Optimal. Leaf size=77 \[ \frac {823543}{85184 (1-2 x)^2}-\frac {7411887}{234256 (1-2 x)}-\frac {95499 x}{10000}-\frac {2187 x^2}{2000}-\frac {1}{8318750 (3+5 x)^2}-\frac {237}{45753125 (3+5 x)}-\frac {25059237 \log (1-2 x)}{1288408}+\frac {24279 \log (3+5 x)}{503284375} \]
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Rubi [A]
time = 0.03, antiderivative size = 77, 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 {2187 x^2}{2000}-\frac {95499 x}{10000}-\frac {7411887}{234256 (1-2 x)}-\frac {237}{45753125 (5 x+3)}+\frac {823543}{85184 (1-2 x)^2}-\frac {1}{8318750 (5 x+3)^2}-\frac {25059237 \log (1-2 x)}{1288408}+\frac {24279 \log (5 x+3)}{503284375} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {95499}{10000}-\frac {2187 x}{1000}-\frac {823543}{21296 (-1+2 x)^3}-\frac {7411887}{117128 (-1+2 x)^2}-\frac {25059237}{644204 (-1+2 x)}+\frac {1}{831875 (3+5 x)^3}+\frac {237}{9150625 (3+5 x)^2}+\frac {24279}{100656875 (3+5 x)}\right ) \, dx\\ &=\frac {823543}{85184 (1-2 x)^2}-\frac {7411887}{234256 (1-2 x)}-\frac {95499 x}{10000}-\frac {2187 x^2}{2000}-\frac {1}{8318750 (3+5 x)^2}-\frac {237}{45753125 (3+5 x)}-\frac {25059237 \log (1-2 x)}{1288408}+\frac {24279 \log (3+5 x)}{503284375}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 65, normalized size = 0.84 \begin {gather*} \frac {-\frac {11 \left (734029874011+410862940766 x-5105353973121 x^2-5957126547060 x^3+2092320420300 x^4+2860441452000 x^5+320198670000 x^6\right )}{\left (-3+x+10 x^2\right )^2}-626480925000 \log (3-6 x)+1553856 \log (-3 (3+5 x))}{32210200000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 62, normalized size = 0.81
method | result | size |
risch | \(-\frac {2187 x^{2}}{2000}-\frac {95499 x}{10000}+\frac {\frac {115810726791}{73205000} x^{3}+\frac {3950432948061}{2928200000} x^{2}-\frac {131252111833}{1464100000} x -\frac {579053717731}{2928200000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {25059237 \ln \left (-1+2 x \right )}{1288408}+\frac {24279 \ln \left (3+5 x \right )}{503284375}\) | \(57\) |
norman | \(\frac {-\frac {16762567687}{5490375} x^{4}+\frac {172034377919}{109807500} x^{3}+\frac {685912966799}{219615000} x^{2}-\frac {48843}{50} x^{5}-\frac {2187}{20} x^{6}-\frac {33758107129}{73205000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {25059237 \ln \left (-1+2 x \right )}{1288408}+\frac {24279 \ln \left (3+5 x \right )}{503284375}\) | \(60\) |
default | \(-\frac {2187 x^{2}}{2000}-\frac {95499 x}{10000}+\frac {823543}{85184 \left (-1+2 x \right )^{2}}+\frac {7411887}{234256 \left (-1+2 x \right )}-\frac {25059237 \ln \left (-1+2 x \right )}{1288408}-\frac {1}{8318750 \left (3+5 x \right )^{2}}-\frac {237}{45753125 \left (3+5 x \right )}+\frac {24279 \ln \left (3+5 x \right )}{503284375}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 64, normalized size = 0.83 \begin {gather*} -\frac {2187}{2000} \, x^{2} - \frac {95499}{10000} \, x + \frac {4632429071640 \, x^{3} + 3950432948061 \, x^{2} - 262504223666 \, x - 579053717731}{2928200000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {24279}{503284375} \, \log \left (5 \, x + 3\right ) - \frac {25059237}{1288408} \, \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 = 0.70, size = 110, normalized size = 1.43 \begin {gather*} -\frac {3522185370000 \, x^{6} + 31464855972000 \, x^{5} + 4073994411300 \, x^{4} - 69316698060060 \, x^{3} - 44983390879251 \, x^{2} - 1553856 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 626480925000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 5655984161146 \, x + 6369590895041}{32210200000 \, {\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 = 0.11, size = 66, normalized size = 0.86 \begin {gather*} - \frac {2187 x^{2}}{2000} - \frac {95499 x}{10000} - \frac {- 4632429071640 x^{3} - 3950432948061 x^{2} + 262504223666 x + 579053717731}{292820000000 x^{4} + 58564000000 x^{3} - 172763800000 x^{2} - 17569200000 x + 26353800000} - \frac {25059237 \log {\left (x - \frac {1}{2} \right )}}{1288408} + \frac {24279 \log {\left (x + \frac {3}{5} \right )}}{503284375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.63, size = 58, normalized size = 0.75 \begin {gather*} -\frac {2187}{2000} \, x^{2} - \frac {95499}{10000} \, x + \frac {4632429071640 \, x^{3} + 3950432948061 \, x^{2} - 262504223666 \, x - 579053717731}{2928200000 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {24279}{503284375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {25059237}{1288408} \, \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 = 1.09, size = 58, normalized size = 0.75 \begin {gather*} \frac {24279\,\ln \left (x+\frac {3}{5}\right )}{503284375}-\frac {25059237\,\ln \left (x-\frac {1}{2}\right )}{1288408}-\frac {95499\,x}{10000}-\frac {-\frac {115810726791\,x^3}{7320500000}-\frac {3950432948061\,x^2}{292820000000}+\frac {131252111833\,x}{146410000000}+\frac {579053717731}{292820000000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}}-\frac {2187\,x^2}{2000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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