Optimal. Leaf size=80 \[ \frac {5764801}{30976 (1-2 x)^2}-\frac {79883671}{85184 (1-2 x)}-\frac {81001863 x}{100000}-\frac {4863159 x^2}{20000}-\frac {123201 x^3}{2000}-\frac {6561 x^4}{800}-\frac {1}{20796875 (3+5 x)}-\frac {1845559863 \log (1-2 x)}{1874048}+\frac {54 \log (3+5 x)}{45753125} \]
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Rubi [A]
time = 0.03, antiderivative size = 80, 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 {6561 x^4}{800}-\frac {123201 x^3}{2000}-\frac {4863159 x^2}{20000}-\frac {81001863 x}{100000}-\frac {79883671}{85184 (1-2 x)}-\frac {1}{20796875 (5 x+3)}+\frac {5764801}{30976 (1-2 x)^2}-\frac {1845559863 \log (1-2 x)}{1874048}+\frac {54 \log (5 x+3)}{45753125} \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)^3 (3+5 x)^2} \, dx &=\int \left (-\frac {81001863}{100000}-\frac {4863159 x}{10000}-\frac {369603 x^2}{2000}-\frac {6561 x^3}{200}-\frac {5764801}{7744 (-1+2 x)^3}-\frac {79883671}{42592 (-1+2 x)^2}-\frac {1845559863}{937024 (-1+2 x)}+\frac {1}{4159375 (3+5 x)^2}+\frac {54}{9150625 (3+5 x)}\right ) \, dx\\ &=\frac {5764801}{30976 (1-2 x)^2}-\frac {79883671}{85184 (1-2 x)}-\frac {81001863 x}{100000}-\frac {4863159 x^2}{20000}-\frac {123201 x^3}{2000}-\frac {6561 x^4}{800}-\frac {1}{20796875 (3+5 x)}-\frac {1845559863 \log (1-2 x)}{1874048}+\frac {54 \log (3+5 x)}{45753125}\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 98, normalized size = 1.22 \begin {gather*} \frac {5764801}{30976 (1-2 x)^2}+\frac {79883671}{85184 (-1+2 x)}-\frac {18607401 (2+3 x)}{100000}-\frac {315171 (2+3 x)^2}{20000}-\frac {2943 (2+3 x)^3}{2000}-\frac {81}{800} (2+3 x)^4-\frac {1}{20796875 (3+5 x)}-\frac {1845559863 \log (3-6 x)}{1874048}+\frac {54 \log (-3 (3+5 x))}{45753125} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 63, normalized size = 0.79
method | result | size |
risch | \(-\frac {6561 x^{4}}{800}-\frac {123201 x^{3}}{2000}-\frac {4863159 x^{2}}{20000}-\frac {81001863 x}{100000}+\frac {\frac {6240911796747}{665500000} x^{2}+\frac {9946855297899}{5324000000} x -\frac {12005712797131}{5324000000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {1845559863 \ln \left (-1+2 x \right )}{1874048}+\frac {54 \ln \left (3+5 x \right )}{45753125}\) | \(62\) |
default | \(-\frac {6561 x^{4}}{800}-\frac {123201 x^{3}}{2000}-\frac {4863159 x^{2}}{20000}-\frac {81001863 x}{100000}+\frac {5764801}{30976 \left (-1+2 x \right )^{2}}+\frac {79883671}{85184 \left (-1+2 x \right )}-\frac {1845559863 \ln \left (-1+2 x \right )}{1874048}-\frac {1}{20796875 \left (3+5 x \right )}+\frac {54 \ln \left (3+5 x \right )}{45753125}\) | \(63\) |
norman | \(\frac {\frac {331620868303}{39930000} x^{2}-\frac {930122763613}{159720000} x +\frac {3678495782933}{159720000} x^{3}-\frac {55394037}{4000} x^{4}-\frac {3450357}{800} x^{5}-\frac {5832}{5} x^{6}-\frac {6561}{40} x^{7}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {1845559863 \ln \left (-1+2 x \right )}{1874048}+\frac {54 \ln \left (3+5 x \right )}{45753125}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 64, normalized size = 0.80 \begin {gather*} -\frac {6561}{800} \, x^{4} - \frac {123201}{2000} \, x^{3} - \frac {4863159}{20000} \, x^{2} - \frac {81001863}{100000} \, x + \frac {49927294373976 \, x^{2} + 9946855297899 \, x - 12005712797131}{5324000000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac {54}{45753125} \, \log \left (5 \, x + 3\right ) - \frac {1845559863}{1874048} \, \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 = 0.90, size = 100, normalized size = 1.25 \begin {gather*} -\frac {9605960100000 \, x^{7} + 68309049600000 \, x^{6} + 252583384185000 \, x^{5} + 811024095717000 \, x^{4} - 468362848619160 \, x^{3} - 838544848893576 \, x^{2} - 69120 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 57673745718750 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 32898384865071 \, x + 132062840768441}{58564000000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 70, normalized size = 0.88 \begin {gather*} - \frac {6561 x^{4}}{800} - \frac {123201 x^{3}}{2000} - \frac {4863159 x^{2}}{20000} - \frac {81001863 x}{100000} - \frac {- 49927294373976 x^{2} - 9946855297899 x + 12005712797131}{106480000000 x^{3} - 42592000000 x^{2} - 37268000000 x + 15972000000} - \frac {1845559863 \log {\left (x - \frac {1}{2} \right )}}{1874048} + \frac {54 \log {\left (x + \frac {3}{5} \right )}}{45753125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.55, size = 112, normalized size = 1.40 \begin {gather*} -\frac {{\left (5 \, x + 3\right )}^{4} {\left (\frac {11185606872}{5 \, x + 3} + \frac {158583727962}{{\left (5 \, x + 3\right )}^{2}} + \frac {3495217526460}{{\left (5 \, x + 3\right )}^{3}} - \frac {86510680819405}{{\left (5 \, x + 3\right )}^{4}} + \frac {317205578854725}{{\left (5 \, x + 3\right )}^{5}} + 768476808\right )}}{14641000000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} - \frac {1}{20796875 \, {\left (5 \, x + 3\right )}} + \frac {393919443}{400000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {1845559863}{1874048} \, \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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Mupad [B]
time = 0.04, size = 60, normalized size = 0.75 \begin {gather*} \frac {54\,\ln \left (x+\frac {3}{5}\right )}{45753125}-\frac {1845559863\,\ln \left (x-\frac {1}{2}\right )}{1874048}-\frac {81001863\,x}{100000}-\frac {\frac {6240911796747\,x^2}{13310000000}+\frac {9946855297899\,x}{106480000000}-\frac {12005712797131}{106480000000}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}}-\frac {4863159\,x^2}{20000}-\frac {123201\,x^3}{2000}-\frac {6561\,x^4}{800} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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