Optimal. Leaf size=72 \[ -\frac {2187 x^6}{100}-\frac {303993 x^5}{2500}-\frac {6194313 x^4}{20000}-\frac {24660207 x^3}{50000}-\frac {118543581 x^2}{200000}-\frac {3579885909 x}{5000000}-\frac {1}{4296875 (5 x+3)}-\frac {5764801 \log (1-2 x)}{15488}+\frac {266 \log (5 x+3)}{47265625} \]
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Rubi [A] time = 0.03, antiderivative size = 72, 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} \begin {gather*} -\frac {2187 x^6}{100}-\frac {303993 x^5}{2500}-\frac {6194313 x^4}{20000}-\frac {24660207 x^3}{50000}-\frac {118543581 x^2}{200000}-\frac {3579885909 x}{5000000}-\frac {1}{4296875 (5 x+3)}-\frac {5764801 \log (1-2 x)}{15488}+\frac {266 \log (5 x+3)}{47265625} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {3579885909}{5000000}-\frac {118543581 x}{100000}-\frac {73980621 x^2}{50000}-\frac {6194313 x^3}{5000}-\frac {303993 x^4}{500}-\frac {6561 x^5}{50}-\frac {5764801}{7744 (-1+2 x)}+\frac {1}{859375 (3+5 x)^2}+\frac {266}{9453125 (3+5 x)}\right ) \, dx\\ &=-\frac {3579885909 x}{5000000}-\frac {118543581 x^2}{200000}-\frac {24660207 x^3}{50000}-\frac {6194313 x^4}{20000}-\frac {303993 x^5}{2500}-\frac {2187 x^6}{100}-\frac {1}{4296875 (3+5 x)}-\frac {5764801 \log (1-2 x)}{15488}+\frac {266 \log (3+5 x)}{47265625}\\ \end {align*}
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Mathematica [A] time = 0.07, size = 64, normalized size = 0.89 \begin {gather*} \frac {22 \left (-6014250000 x^6-33439230000 x^5-85171803750 x^4-135631138500 x^3-162997423875 x^2-196893724995 x-\frac {64}{5 x+3}-86057647830\right )-2251875390625 \log (3-6 x)+34048 \log (-3 (5 x+3))}{6050000000} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^8}{(1-2 x) (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.30, size = 70, normalized size = 0.97 \begin {gather*} -\frac {661567500000 \, x^{7} + 4075255800000 \, x^{6} + 11575887592500 \, x^{5} + 20540764282500 \, x^{4} + 26881371767250 \, x^{3} + 32416139725200 \, x^{2} - 34048 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 2251875390625 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 12994985849670 \, x + 1408}{6050000000 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 99, normalized size = 1.38 \begin {gather*} -\frac {27}{125000000} \, {\left (5 \, x + 3\right )}^{6} {\left (\frac {63504}{5 \, x + 3} + \frac {466830}{{\left (5 \, x + 3\right )}^{2}} + \frac {3450300}{{\left (5 \, x + 3\right )}^{3}} + \frac {28481775}{{\left (5 \, x + 3\right )}^{4}} + \frac {313308485}{{\left (5 \, x + 3\right )}^{5}} + 6480\right )} - \frac {1}{4296875 \, {\left (5 \, x + 3\right )}} + \frac {18610540137}{50000000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {5764801}{15488} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 55, normalized size = 0.76 \begin {gather*} -\frac {2187 x^{6}}{100}-\frac {303993 x^{5}}{2500}-\frac {6194313 x^{4}}{20000}-\frac {24660207 x^{3}}{50000}-\frac {118543581 x^{2}}{200000}-\frac {3579885909 x}{5000000}-\frac {5764801 \ln \left (2 x -1\right )}{15488}+\frac {266 \ln \left (5 x +3\right )}{47265625}-\frac {1}{4296875 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 54, normalized size = 0.75 \begin {gather*} -\frac {2187}{100} \, x^{6} - \frac {303993}{2500} \, x^{5} - \frac {6194313}{20000} \, x^{4} - \frac {24660207}{50000} \, x^{3} - \frac {118543581}{200000} \, x^{2} - \frac {3579885909}{5000000} \, x - \frac {1}{4296875 \, {\left (5 \, x + 3\right )}} + \frac {266}{47265625} \, \log \left (5 \, x + 3\right ) - \frac {5764801}{15488} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 50, normalized size = 0.69 \begin {gather*} \frac {266\,\ln \left (x+\frac {3}{5}\right )}{47265625}-\frac {5764801\,\ln \left (x-\frac {1}{2}\right )}{15488}-\frac {3579885909\,x}{5000000}-\frac {1}{21484375\,\left (x+\frac {3}{5}\right )}-\frac {118543581\,x^2}{200000}-\frac {24660207\,x^3}{50000}-\frac {6194313\,x^4}{20000}-\frac {303993\,x^5}{2500}-\frac {2187\,x^6}{100} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 65, normalized size = 0.90 \begin {gather*} - \frac {2187 x^{6}}{100} - \frac {303993 x^{5}}{2500} - \frac {6194313 x^{4}}{20000} - \frac {24660207 x^{3}}{50000} - \frac {118543581 x^{2}}{200000} - \frac {3579885909 x}{5000000} - \frac {5764801 \log {\left (x - \frac {1}{2} \right )}}{15488} + \frac {266 \log {\left (x + \frac {3}{5} \right )}}{47265625} - \frac {1}{21484375 x + 12890625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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