Optimal. Leaf size=86 \[ -\frac {9}{28 (2+3 x)^4}-\frac {216}{49 (2+3 x)^3}-\frac {34371}{686 (2+3 x)^2}-\frac {1612242}{2401 (2+3 x)}-\frac {3125}{11 (3+5 x)}-\frac {64 \log (1-2 x)}{2033647}+\frac {70752609 \log (2+3 x)}{16807}-\frac {509375}{121} \log (3+5 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 86, 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 {1612242}{2401 (3 x+2)}-\frac {3125}{11 (5 x+3)}-\frac {34371}{686 (3 x+2)^2}-\frac {216}{49 (3 x+2)^3}-\frac {9}{28 (3 x+2)^4}-\frac {64 \log (1-2 x)}{2033647}+\frac {70752609 \log (3 x+2)}{16807}-\frac {509375}{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+3 x)^5 (3+5 x)^2} \, dx &=\int \left (-\frac {128}{2033647 (-1+2 x)}+\frac {27}{7 (2+3 x)^5}+\frac {1944}{49 (2+3 x)^4}+\frac {103113}{343 (2+3 x)^3}+\frac {4836726}{2401 (2+3 x)^2}+\frac {212257827}{16807 (2+3 x)}+\frac {15625}{11 (3+5 x)^2}-\frac {2546875}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {9}{28 (2+3 x)^4}-\frac {216}{49 (2+3 x)^3}-\frac {34371}{686 (2+3 x)^2}-\frac {1612242}{2401 (2+3 x)}-\frac {3125}{11 (3+5 x)}-\frac {64 \log (1-2 x)}{2033647}+\frac {70752609 \log (2+3 x)}{16807}-\frac {509375}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 84, normalized size = 0.98 \begin {gather*} -\frac {9}{28 (2+3 x)^4}-\frac {216}{49 (2+3 x)^3}-\frac {34371}{686 (2+3 x)^2}-\frac {1612242}{2401 (2+3 x)}-\frac {3125}{33+55 x}-\frac {64 \log (1-2 x)}{2033647}+\frac {70752609 \log (4+6 x)}{16807}-\frac {509375}{121} \log (6+10 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 71, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {3001932495}{26411} x^{4}-\frac {15810178239}{52822} x^{3}-\frac {15605602857}{52822} x^{2}-\frac {13685553417}{105644} x -\frac {2249141207}{105644}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}-\frac {64 \ln \left (-1+2 x \right )}{2033647}+\frac {70752609 \ln \left (2+3 x \right )}{16807}-\frac {509375 \ln \left (3+5 x \right )}{121}\) | \(62\) |
norman | \(\frac {\frac {24674363487}{52822} x^{3}+\frac {5336793755}{158466} x +\frac {43287225301}{211288} x^{2}+\frac {303634062945}{1690304} x^{5}+\frac {799747592607}{1690304} x^{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )}-\frac {64 \ln \left (-1+2 x \right )}{2033647}+\frac {70752609 \ln \left (2+3 x \right )}{16807}-\frac {509375 \ln \left (3+5 x \right )}{121}\) | \(65\) |
default | \(-\frac {64 \ln \left (-1+2 x \right )}{2033647}-\frac {9}{28 \left (2+3 x \right )^{4}}-\frac {216}{49 \left (2+3 x \right )^{3}}-\frac {34371}{686 \left (2+3 x \right )^{2}}-\frac {1612242}{2401 \left (2+3 x \right )}+\frac {70752609 \ln \left (2+3 x \right )}{16807}-\frac {3125}{11 \left (3+5 x \right )}-\frac {509375 \ln \left (3+5 x \right )}{121}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 74, normalized size = 0.86 \begin {gather*} -\frac {12007729980 \, x^{4} + 31620356478 \, x^{3} + 31211205714 \, x^{2} + 13685553417 \, x + 2249141207}{105644 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - \frac {509375}{121} \, \log \left (5 \, x + 3\right ) + \frac {70752609}{16807} \, \log \left (3 \, x + 2\right ) - \frac {64}{2033647} \, \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. 148 vs.
\(2 (70) = 140\).
time = 1.00, size = 148, normalized size = 1.72 \begin {gather*} -\frac {924595208460 \, x^{4} + 2434767448806 \, x^{3} + 2403262839978 \, x^{2} + 34244262500 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 34244262756 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 256 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (2 \, x - 1\right ) + 1053787613109 \, x + 173183872939}{8134588 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 75, normalized size = 0.87 \begin {gather*} - \frac {12007729980 x^{4} + 31620356478 x^{3} + 31211205714 x^{2} + 13685553417 x + 2249141207}{42785820 x^{5} + 139767012 x^{4} + 182552832 x^{3} + 119166432 x^{2} + 38876992 x + 5070912} - \frac {64 \log {\left (x - \frac {1}{2} \right )}}{2033647} - \frac {509375 \log {\left (x + \frac {3}{5} \right )}}{121} + \frac {70752609 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.10, size = 82, normalized size = 0.95 \begin {gather*} -\frac {3125}{11 \, {\left (5 \, x + 3\right )}} + \frac {135 \, {\left (\frac {34747884}{5 \, x + 3} + \frac {13347468}{{\left (5 \, x + 3\right )}^{2}} + \frac {1775512}{{\left (5 \, x + 3\right )}^{3}} + 30897639\right )}}{9604 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{4}} + \frac {70752609}{16807} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {64}{2033647} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 66, normalized size = 0.77 \begin {gather*} \frac {70752609\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {64\,\ln \left (x-\frac {1}{2}\right )}{2033647}-\frac {509375\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {\frac {7412179\,x^4}{26411}+\frac {585562157\,x^3}{792330}+\frac {577985291\,x^2}{792330}+\frac {4561851139\,x}{14261940}+\frac {2249141207}{42785820}}{x^5+\frac {49\,x^4}{15}+\frac {64\,x^3}{15}+\frac {376\,x^2}{135}+\frac {368\,x}{405}+\frac {16}{135}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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