Optimal. Leaf size=91 \[ \frac {40353607}{340736 (1-2 x)^2}-\frac {17294403}{29282 (1-2 x)}-\frac {50150097 x}{100000}-\frac {7459857 x^2}{50000}-\frac {373977 x^3}{10000}-\frac {19683 x^4}{4000}-\frac {1}{207968750 (3+5 x)^2}-\frac {303}{1143828125 (3+5 x)}-\frac {12657032367 \log (1-2 x)}{20614528}+\frac {8202 \log (3+5 x)}{2516421875} \]
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Rubi [A]
time = 0.04, antiderivative size = 91, 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 {19683 x^4}{4000}-\frac {373977 x^3}{10000}-\frac {7459857 x^2}{50000}-\frac {50150097 x}{100000}-\frac {17294403}{29282 (1-2 x)}-\frac {303}{1143828125 (5 x+3)}+\frac {40353607}{340736 (1-2 x)^2}-\frac {1}{207968750 (5 x+3)^2}-\frac {12657032367 \log (1-2 x)}{20614528}+\frac {8202 \log (5 x+3)}{2516421875} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^9}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {50150097}{100000}-\frac {7459857 x}{25000}-\frac {1121931 x^2}{10000}-\frac {19683 x^3}{1000}-\frac {40353607}{85184 (-1+2 x)^3}-\frac {17294403}{14641 (-1+2 x)^2}-\frac {12657032367}{10307264 (-1+2 x)}+\frac {1}{20796875 (3+5 x)^3}+\frac {303}{228765625 (3+5 x)^2}+\frac {8202}{503284375 (3+5 x)}\right ) \, dx\\ &=\frac {40353607}{340736 (1-2 x)^2}-\frac {17294403}{29282 (1-2 x)}-\frac {50150097 x}{100000}-\frac {7459857 x^2}{50000}-\frac {373977 x^3}{10000}-\frac {19683 x^4}{4000}-\frac {1}{207968750 (3+5 x)^2}-\frac {303}{1143828125 (3+5 x)}-\frac {12657032367 \log (1-2 x)}{20614528}+\frac {8202 \log (3+5 x)}{2516421875}\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 75, normalized size = 0.82 \begin {gather*} \frac {-\frac {11 \left (1977372328510687+1867950230356442 x-12213049363361937 x^2-15846035365304040 x^3+8450955823285800 x^4+14903967293820000 x^5+4502793796875000 x^6+1123897331700000 x^7+144089401500000 x^8\right )}{\left (-3+x+10 x^2\right )^2}-1977661307343750 \log (3-6 x)+10498560 \log (-3 (3+5 x))}{3221020000000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 72, normalized size = 0.79
method | result | size |
risch | \(-\frac {19683 x^{4}}{4000}-\frac {373977 x^{3}}{10000}-\frac {7459857 x^{2}}{50000}-\frac {50150097 x}{100000}+\frac {\frac {6755626170663}{228765625} x^{3}+\frac {6920013076005537}{292820000000} x^{2}-\frac {517480964491321}{146410000000} x -\frac {1244386341093487}{292820000000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {12657032367 \ln \left (-1+2 x \right )}{20614528}+\frac {8202 \ln \left (3+5 x \right )}{2516421875}\) | \(67\) |
norman | \(\frac {-\frac {237500757975359}{1756920000} x^{4}+\frac {288586037923477}{8784600000} x^{3}+\frac {1834873597712017}{17569200000} x^{2}-\frac {50898051}{1000} x^{5}-\frac {492075}{32} x^{6}-\frac {767637}{200} x^{7}-\frac {19683}{40} x^{8}-\frac {95585953480907}{5856400000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {12657032367 \ln \left (-1+2 x \right )}{20614528}+\frac {8202 \ln \left (3+5 x \right )}{2516421875}\) | \(70\) |
default | \(-\frac {19683 x^{4}}{4000}-\frac {373977 x^{3}}{10000}-\frac {7459857 x^{2}}{50000}-\frac {50150097 x}{100000}+\frac {40353607}{340736 \left (-1+2 x \right )^{2}}+\frac {17294403}{29282 \left (-1+2 x \right )}-\frac {12657032367 \ln \left (-1+2 x \right )}{20614528}-\frac {1}{207968750 \left (3+5 x \right )^{2}}-\frac {303}{1143828125 \left (3+5 x \right )}+\frac {8202 \ln \left (3+5 x \right )}{2516421875}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 74, normalized size = 0.81 \begin {gather*} -\frac {19683}{4000} \, x^{4} - \frac {373977}{10000} \, x^{3} - \frac {7459857}{50000} \, x^{2} - \frac {50150097}{100000} \, x + \frac {8647201498448640 \, x^{3} + 6920013076005537 \, x^{2} - 1034961928982642 \, x - 1244386341093487}{292820000000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {8202}{2516421875} \, \log \left (5 \, x + 3\right ) - \frac {12657032367}{20614528} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.99, size = 120, normalized size = 1.32 \begin {gather*} -\frac {1584983416500000 \, x^{8} + 12362870648700000 \, x^{7} + 49530731765625000 \, x^{6} + 163943640232020000 \, x^{5} + 3373337816263800 \, x^{4} - 192223824266320440 \, x^{3} - 81487109015452107 \, x^{2} - 10498560 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1977661307343750 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 25922683108313662 \, x + 13688249752028357}{3221020000000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 80, normalized size = 0.88 \begin {gather*} - \frac {19683 x^{4}}{4000} - \frac {373977 x^{3}}{10000} - \frac {7459857 x^{2}}{50000} - \frac {50150097 x}{100000} - \frac {- 8647201498448640 x^{3} - 6920013076005537 x^{2} + 1034961928982642 x + 1244386341093487}{29282000000000 x^{4} + 5856400000000 x^{3} - 17276380000000 x^{2} - 1756920000000 x + 2635380000000} - \frac {12657032367 \log {\left (x - \frac {1}{2} \right )}}{20614528} + \frac {8202 \log {\left (x + \frac {3}{5} \right )}}{2516421875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.67, size = 68, normalized size = 0.75 \begin {gather*} -\frac {19683}{4000} \, x^{4} - \frac {373977}{10000} \, x^{3} - \frac {7459857}{50000} \, x^{2} - \frac {50150097}{100000} \, x + \frac {8647201498448640 \, x^{3} + 6920013076005537 \, x^{2} - 1034961928982642 \, x - 1244386341093487}{292820000000 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {8202}{2516421875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {12657032367}{20614528} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 68, normalized size = 0.75 \begin {gather*} \frac {8202\,\ln \left (x+\frac {3}{5}\right )}{2516421875}-\frac {12657032367\,\ln \left (x-\frac {1}{2}\right )}{20614528}-\frac {50150097\,x}{100000}-\frac {-\frac {6755626170663\,x^3}{22876562500}-\frac {6920013076005537\,x^2}{29282000000000}+\frac {517480964491321\,x}{14641000000000}+\frac {1244386341093487}{29282000000000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}}-\frac {7459857\,x^2}{50000}-\frac {373977\,x^3}{10000}-\frac {19683\,x^4}{4000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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