Optimal. Leaf size=97 \[ \frac{64}{1294139 (1-2 x)}+\frac{15192225}{117649 (3 x+2)}+\frac{434043}{33614 (3 x+2)^2}+\frac{4131}{2401 (3 x+2)^3}+\frac{351}{1372 (3 x+2)^4}+\frac{9}{245 (3 x+2)^5}-\frac{14912 \log (1-2 x)}{99648703}-\frac{531729603 \log (3 x+2)}{823543}+\frac{78125}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0544353, antiderivative size = 97, 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} \[ \frac{64}{1294139 (1-2 x)}+\frac{15192225}{117649 (3 x+2)}+\frac{434043}{33614 (3 x+2)^2}+\frac{4131}{2401 (3 x+2)^3}+\frac{351}{1372 (3 x+2)^4}+\frac{9}{245 (3 x+2)^5}-\frac{14912 \log (1-2 x)}{99648703}-\frac{531729603 \log (3 x+2)}{823543}+\frac{78125}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (2+3 x)^6 (3+5 x)} \, dx &=\int \left (\frac{128}{1294139 (-1+2 x)^2}-\frac{29824}{99648703 (-1+2 x)}-\frac{27}{49 (2+3 x)^6}-\frac{1053}{343 (2+3 x)^5}-\frac{37179}{2401 (2+3 x)^4}-\frac{1302129}{16807 (2+3 x)^3}-\frac{45576675}{117649 (2+3 x)^2}-\frac{1595188809}{823543 (2+3 x)}+\frac{390625}{121 (3+5 x)}\right ) \, dx\\ &=\frac{64}{1294139 (1-2 x)}+\frac{9}{245 (2+3 x)^5}+\frac{351}{1372 (2+3 x)^4}+\frac{4131}{2401 (2+3 x)^3}+\frac{434043}{33614 (2+3 x)^2}+\frac{15192225}{117649 (2+3 x)}-\frac{14912 \log (1-2 x)}{99648703}-\frac{531729603 \log (2+3 x)}{823543}+\frac{78125}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.047487, size = 87, normalized size = 0.9 \[ \frac{\frac{19712}{1-2 x}+\frac{51471258300}{3 x+2}+\frac{5146881894}{(3 x+2)^2}+\frac{685795572}{(3 x+2)^3}+\frac{101972871}{(3 x+2)^4}+\frac{73211292}{5 (3 x+2)^5}-59648 \log (5-10 x)-257357127852 \log (5 (3 x+2))+257357187500 \log (5 x+3)}{398594812} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 80, normalized size = 0.8 \begin{align*} -{\frac{64}{2588278\,x-1294139}}-{\frac{14912\,\ln \left ( 2\,x-1 \right ) }{99648703}}+{\frac{9}{245\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{351}{1372\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{4131}{2401\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{434043}{33614\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{15192225}{235298+352947\,x}}-{\frac{531729603\,\ln \left ( 2+3\,x \right ) }{823543}}+{\frac{78125\,\ln \left ( 3+5\,x \right ) }{121}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03486, size = 113, normalized size = 1.16 \begin{align*} \frac{541450587960 \, x^{5} + 1191190085640 \, x^{4} + 749805990750 \, x^{3} - 73492321230 \, x^{2} - 220760702913 \, x - 56342700586}{25882780 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac{78125}{121} \, \log \left (5 \, x + 3\right ) - \frac{531729603}{823543} \, \log \left (3 \, x + 2\right ) - \frac{14912}{99648703} \, \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 = 1.27316, size = 637, normalized size = 6.57 \begin{align*} \frac{41691695272920 \, x^{5} + 91721636594280 \, x^{4} + 57735061287750 \, x^{3} - 5658908734710 \, x^{2} + 1286785937500 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (5 \, x + 3\right ) - 1286785639260 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) - 298240 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) - 16998574124301 \, x - 4338387945122}{1992974060 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.255427, size = 85, normalized size = 0.88 \begin{align*} \frac{541450587960 x^{5} + 1191190085640 x^{4} + 749805990750 x^{3} - 73492321230 x^{2} - 220760702913 x - 56342700586}{12579031080 x^{6} + 35640588060 x^{5} + 34941753000 x^{4} + 9317800800 x^{3} - 6211867200 x^{2} - 4555369280 x - 828248960} - \frac{14912 \log{\left (x - \frac{1}{2} \right )}}{99648703} + \frac{78125 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{531729603 \log{\left (x + \frac{2}{3} \right )}}{823543} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.28072, size = 126, normalized size = 1.3 \begin{align*} -\frac{64}{1294139 \,{\left (2 \, x - 1\right )}} - \frac{54 \,{\left (\frac{6617665845}{2 \, x - 1} + \frac{23331909825}{{\left (2 \, x - 1\right )}^{2}} + \frac{36565643625}{{\left (2 \, x - 1\right )}^{3}} + \frac{21492731575}{{\left (2 \, x - 1\right )}^{4}} + 703958526\right )}}{4117715 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{5}} - \frac{531729603}{823543} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{78125}{121} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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