Optimal. Leaf size=97 \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.0533089, 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} \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)^2} \, dx &=\int \left (\frac{128}{2033647 (-1+2 x)^2}-\frac{30080}{156590819 (-1+2 x)}+\frac{81}{49 (2+3 x)^5}+\frac{5994}{343 (2+3 x)^4}+\frac{321327}{2401 (2+3 x)^3}+\frac{15152832}{16807 (2+3 x)^2}+\frac{667079145}{117649 (2+3 x)}+\frac{78125}{121 (3+5 x)^2}-\frac{12578125}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{64}{2033647 (1-2 x)}-\frac{27}{196 (2+3 x)^4}-\frac{666}{343 (2+3 x)^3}-\frac{107109}{4802 (2+3 x)^2}-\frac{5050944}{16807 (2+3 x)}-\frac{15625}{121 (3+5 x)}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (2+3 x)}{117649}-\frac{2515625 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0912253, size = 75, normalized size = 0.77 \[ \frac{-\frac{77 \left (830228340600 x^5+1771154199360 x^4+1064845635750 x^3-132753874800 x^2-317609203475 x-77754195847\right )}{(3 x+2)^4 \left (10 x^2+x-3\right )}-60160 \log (3-6 x)+1183843122660 \log (3 x+2)-1183843062500 \log (-3 (5 x+3))}{626363276} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 80, normalized size = 0.8 \begin{align*} -{\frac{64}{4067294\,x-2033647}}-{\frac{15040\,\ln \left ( 2\,x-1 \right ) }{156590819}}-{\frac{27}{196\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{666}{343\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107109}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5050944}{33614+50421\,x}}+{\frac{222359715\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{15625}{363+605\,x}}-{\frac{2515625\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.31642, size = 113, normalized size = 1.16 \begin{align*} -\frac{830228340600 \, x^{5} + 1771154199360 \, x^{4} + 1064845635750 \, x^{3} - 132753874800 \, x^{2} - 317609203475 \, x - 77754195847}{8134588 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} - \frac{2515625}{1331} \, \log \left (5 \, x + 3\right ) + \frac{222359715}{117649} \, \log \left (3 \, x + 2\right ) - \frac{15040}{156590819} \, \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 = 1.497, size = 639, normalized size = 6.59 \begin{align*} -\frac{63927582226200 \, x^{5} + 136378873350720 \, x^{4} + 81993113952750 \, x^{3} - 10222048359600 \, x^{2} + 1183843062500 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (5 \, x + 3\right ) - 1183843122660 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (3 \, x + 2\right ) + 60160 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (2 \, x - 1\right ) - 24455908667575 \, x - 5987073080219}{626363276 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.258554, size = 85, normalized size = 0.88 \begin{align*} - \frac{830228340600 x^{5} + 1771154199360 x^{4} + 1064845635750 x^{3} - 132753874800 x^{2} - 317609203475 x - 77754195847}{6589016280 x^{6} + 18229611708 x^{5} + 17351076204 x^{4} + 4295062464 x^{3} - 3188758496 x^{2} - 2212607936 x - 390460224} - \frac{15040 \log{\left (x - \frac{1}{2} \right )}}{156590819} - \frac{2515625 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{222359715 \log{\left (x + \frac{2}{3} \right )}}{117649} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.02392, size = 140, normalized size = 1.44 \begin{align*} -\frac{15625}{121 \,{\left (5 \, x + 3\right )}} + \frac{25 \,{\left (\frac{6062344264539}{5 \, x + 3} + \frac{7964082495612}{{\left (5 \, x + 3\right )}^{2}} + \frac{3205106234076}{{\left (5 \, x + 3\right )}^{3}} + \frac{435889532968}{{\left (5 \, x + 3\right )}^{4}} - 1385260555122\right )}}{89480468 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + \frac{222359715}{117649} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{15040}{156590819} \, \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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