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 = 0.05, antiderivative size = 97, 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} \[ \frac {64}{1294139 (1-2 x)}+\frac {15192225}{117649 (3 x+2)}+\frac {434043}{33614 (3 x+2)^2}+\frac {4131}{2401 (3 x+2)^3}+\frac {351}{1372 (3 x+2)^4}+\frac {9}{245 (3 x+2)^5}-\frac {14912 \log (1-2 x)}{99648703}-\frac {531729603 \log (3 x+2)}{823543}+\frac {78125}{121} \log (5 x+3) \]
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*}
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Mathematica [A] time = 0.07, size = 87, normalized size = 0.90 \[ \frac {\frac {19712}{1-2 x}+\frac {51471258300}{3 x+2}+\frac {5146881894}{(3 x+2)^2}+\frac {685795572}{(3 x+2)^3}+\frac {101972871}{(3 x+2)^4}+\frac {73211292}{5 (3 x+2)^5}-59648 \log (5-10 x)-257357127852 \log (5 (3 x+2))+257357187500 \log (5 x+3)}{398594812} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.87, size = 173, normalized size = 1.78 \[ \frac {41691695272920 \, x^{5} + 91721636594280 \, x^{4} + 57735061287750 \, x^{3} - 5658908734710 \, x^{2} + 1286785937500 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (5 \, x + 3\right ) - 1286785639260 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) - 298240 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) - 16998574124301 \, x - 4338387945122}{1992974060 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 93, normalized size = 0.96 \[ -\frac {64}{1294139 \, {\left (2 \, x - 1\right )}} - \frac {54 \, {\left (\frac {6617665845}{2 \, x - 1} + \frac {23331909825}{{\left (2 \, x - 1\right )}^{2}} + \frac {36565643625}{{\left (2 \, x - 1\right )}^{3}} + \frac {21492731575}{{\left (2 \, x - 1\right )}^{4}} + 703958526\right )}}{4117715 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{5}} - \frac {531729603}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) + \frac {78125}{121} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 80, normalized size = 0.82 \[ -\frac {14912 \ln \left (2 x -1\right )}{99648703}-\frac {531729603 \ln \left (3 x +2\right )}{823543}+\frac {78125 \ln \left (5 x +3\right )}{121}+\frac {9}{245 \left (3 x +2\right )^{5}}+\frac {351}{1372 \left (3 x +2\right )^{4}}+\frac {4131}{2401 \left (3 x +2\right )^{3}}+\frac {434043}{33614 \left (3 x +2\right )^{2}}+\frac {15192225}{117649 \left (3 x +2\right )}-\frac {64}{1294139 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 84, normalized size = 0.87 \[ \frac {541450587960 \, x^{5} + 1191190085640 \, x^{4} + 749805990750 \, x^{3} - 73492321230 \, x^{2} - 220760702913 \, x - 56342700586}{25882780 \, {\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac {78125}{121} \, \log \left (5 \, x + 3\right ) - \frac {531729603}{823543} \, \log \left (3 \, x + 2\right ) - \frac {14912}{99648703} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 76, normalized size = 0.78 \[ \frac {78125\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {531729603\,\ln \left (x+\frac {2}{3}\right )}{823543}-\frac {14912\,\ln \left (x-\frac {1}{2}\right )}{99648703}-\frac {-\frac {55704793\,x^5}{1294139}-\frac {367651261\,x^4}{3882417}-\frac {2777059225\,x^3}{46589004}+\frac {816581347\,x^2}{139767012}+\frac {73586900971\,x}{4193010360}+\frac {28171350293}{6289515540}}{x^6+\frac {17\,x^5}{6}+\frac {25\,x^4}{9}+\frac {20\,x^3}{27}-\frac {40\,x^2}{81}-\frac {88\,x}{243}-\frac {16}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 85, normalized size = 0.88 \[ \frac {541450587960 x^{5} + 1191190085640 x^{4} + 749805990750 x^{3} - 73492321230 x^{2} - 220760702913 x - 56342700586}{12579031080 x^{6} + 35640588060 x^{5} + 34941753000 x^{4} + 9317800800 x^{3} - 6211867200 x^{2} - 4555369280 x - 828248960} - \frac {14912 \log {\left (x - \frac {1}{2} \right )}}{99648703} + \frac {78125 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {531729603 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
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