Optimal. Leaf size=76 \[ \frac{6561 x^5}{500}+\frac{168399 x^4}{2000}+\frac{2626101 x^3}{10000}+\frac{14171517 x^2}{25000}+\frac{231915717 x}{200000}+\frac{5764801}{15488 (1-2 x)}-\frac{1}{9453125 (5 x+3)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (5 x+3)}{103984375} \]
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Rubi [A] time = 0.0437943, antiderivative size = 76, 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} \[ \frac{6561 x^5}{500}+\frac{168399 x^4}{2000}+\frac{2626101 x^3}{10000}+\frac{14171517 x^2}{25000}+\frac{231915717 x}{200000}+\frac{5764801}{15488 (1-2 x)}-\frac{1}{9453125 (5 x+3)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (5 x+3)}{103984375} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^8}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac{231915717}{200000}+\frac{14171517 x}{12500}+\frac{7878303 x^2}{10000}+\frac{168399 x^3}{500}+\frac{6561 x^4}{100}+\frac{5764801}{7744 (-1+2 x)^2}+\frac{79883671}{42592 (-1+2 x)}+\frac{1}{1890625 (3+5 x)^2}+\frac{268}{20796875 (3+5 x)}\right ) \, dx\\ &=\frac{5764801}{15488 (1-2 x)}+\frac{231915717 x}{200000}+\frac{14171517 x^2}{25000}+\frac{2626101 x^3}{10000}+\frac{168399 x^4}{2000}+\frac{6561 x^5}{500}-\frac{1}{9453125 (3+5 x)}+\frac{79883671 \log (1-2 x)}{85184}+\frac{268 \log (3+5 x)}{103984375}\\ \end{align*}
Mathematica [A] time = 0.0401964, size = 95, normalized size = 1.25 \[ -\frac{2251875390881 x+1351125234247}{1210000000 \left (10 x^2+x-3\right )}+\frac{27}{500} (3 x+2)^5+\frac{999 (3 x+2)^4}{2000}+\frac{35703 (3 x+2)^3}{10000}+\frac{78921 (3 x+2)^2}{3125}+\frac{44471943 (3 x+2)}{200000}+\frac{79883671 \log (3-6 x)}{85184}+\frac{268 \log (-3 (5 x+3))}{103984375} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 59, normalized size = 0.8 \begin{align*}{\frac{6561\,{x}^{5}}{500}}+{\frac{168399\,{x}^{4}}{2000}}+{\frac{2626101\,{x}^{3}}{10000}}+{\frac{14171517\,{x}^{2}}{25000}}+{\frac{231915717\,x}{200000}}-{\frac{5764801}{30976\,x-15488}}+{\frac{79883671\,\ln \left ( 2\,x-1 \right ) }{85184}}-{\frac{1}{28359375+47265625\,x}}+{\frac{268\,\ln \left ( 3+5\,x \right ) }{103984375}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.49002, size = 77, normalized size = 1.01 \begin{align*} \frac{6561}{500} \, x^{5} + \frac{168399}{2000} \, x^{4} + \frac{2626101}{10000} \, x^{3} + \frac{14171517}{25000} \, x^{2} + \frac{231915717}{200000} \, x - \frac{2251875390881 \, x + 1351125234247}{1210000000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{268}{103984375} \, \log \left (5 \, x + 3\right ) + \frac{79883671}{85184} \, \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 = 1.36721, size = 375, normalized size = 4.93 \begin{align*} \frac{1746538200000 \, x^{7} + 11381607270000 \, x^{6} + 35550138195000 \, x^{5} + 75582410904000 \, x^{4} + 151398804021300 \, x^{3} - 7200755986050 \, x^{2} + 34304 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 12481823593750 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 71072602198741 \, x - 14862377576717}{13310000000 \,{\left (10 \, x^{2} + x - 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.167316, size = 66, normalized size = 0.87 \begin{align*} \frac{6561 x^{5}}{500} + \frac{168399 x^{4}}{2000} + \frac{2626101 x^{3}}{10000} + \frac{14171517 x^{2}}{25000} + \frac{231915717 x}{200000} - \frac{2251875390881 x + 1351125234247}{12100000000 x^{2} + 1210000000 x - 3630000000} + \frac{79883671 \log{\left (x - \frac{1}{2} \right )}}{85184} + \frac{268 \log{\left (x + \frac{3}{5} \right )}}{103984375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.37072, size = 151, normalized size = 1.99 \begin{align*} -\frac{{\left (5 \, x + 3\right )}^{5}{\left (\frac{1618458732}{5 \, x + 3} + \frac{15560361630}{{\left (5 \, x + 3\right )}^{2}} + \frac{171888467850}{{\left (5 \, x + 3\right )}^{3}} + \frac{2836763461125}{{\left (5 \, x + 3\right )}^{4}} - \frac{31204564033975}{{\left (5 \, x + 3\right )}^{5}} + 139723056\right )}}{16637500000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{9453125 \,{\left (5 \, x + 3\right )}} - \frac{4688889417}{5000000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{79883671}{85184} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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