Optimal. Leaf size=84 \[ \frac {5764801}{170368 (1-2 x)^2}-\frac {130943337}{937024 (1-2 x)}-\frac {242028 x}{3125}-\frac {330237 x^2}{20000}-\frac {2187 x^3}{1000}-\frac {1}{41593750 (3+5 x)^2}-\frac {54}{45753125 (3+5 x)}-\frac {595421589 \log (1-2 x)}{5153632}+\frac {1284 \log (3+5 x)}{100656875} \]
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Rubi [A]
time = 0.03, antiderivative size = 84, 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^3}{1000}-\frac {330237 x^2}{20000}-\frac {242028 x}{3125}-\frac {130943337}{937024 (1-2 x)}-\frac {54}{45753125 (5 x+3)}+\frac {5764801}{170368 (1-2 x)^2}-\frac {1}{41593750 (5 x+3)^2}-\frac {595421589 \log (1-2 x)}{5153632}+\frac {1284 \log (5 x+3)}{100656875} \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)^3} \, dx &=\int \left (-\frac {242028}{3125}-\frac {330237 x}{10000}-\frac {6561 x^2}{1000}-\frac {5764801}{42592 (-1+2 x)^3}-\frac {130943337}{468512 (-1+2 x)^2}-\frac {595421589}{2576816 (-1+2 x)}+\frac {1}{4159375 (3+5 x)^3}+\frac {54}{9150625 (3+5 x)^2}+\frac {1284}{20131375 (3+5 x)}\right ) \, dx\\ &=\frac {5764801}{170368 (1-2 x)^2}-\frac {130943337}{937024 (1-2 x)}-\frac {242028 x}{3125}-\frac {330237 x^2}{20000}-\frac {2187 x^3}{1000}-\frac {1}{41593750 (3+5 x)^2}-\frac {54}{45753125 (3+5 x)}-\frac {595421589 \log (1-2 x)}{5153632}+\frac {1284 \log (3+5 x)}{100656875}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 70, normalized size = 0.83 \begin {gather*} \frac {-\frac {11 \left (39754322426279+31893783102814 x-254889143270829 x^2-314407515766380 x^3+148045752548100 x^4+232677700200000 x^5+49630793850000 x^6+6403973400000 x^7\right )}{\left (-3+x+10 x^2\right )^2}-37213849312500 \log (3-6 x)+4108800 \log (-3 (3+5 x))}{322102000000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 67, normalized size = 0.80
method | result | size |
risch | \(-\frac {2187 x^{3}}{1000}-\frac {330237 x^{2}}{20000}-\frac {242028 x}{3125}+\frac {\frac {2045989633713}{292820000} x^{3}+\frac {167989904414289}{29282000000} x^{2}-\frac {9689497987007}{14641000000} x -\frac {27910387088759}{29282000000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {595421589 \ln \left (-1+2 x \right )}{5153632}+\frac {1284 \ln \left (3+5 x \right )}{100656875}\) | \(62\) |
norman | \(\frac {-\frac {407765282557}{17569200} x^{4}+\frac {624284716271}{87846000} x^{3}+\frac {3411068062691}{175692000} x^{2}-\frac {79461}{10} x^{5}-\frac {67797}{40} x^{6}-\frac {2187}{10} x^{7}-\frac {175189994161}{58564000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {595421589 \ln \left (-1+2 x \right )}{5153632}+\frac {1284 \ln \left (3+5 x \right )}{100656875}\) | \(65\) |
default | \(-\frac {2187 x^{3}}{1000}-\frac {330237 x^{2}}{20000}-\frac {242028 x}{3125}+\frac {5764801}{170368 \left (-1+2 x \right )^{2}}+\frac {130943337}{937024 \left (-1+2 x \right )}-\frac {595421589 \ln \left (-1+2 x \right )}{5153632}-\frac {1}{41593750 \left (3+5 x \right )^{2}}-\frac {54}{45753125 \left (3+5 x \right )}+\frac {1284 \ln \left (3+5 x \right )}{100656875}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 69, normalized size = 0.82 \begin {gather*} -\frac {2187}{1000} \, x^{3} - \frac {330237}{20000} \, x^{2} - \frac {242028}{3125} \, x + \frac {204598963371300 \, x^{3} + 167989904414289 \, x^{2} - 19378995974014 \, x - 27910387088759}{29282000000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {1284}{100656875} \, \log \left (5 \, x + 3\right ) - \frac {595421589}{5153632} \, \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 = 0.64, size = 115, normalized size = 1.37 \begin {gather*} -\frac {70443707400000 \, x^{7} + 545938732350000 \, x^{6} + 2559454702200000 \, x^{5} + 180911181221100 \, x^{4} - 3748001092791780 \, x^{3} - 1949701238862399 \, x^{2} - 4108800 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 37213849312500 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 437687139939434 \, x + 307014257976349}{322102000000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 73, normalized size = 0.87 \begin {gather*} - \frac {2187 x^{3}}{1000} - \frac {330237 x^{2}}{20000} - \frac {242028 x}{3125} - \frac {- 204598963371300 x^{3} - 167989904414289 x^{2} + 19378995974014 x + 27910387088759}{2928200000000 x^{4} + 585640000000 x^{3} - 1727638000000 x^{2} - 175692000000 x + 263538000000} - \frac {595421589 \log {\left (x - \frac {1}{2} \right )}}{5153632} + \frac {1284 \log {\left (x + \frac {3}{5} \right )}}{100656875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 63, normalized size = 0.75 \begin {gather*} -\frac {2187}{1000} \, x^{3} - \frac {330237}{20000} \, x^{2} - \frac {242028}{3125} \, x + \frac {204598963371300 \, x^{3} + 167989904414289 \, x^{2} - 19378995974014 \, x - 27910387088759}{29282000000 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {1284}{100656875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {595421589}{5153632} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.08, size = 63, normalized size = 0.75 \begin {gather*} \frac {1284\,\ln \left (x+\frac {3}{5}\right )}{100656875}-\frac {595421589\,\ln \left (x-\frac {1}{2}\right )}{5153632}-\frac {242028\,x}{3125}-\frac {-\frac {2045989633713\,x^3}{29282000000}-\frac {167989904414289\,x^2}{2928200000000}+\frac {9689497987007\,x}{1464100000000}+\frac {27910387088759}{2928200000000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}}-\frac {330237\,x^2}{20000}-\frac {2187\,x^3}{1000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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