Optimal. Leaf size=72 \[ \frac {5764801}{2816 (1-2 x)}+\frac {2041906293 x}{250000}+\frac {1839811401 x^2}{400000}+\frac {26773659 x^3}{10000}+\frac {9899091 x^4}{8000}+\frac {94041 x^5}{250}+\frac {2187 x^6}{40}+\frac {188591347 \log (1-2 x)}{30976}+\frac {\log (3+5 x)}{9453125} \]
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Rubi [A]
time = 0.02, 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 = {90}
\begin {gather*} \frac {2187 x^6}{40}+\frac {94041 x^5}{250}+\frac {9899091 x^4}{8000}+\frac {26773659 x^3}{10000}+\frac {1839811401 x^2}{400000}+\frac {2041906293 x}{250000}+\frac {5764801}{2816 (1-2 x)}+\frac {188591347 \log (1-2 x)}{30976}+\frac {\log (5 x+3)}{9453125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {2041906293}{250000}+\frac {1839811401 x}{200000}+\frac {80320977 x^2}{10000}+\frac {9899091 x^3}{2000}+\frac {94041 x^4}{50}+\frac {6561 x^5}{20}+\frac {5764801}{1408 (-1+2 x)^2}+\frac {188591347}{15488 (-1+2 x)}+\frac {1}{1890625 (3+5 x)}\right ) \, dx\\ &=\frac {5764801}{2816 (1-2 x)}+\frac {2041906293 x}{250000}+\frac {1839811401 x^2}{400000}+\frac {26773659 x^3}{10000}+\frac {9899091 x^4}{8000}+\frac {94041 x^5}{250}+\frac {2187 x^6}{40}+\frac {188591347 \log (1-2 x)}{30976}+\frac {\log (3+5 x)}{9453125}\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 66, normalized size = 0.92 \begin {gather*} \frac {7988912316+\frac {90075015625}{22-44 x}+16335250344 x+9199057005 x^2+5354731800 x^3+2474772750 x^4+752328000 x^5+109350000 x^6}{2000000}+\frac {188591347 \log (3-6 x)}{30976}+\frac {\log (-3 (3+5 x))}{9453125} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 55, normalized size = 0.76
method | result | size |
risch | \(\frac {2187 x^{6}}{40}+\frac {94041 x^{5}}{250}+\frac {9899091 x^{4}}{8000}+\frac {26773659 x^{3}}{10000}+\frac {1839811401 x^{2}}{400000}+\frac {2041906293 x}{250000}-\frac {5764801}{5632 \left (-\frac {1}{2}+x \right )}+\frac {188591347 \ln \left (-1+2 x \right )}{30976}+\frac {\ln \left (3+5 x \right )}{9453125}\) | \(53\) |
default | \(\frac {2187 x^{6}}{40}+\frac {94041 x^{5}}{250}+\frac {9899091 x^{4}}{8000}+\frac {26773659 x^{3}}{10000}+\frac {1839811401 x^{2}}{400000}+\frac {2041906293 x}{250000}-\frac {5764801}{2816 \left (-1+2 x \right )}+\frac {188591347 \ln \left (-1+2 x \right )}{30976}+\frac {\ln \left (3+5 x \right )}{9453125}\) | \(55\) |
norman | \(\frac {-\frac {269762769409}{22000000} x +\frac {23471443683}{2000000} x^{2}+\frac {1304338221}{200000} x^{3}+\frac {164693817}{40000} x^{4}+\frac {1678887}{800} x^{5}+\frac {697653}{1000} x^{6}+\frac {2187}{20} x^{7}}{-1+2 x}+\frac {188591347 \ln \left (-1+2 x \right )}{30976}+\frac {\ln \left (3+5 x \right )}{9453125}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 54, normalized size = 0.75 \begin {gather*} \frac {2187}{40} \, x^{6} + \frac {94041}{250} \, x^{5} + \frac {9899091}{8000} \, x^{4} + \frac {26773659}{10000} \, x^{3} + \frac {1839811401}{400000} \, x^{2} + \frac {2041906293}{250000} \, x - \frac {5764801}{2816 \, {\left (2 \, x - 1\right )}} + \frac {1}{9453125} \, \log \left (5 \, x + 3\right ) + \frac {188591347}{30976} \, \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 = 0.39, size = 70, normalized size = 0.97 \begin {gather*} \frac {264627000000 \, x^{7} + 1688320260000 \, x^{6} + 5078633175000 \, x^{5} + 9963975928500 \, x^{4} + 15782492474100 \, x^{3} + 28400446856430 \, x^{2} + 256 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 14733698984375 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 19765652916240 \, x - 4954125859375}{2420000000 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 63, normalized size = 0.88 \begin {gather*} \frac {2187 x^{6}}{40} + \frac {94041 x^{5}}{250} + \frac {9899091 x^{4}}{8000} + \frac {26773659 x^{3}}{10000} + \frac {1839811401 x^{2}}{400000} + \frac {2041906293 x}{250000} + \frac {188591347 \log {\left (x - \frac {1}{2} \right )}}{30976} + \frac {\log {\left (x + \frac {3}{5} \right )}}{9453125} - \frac {5764801}{5632 x - 2816} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.74, size = 99, normalized size = 1.38 \begin {gather*} \frac {27}{16000000} \, {\left (2 \, x - 1\right )}^{6} {\left (\frac {10003500}{2 \, x - 1} + \frac {88252875}{{\left (2 \, x - 1\right )}^{2}} + \frac {461424900}{{\left (2 \, x - 1\right )}^{3}} + \frac {1628610330}{{\left (2 \, x - 1\right )}^{4}} + \frac {4599014548}{{\left (2 \, x - 1\right )}^{5}} + 506250\right )} - \frac {5764801}{2816 \, {\left (2 \, x - 1\right )}} - \frac {121766107311}{20000000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{9453125} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 50, normalized size = 0.69 \begin {gather*} \frac {2041906293\,x}{250000}+\frac {188591347\,\ln \left (x-\frac {1}{2}\right )}{30976}+\frac {\ln \left (x+\frac {3}{5}\right )}{9453125}-\frac {5764801}{5632\,\left (x-\frac {1}{2}\right )}+\frac {1839811401\,x^2}{400000}+\frac {26773659\,x^3}{10000}+\frac {9899091\,x^4}{8000}+\frac {94041\,x^5}{250}+\frac {2187\,x^6}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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