Optimal. Leaf size=77 \[ -\frac{2187 x^2}{2000}-\frac{95499 x}{10000}-\frac{7411887}{234256 (1-2 x)}-\frac{237}{45753125 (5 x+3)}+\frac{823543}{85184 (1-2 x)^2}-\frac{1}{8318750 (5 x+3)^2}-\frac{25059237 \log (1-2 x)}{1288408}+\frac{24279 \log (5 x+3)}{503284375} \]
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Rubi [A] time = 0.0413385, antiderivative size = 77, normalized size of antiderivative = 1., 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 = {88} \[ -\frac{2187 x^2}{2000}-\frac{95499 x}{10000}-\frac{7411887}{234256 (1-2 x)}-\frac{237}{45753125 (5 x+3)}+\frac{823543}{85184 (1-2 x)^2}-\frac{1}{8318750 (5 x+3)^2}-\frac{25059237 \log (1-2 x)}{1288408}+\frac{24279 \log (5 x+3)}{503284375} \]
Antiderivative was successfully verified.
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Rule 88
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*}
Mathematica [A] time = 0.034195, size = 65, normalized size = 0.84 \[ \frac{-\frac{11 \left (320198670000 x^6+2860441452000 x^5+2092320420300 x^4-5957126547060 x^3-5105353973121 x^2+410862940766 x+734029874011\right )}{\left (10 x^2+x-3\right )^2}-626480925000 \log (3-6 x)+1553856 \log (-3 (5 x+3))}{32210200000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 62, normalized size = 0.8 \begin{align*} -{\frac{2187\,{x}^{2}}{2000}}-{\frac{95499\,x}{10000}}+{\frac{823543}{85184\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{7411887}{468512\,x-234256}}-{\frac{25059237\,\ln \left ( 2\,x-1 \right ) }{1288408}}-{\frac{1}{8318750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{237}{137259375+228765625\,x}}+{\frac{24279\,\ln \left ( 3+5\,x \right ) }{503284375}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05496, size = 86, normalized size = 1.12 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60628, size = 429, normalized size = 5.57 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.201562, size = 66, normalized size = 0.86 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.38399, size = 78, normalized size = 1.01 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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