Optimal. Leaf size=80 \[ \frac {5764801}{85184 (1-2 x)}+\frac {7680987 x}{50000}+\frac {6093711 x^2}{100000}+\frac {12393 x^3}{625}+\frac {6561 x^4}{2000}-\frac {1}{18906250 (3+5 x)^2}-\frac {268}{103984375 (3+5 x)}+\frac {130943337 \log (1-2 x)}{937024}+\frac {6312 \log (3+5 x)}{228765625} \]
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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}{2000}+\frac {12393 x^3}{625}+\frac {6093711 x^2}{100000}+\frac {7680987 x}{50000}+\frac {5764801}{85184 (1-2 x)}-\frac {268}{103984375 (5 x+3)}-\frac {1}{18906250 (5 x+3)^2}+\frac {130943337 \log (1-2 x)}{937024}+\frac {6312 \log (5 x+3)}{228765625} \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)^3} \, dx &=\int \left (\frac {7680987}{50000}+\frac {6093711 x}{50000}+\frac {37179 x^2}{625}+\frac {6561 x^3}{500}+\frac {5764801}{42592 (-1+2 x)^2}+\frac {130943337}{468512 (-1+2 x)}+\frac {1}{1890625 (3+5 x)^3}+\frac {268}{20796875 (3+5 x)^2}+\frac {6312}{45753125 (3+5 x)}\right ) \, dx\\ &=\frac {5764801}{85184 (1-2 x)}+\frac {7680987 x}{50000}+\frac {6093711 x^2}{100000}+\frac {12393 x^3}{625}+\frac {6561 x^4}{2000}-\frac {1}{18906250 (3+5 x)^2}-\frac {268}{103984375 (3+5 x)}+\frac {130943337 \log (1-2 x)}{937024}+\frac {6312 \log (3+5 x)}{228765625}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 74, normalized size = 0.92 \begin {gather*} \frac {3 \left (\frac {11}{3} \left (536108166000+\frac {450375078125}{1-2 x}+1022339369700 x+405536467050 x^2+131960664000 x^3+21831727500 x^4-\frac {352}{(3+5 x)^2}-\frac {17152}{3+5 x}\right )+3409982734375 \log (3-6 x)+673280 \log (-3 (3+5 x))\right )}{73205000000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 63, normalized size = 0.79
method | result | size |
risch | \(\frac {6561 x^{4}}{2000}+\frac {12393 x^{3}}{625}+\frac {6093711 x^{2}}{100000}+\frac {7680987 x}{50000}+\frac {-\frac {2251875424929}{1331000000} x^{2}-\frac {6755626180803}{3327500000} x -\frac {4053375651317}{6655000000}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {130943337 \ln \left (-1+2 x \right )}{937024}+\frac {6312 \ln \left (3+5 x \right )}{228765625}\) | \(62\) |
default | \(\frac {6561 x^{4}}{2000}+\frac {12393 x^{3}}{625}+\frac {6093711 x^{2}}{100000}+\frac {7680987 x}{50000}-\frac {5764801}{85184 \left (-1+2 x \right )}+\frac {130943337 \ln \left (-1+2 x \right )}{937024}-\frac {1}{18906250 \left (3+5 x \right )^{2}}-\frac {268}{103984375 \left (3+5 x \right )}+\frac {6312 \ln \left (3+5 x \right )}{228765625}\) | \(63\) |
norman | \(\frac {-\frac {7729272953531}{1197900000} x^{2}+\frac {259525466657}{239580000} x^{3}-\frac {1038468349229}{399300000} x +\frac {38185263}{4000} x^{4}+\frac {1480599}{400} x^{5}+\frac {442503}{400} x^{6}+\frac {6561}{40} x^{7}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {130943337 \ln \left (-1+2 x \right )}{937024}+\frac {6312 \ln \left (3+5 x \right )}{228765625}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 64, normalized size = 0.80 \begin {gather*} \frac {6561}{2000} \, x^{4} + \frac {12393}{625} \, x^{3} + \frac {6093711}{100000} \, x^{2} + \frac {7680987}{50000} \, x - \frac {11259377124645 \, x^{2} + 13511252361606 \, x + 4053375651317}{6655000000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {6312}{228765625} \, \log \left (5 \, x + 3\right ) + \frac {130943337}{937024} \, \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 = 0.48, size = 100, normalized size = 1.25 \begin {gather*} \frac {12007450125000 \, x^{7} + 80983580287500 \, x^{6} + 270968124487500 \, x^{5} + 698838044478750 \, x^{4} + 327005737947900 \, x^{3} - 298950055409445 \, x^{2} + 2019840 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 10229948203125 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 249835373577966 \, x - 44587132164487}{73205000000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 71, normalized size = 0.89 \begin {gather*} \frac {6561 x^{4}}{2000} + \frac {12393 x^{3}}{625} + \frac {6093711 x^{2}}{100000} + \frac {7680987 x}{50000} + \frac {- 11259377124645 x^{2} - 13511252361606 x - 4053375651317}{332750000000 x^{3} + 232925000000 x^{2} - 79860000000 x - 59895000000} + \frac {130943337 \log {\left (x - \frac {1}{2} \right )}}{937024} + \frac {6312 \log {\left (x + \frac {3}{5} \right )}}{228765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 112, normalized size = 1.40 \begin {gather*} \frac {{\left (2 \, x - 1\right )}^{4} {\left (\frac {1230096557250}{2 \, x - 1} + \frac {11539159570125}{{\left (2 \, x - 1\right )}^{2}} + \frac {69299175042900}{{\left (2 \, x - 1\right )}^{3}} + \frac {182728002843460}{{\left (2 \, x - 1\right )}^{4}} + \frac {163740919200408}{{\left (2 \, x - 1\right )}^{5}} + 60037250625\right )}}{11712800000 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} - \frac {5764801}{85184 \, {\left (2 \, x - 1\right )}} - \frac {139743873}{1000000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {6312}{228765625} \, \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 = 1.06, size = 59, normalized size = 0.74 \begin {gather*} \frac {7680987\,x}{50000}+\frac {130943337\,\ln \left (x-\frac {1}{2}\right )}{937024}+\frac {6312\,\ln \left (x+\frac {3}{5}\right )}{228765625}+\frac {\frac {2251875424929\,x^2}{66550000000}+\frac {6755626180803\,x}{166375000000}+\frac {4053375651317}{332750000000}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}}+\frac {6093711\,x^2}{100000}+\frac {12393\,x^3}{625}+\frac {6561\,x^4}{2000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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