Optimal. Leaf size=72 \[ \frac {41666223 x}{1953125}+\frac {11111259 x^2}{781250}-\frac {17453753 x^3}{234375}-\frac {5848749 x^4}{62500}+\frac {2212083 x^5}{15625}+\frac {331713 x^6}{1250}-\frac {40338 x^7}{875}-\frac {13851 x^8}{50}-\frac {648 x^9}{5}+\frac {1331 \log (3+5 x)}{9765625} \]
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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 {648 x^9}{5}-\frac {13851 x^8}{50}-\frac {40338 x^7}{875}+\frac {331713 x^6}{1250}+\frac {2212083 x^5}{15625}-\frac {5848749 x^4}{62500}-\frac {17453753 x^3}{234375}+\frac {11111259 x^2}{781250}+\frac {41666223 x}{1953125}+\frac {1331 \log (5 x+3)}{9765625} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)^6}{3+5 x} \, dx &=\int \left (\frac {41666223}{1953125}+\frac {11111259 x}{390625}-\frac {17453753 x^2}{78125}-\frac {5848749 x^3}{15625}+\frac {2212083 x^4}{3125}+\frac {995139 x^5}{625}-\frac {40338 x^6}{125}-\frac {55404 x^7}{25}-\frac {5832 x^8}{5}+\frac {1331}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac {41666223 x}{1953125}+\frac {11111259 x^2}{781250}-\frac {17453753 x^3}{234375}-\frac {5848749 x^4}{62500}+\frac {2212083 x^5}{15625}+\frac {331713 x^6}{1250}-\frac {40338 x^7}{875}-\frac {13851 x^8}{50}-\frac {648 x^9}{5}+\frac {1331 \log (3+5 x)}{9765625}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 57, normalized size = 0.79 \begin {gather*} \frac {18072649071+87499068300 x+58334109750 x^2-305440677500 x^3-383824153125 x^4+580671787500 x^5+1088433281250 x^6-189084375000 x^7-1136214843750 x^8-531562500000 x^9+559020 \log (3+5 x)}{4101562500} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 53, normalized size = 0.74
method | result | size |
default | \(\frac {41666223 x}{1953125}+\frac {11111259 x^{2}}{781250}-\frac {17453753 x^{3}}{234375}-\frac {5848749 x^{4}}{62500}+\frac {2212083 x^{5}}{15625}+\frac {331713 x^{6}}{1250}-\frac {40338 x^{7}}{875}-\frac {13851 x^{8}}{50}-\frac {648 x^{9}}{5}+\frac {1331 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
norman | \(\frac {41666223 x}{1953125}+\frac {11111259 x^{2}}{781250}-\frac {17453753 x^{3}}{234375}-\frac {5848749 x^{4}}{62500}+\frac {2212083 x^{5}}{15625}+\frac {331713 x^{6}}{1250}-\frac {40338 x^{7}}{875}-\frac {13851 x^{8}}{50}-\frac {648 x^{9}}{5}+\frac {1331 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
risch | \(\frac {41666223 x}{1953125}+\frac {11111259 x^{2}}{781250}-\frac {17453753 x^{3}}{234375}-\frac {5848749 x^{4}}{62500}+\frac {2212083 x^{5}}{15625}+\frac {331713 x^{6}}{1250}-\frac {40338 x^{7}}{875}-\frac {13851 x^{8}}{50}-\frac {648 x^{9}}{5}+\frac {1331 \ln \left (3+5 x \right )}{9765625}\) | \(53\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{9765625}-\frac {531441 x \left (\frac {109375000}{6561} x^{8}-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{68359375}-\frac {1003833 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{10937500}+\frac {177147 x \left (-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{5468750}+\frac {56133 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}-\frac {80919 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{312500}-\frac {567 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}+\frac {264 x \left (-5 x +6\right )}{25}-\frac {336 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {192 x}{5}\) | \(217\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 52, normalized size = 0.72 \begin {gather*} -\frac {648}{5} \, x^{9} - \frac {13851}{50} \, x^{8} - \frac {40338}{875} \, x^{7} + \frac {331713}{1250} \, x^{6} + \frac {2212083}{15625} \, x^{5} - \frac {5848749}{62500} \, x^{4} - \frac {17453753}{234375} \, x^{3} + \frac {11111259}{781250} \, x^{2} + \frac {41666223}{1953125} \, x + \frac {1331}{9765625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 52, normalized size = 0.72 \begin {gather*} -\frac {648}{5} \, x^{9} - \frac {13851}{50} \, x^{8} - \frac {40338}{875} \, x^{7} + \frac {331713}{1250} \, x^{6} + \frac {2212083}{15625} \, x^{5} - \frac {5848749}{62500} \, x^{4} - \frac {17453753}{234375} \, x^{3} + \frac {11111259}{781250} \, x^{2} + \frac {41666223}{1953125} \, x + \frac {1331}{9765625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 68, normalized size = 0.94 \begin {gather*} - \frac {648 x^{9}}{5} - \frac {13851 x^{8}}{50} - \frac {40338 x^{7}}{875} + \frac {331713 x^{6}}{1250} + \frac {2212083 x^{5}}{15625} - \frac {5848749 x^{4}}{62500} - \frac {17453753 x^{3}}{234375} + \frac {11111259 x^{2}}{781250} + \frac {41666223 x}{1953125} + \frac {1331 \log {\left (5 x + 3 \right )}}{9765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.08, size = 53, normalized size = 0.74 \begin {gather*} -\frac {648}{5} \, x^{9} - \frac {13851}{50} \, x^{8} - \frac {40338}{875} \, x^{7} + \frac {331713}{1250} \, x^{6} + \frac {2212083}{15625} \, x^{5} - \frac {5848749}{62500} \, x^{4} - \frac {17453753}{234375} \, x^{3} + \frac {11111259}{781250} \, x^{2} + \frac {41666223}{1953125} \, x + \frac {1331}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\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 {41666223\,x}{1953125}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{9765625}+\frac {11111259\,x^2}{781250}-\frac {17453753\,x^3}{234375}-\frac {5848749\,x^4}{62500}+\frac {2212083\,x^5}{15625}+\frac {331713\,x^6}{1250}-\frac {40338\,x^7}{875}-\frac {13851\,x^8}{50}-\frac {648\,x^9}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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