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 = 0.04, 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 = {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*}
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Mathematica [A] time = 0.05, 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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fricas [A] time = 0.83, size = 79, normalized size = 1.04 \[ \frac {1746538200000 \, x^{7} + 11381607270000 \, x^{6} + 35550138195000 \, x^{5} + 75582410904000 \, x^{4} + 151398804021300 \, x^{3} - 7200755986050 \, x^{2} + 34304 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 12481823593750 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 71072602198741 \, x - 14862377576717}{13310000000 \, {\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 112, normalized size = 1.47 \[ -\frac {{\left (5 \, x + 3\right )}^{5} {\left (\frac {1618458732}{5 \, x + 3} + \frac {15560361630}{{\left (5 \, x + 3\right )}^{2}} + \frac {171888467850}{{\left (5 \, x + 3\right )}^{3}} + \frac {2836763461125}{{\left (5 \, x + 3\right )}^{4}} - \frac {31204564033975}{{\left (5 \, x + 3\right )}^{5}} + 139723056\right )}}{16637500000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{9453125 \, {\left (5 \, x + 3\right )}} - \frac {4688889417}{5000000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {79883671}{85184} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 59, normalized size = 0.78 \[ \frac {6561 x^{5}}{500}+\frac {168399 x^{4}}{2000}+\frac {2626101 x^{3}}{10000}+\frac {14171517 x^{2}}{25000}+\frac {231915717 x}{200000}+\frac {79883671 \ln \left (2 x -1\right )}{85184}+\frac {268 \ln \left (5 x +3\right )}{103984375}-\frac {1}{9453125 \left (5 x +3\right )}-\frac {5764801}{15488 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 57, normalized size = 0.75 \[ \frac {6561}{500} \, x^{5} + \frac {168399}{2000} \, x^{4} + \frac {2626101}{10000} \, x^{3} + \frac {14171517}{25000} \, x^{2} + \frac {231915717}{200000} \, x - \frac {2251875390881 \, x + 1351125234247}{1210000000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {268}{103984375} \, \log \left (5 \, x + 3\right ) + \frac {79883671}{85184} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 53, normalized size = 0.70 \[ \frac {231915717\,x}{200000}+\frac {79883671\,\ln \left (x-\frac {1}{2}\right )}{85184}+\frac {268\,\ln \left (x+\frac {3}{5}\right )}{103984375}-\frac {\frac {2251875390881\,x}{12100000000}+\frac {1351125234247}{12100000000}}{x^2+\frac {x}{10}-\frac {3}{10}}+\frac {14171517\,x^2}{25000}+\frac {2626101\,x^3}{10000}+\frac {168399\,x^4}{2000}+\frac {6561\,x^5}{500} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 68, normalized size = 0.89 \[ \frac {6561 x^{5}}{500} + \frac {168399 x^{4}}{2000} + \frac {2626101 x^{3}}{10000} + \frac {14171517 x^{2}}{25000} + \frac {231915717 x}{200000} + \frac {- 2251875390881 x - 1351125234247}{12100000000 x^{2} + 1210000000 x - 3630000000} + \frac {79883671 \log {\left (x - \frac {1}{2} \right )}}{85184} + \frac {268 \log {\left (x + \frac {3}{5} \right )}}{103984375} \]
Verification of antiderivative is not currently implemented for this CAS.
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