderivative size = 86, normalized size of antiderivative = 1., 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} \[ \frac{2704}{3195731 (1-2 x)}-\frac{6156}{2401 (3 x+2)}-\frac{3125}{1331 (5 x+3)}+\frac{8}{41503 (1-2 x)^2}-\frac{81}{686 (3 x+2)^2}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac{32}{41503 (-1+2 x)^3}+\frac{5408}{3195731 (-1+2 x)^2}-\frac{548448}{246071287 (-1+2 x)}+\frac{243}{343 (2+3 x)^3}+\frac{18468}{2401 (2+3 x)^2}+\frac{1000917}{16807 (2+3 x)}+\frac{15625}{1331 (3+5 x)^2}-\frac{1453125}{14641 (3+5 x)}\right ) \, dx\\ &=\frac{8}{41503 (1-2 x)^2}+\frac{2704}{3195731 (1-2 x)}-\frac{81}{686 (2+3 x)^2}-\frac{6156}{2401 (2+3 x)}-\frac{3125}{1331 (3+5 x)}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (2+3 x)}{16807}-\frac{290625 \log (3+5 x)}{14641}\\ \end{align*}
Mathematica [A] time = 0.0611108, size = 74, normalized size = 0.86 \[ \frac{\frac{41503 (6558 x-3251)}{\left (6 x^2+x-2\right )^2}-\frac{154 (16395384 x-7937593)}{6 x^2+x-2}-\frac{1155481250}{5 x+3}-548448 \log (5-10 x)+9769617198 \log (5 (3 x+2))-9769068750 \log (5 x+3)}{492142574} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 71, normalized size = 0.8 \begin{align*}{\frac{8}{41503\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{2704}{6391462\,x-3195731}}-{\frac{274224\,\ln \left ( 2\,x-1 \right ) }{246071287}}-{\frac{81}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{6156}{4802+7203\,x}}+{\frac{333639\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{3125}{3993+6655\,x}}-{\frac{290625\,\ln \left ( 3+5\,x \right ) }{14641}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.82156, size = 100, normalized size = 1.16 \begin{align*} -\frac{1523948040 \, x^{4} + 458007084 \, x^{3} - 957482214 \, x^{2} - 147486147 \, x + 160532983}{6391462 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} - \frac{290625}{14641} \, \log \left (5 \, x + 3\right ) + \frac{333639}{16807} \, \log \left (3 \, x + 2\right ) - \frac{274224}{246071287} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.57332, size = 498, normalized size = 5.79 \begin{align*} -\frac{117343999080 \, x^{4} + 35266545468 \, x^{3} - 73726130478 \, x^{2} + 9769068750 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 9769617198 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 548448 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (2 \, x - 1\right ) - 11356433319 \, x + 12361039691}{492142574 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.2368, size = 75, normalized size = 0.87 \begin{align*} - \frac{1523948040 x^{4} + 458007084 x^{3} - 957482214 x^{2} - 147486147 x + 160532983}{1150463160 x^{5} + 1073765616 x^{4} - 504925498 x^{3} - 568840118 x^{2} + 51131696 x + 76697544} - \frac{274224 \log{\left (x - \frac{1}{2} \right )}}{246071287} - \frac{290625 \log{\left (x + \frac{3}{5} \right )}}{14641} + \frac{333639 \log{\left (x + \frac{2}{3} \right )}}{16807} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.08651, size = 128, normalized size = 1.49 \begin{align*} -\frac{3125}{1331 \,{\left (5 \, x + 3\right )}} - \frac{5 \,{\left (\frac{84659379036}{5 \, x + 3} - \frac{206753119043}{{\left (5 \, x + 3\right )}^{2}} - \frac{95568773322}{{\left (5 \, x + 3\right )}^{3}} - 7983405324\right )}}{70306082 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + \frac{333639}{16807} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{274224}{246071287} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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