Optimal. Leaf size=76 \[ -\frac {62934003 x}{500000}-\frac {9268263 x^2}{100000}-\frac {1535517 x^3}{25000}-\frac {264627 x^4}{10000}-\frac {6561 x^5}{1250}-\frac {1}{8593750 (3+5 x)^2}-\frac {266}{47265625 (3+5 x)}-\frac {5764801 \log (1-2 x)}{85184}+\frac {31024 \log (3+5 x)}{519921875} \]
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Rubi [A]
time = 0.03, antiderivative size = 76, 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 {6561 x^5}{1250}-\frac {264627 x^4}{10000}-\frac {1535517 x^3}{25000}-\frac {9268263 x^2}{100000}-\frac {62934003 x}{500000}-\frac {266}{47265625 (5 x+3)}-\frac {1}{8593750 (5 x+3)^2}-\frac {5764801 \log (1-2 x)}{85184}+\frac {31024 \log (5 x+3)}{519921875} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac {62934003}{500000}-\frac {9268263 x}{50000}-\frac {4606551 x^2}{25000}-\frac {264627 x^3}{2500}-\frac {6561 x^4}{250}-\frac {5764801}{42592 (-1+2 x)}+\frac {1}{859375 (3+5 x)^3}+\frac {266}{9453125 (3+5 x)^2}+\frac {31024}{103984375 (3+5 x)}\right ) \, dx\\ &=-\frac {62934003 x}{500000}-\frac {9268263 x^2}{100000}-\frac {1535517 x^3}{25000}-\frac {264627 x^4}{10000}-\frac {6561 x^5}{1250}-\frac {1}{8593750 (3+5 x)^2}-\frac {266}{47265625 (3+5 x)}-\frac {5764801 \log (1-2 x)}{85184}+\frac {31024 \log (3+5 x)}{519921875}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 68, normalized size = 0.89 \begin {gather*} \frac {22 \left (-85278446550-190375359075 x-140182477875 x^2-92898778500 x^3-40024833750 x^4-7938810000 x^5-\frac {176}{(3+5 x)^2}-\frac {8512}{3+5 x}\right )-2251875390625 \log (3-6 x)+1985536 \log (-3 (3+5 x))}{33275000000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 59, normalized size = 0.78
method | result | size |
risch | \(-\frac {6561 x^{5}}{1250}-\frac {264627 x^{4}}{10000}-\frac {1535517 x^{3}}{25000}-\frac {9268263 x^{2}}{100000}-\frac {62934003 x}{500000}+\frac {-\frac {266 x}{9453125}-\frac {1607}{94531250}}{\left (3+5 x \right )^{2}}-\frac {5764801 \ln \left (-1+2 x \right )}{85184}+\frac {31024 \ln \left (3+5 x \right )}{519921875}\) | \(55\) |
default | \(-\frac {6561 x^{5}}{1250}-\frac {264627 x^{4}}{10000}-\frac {1535517 x^{3}}{25000}-\frac {9268263 x^{2}}{100000}-\frac {62934003 x}{500000}-\frac {5764801 \ln \left (-1+2 x \right )}{85184}-\frac {1}{8593750 \left (3+5 x \right )^{2}}-\frac {266}{47265625 \left (3+5 x \right )}+\frac {31024 \ln \left (3+5 x \right )}{519921875}\) | \(59\) |
norman | \(\frac {-\frac {1028026913117}{907500000} x -\frac {2510245080613}{544500000} x^{2}-\frac {647996517}{100000} x^{3}-\frac {87957009}{20000} x^{4}-\frac {5941593}{2500} x^{5}-\frac {1638063}{2000} x^{6}-\frac {6561}{50} x^{7}}{\left (3+5 x \right )^{2}}-\frac {5764801 \ln \left (-1+2 x \right )}{85184}+\frac {31024 \ln \left (3+5 x \right )}{519921875}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 59, normalized size = 0.78 \begin {gather*} -\frac {6561}{1250} \, x^{5} - \frac {264627}{10000} \, x^{4} - \frac {1535517}{25000} \, x^{3} - \frac {9268263}{100000} \, x^{2} - \frac {62934003}{500000} \, x - \frac {2660 \, x + 1607}{94531250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {31024}{519921875} \, \log \left (5 \, x + 3\right ) - \frac {5764801}{85184} \, \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 = 1.23, size = 85, normalized size = 1.12 \begin {gather*} -\frac {4366345500000 \, x^{7} + 27253273162500 \, x^{6} + 79082602830000 \, x^{5} + 146338473723750 \, x^{4} + 215620841031750 \, x^{3} + 153403867608750 \, x^{2} - 1985536 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2251875390625 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 37694322033170 \, x + 565664}{33275000000 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 66, normalized size = 0.87 \begin {gather*} - \frac {6561 x^{5}}{1250} - \frac {264627 x^{4}}{10000} - \frac {1535517 x^{3}}{25000} - \frac {9268263 x^{2}}{100000} - \frac {62934003 x}{500000} - \frac {2660 x + 1607}{2363281250 x^{2} + 2835937500 x + 850781250} - \frac {5764801 \log {\left (x - \frac {1}{2} \right )}}{85184} + \frac {31024 \log {\left (x + \frac {3}{5} \right )}}{519921875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.54, size = 56, normalized size = 0.74 \begin {gather*} -\frac {6561}{1250} \, x^{5} - \frac {264627}{10000} \, x^{4} - \frac {1535517}{25000} \, x^{3} - \frac {9268263}{100000} \, x^{2} - \frac {62934003}{500000} \, x - \frac {2660 \, x + 1607}{94531250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {31024}{519921875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5764801}{85184} \, \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 = 1.12, size = 53, normalized size = 0.70 \begin {gather*} \frac {31024\,\ln \left (x+\frac {3}{5}\right )}{519921875}-\frac {5764801\,\ln \left (x-\frac {1}{2}\right )}{85184}-\frac {62934003\,x}{500000}-\frac {\frac {266\,x}{236328125}+\frac {1607}{2363281250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {9268263\,x^2}{100000}-\frac {1535517\,x^3}{25000}-\frac {264627\,x^4}{10000}-\frac {6561\,x^5}{1250} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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