Optimal. Leaf size=97 \[ \frac {64}{1294139 (1-2 x)}+\frac {9}{245 (2+3 x)^5}+\frac {351}{1372 (2+3 x)^4}+\frac {4131}{2401 (2+3 x)^3}+\frac {434043}{33614 (2+3 x)^2}+\frac {15192225}{117649 (2+3 x)}-\frac {14912 \log (1-2 x)}{99648703}-\frac {531729603 \log (2+3 x)}{823543}+\frac {78125}{121} \log (3+5 x) \]
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Rubi [A]
time = 0.04, 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 = {90}
\begin {gather*} \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) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.04, size = 87, normalized size = 0.90 \begin {gather*} \frac {\frac {19712}{1-2 x}+\frac {73211292}{5 (2+3 x)^5}+\frac {101972871}{(2+3 x)^4}+\frac {685795572}{(2+3 x)^3}+\frac {5146881894}{(2+3 x)^2}+\frac {51471258300}{2+3 x}-59648 \log (5-10 x)-257357127852 \log (5 (2+3 x))+257357187500 \log (3+5 x)}{398594812} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 80, normalized size = 0.82
method | result | size |
risch | \(\frac {\frac {27072529398}{1294139} x^{5}+\frac {59559504282}{1294139} x^{4}+\frac {74980599075}{2588278} x^{3}-\frac {7349232123}{2588278} x^{2}-\frac {220760702913}{25882780} x -\frac {28171350293}{12941390}}{\left (-1+2 x \right ) \left (2+3 x \right )^{5}}-\frac {14912 \ln \left (-1+2 x \right )}{99648703}-\frac {531729603 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{121}\) | \(67\) |
norman | \(\frac {-\frac {30128739946101}{414124480} x^{5}-\frac {6845638121199}{207062240} x^{6}-\frac {1897228152531}{41412448} x^{4}+\frac {46380243663}{10353112} x^{3}+\frac {69815586633}{5176556} x^{2}+\frac {8912415031}{2588278} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{5}}-\frac {14912 \ln \left (-1+2 x \right )}{99648703}-\frac {531729603 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{121}\) | \(70\) |
default | \(-\frac {64}{1294139 \left (-1+2 x \right )}-\frac {14912 \ln \left (-1+2 x \right )}{99648703}+\frac {9}{245 \left (2+3 x \right )^{5}}+\frac {351}{1372 \left (2+3 x \right )^{4}}+\frac {4131}{2401 \left (2+3 x \right )^{3}}+\frac {434043}{33614 \left (2+3 x \right )^{2}}+\frac {15192225}{117649 \left (2+3 x \right )}-\frac {531729603 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{121}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.45, size = 84, normalized size = 0.87 \begin {gather*} \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 {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. 173 vs.
\(2 (79) = 158\).
time = 0.42, size = 173, normalized size = 1.78 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 85, normalized size = 0.88 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.79, size = 93, normalized size = 0.96 \begin {gather*} -\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 {gather*}
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 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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