Optimal. Leaf size=65 \[ \frac {4166223 x}{390625}-\frac {138741 x^2}{156250}-\frac {1703753 x^3}{46875}-\frac {73749 x^4}{12500}+\frac {243333 x^5}{3125}+\frac {4419 x^6}{125}-\frac {11988 x^7}{175}-\frac {243 x^8}{5}+\frac {1331 \log (3+5 x)}{1953125} \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 {243 x^8}{5}-\frac {11988 x^7}{175}+\frac {4419 x^6}{125}+\frac {243333 x^5}{3125}-\frac {73749 x^4}{12500}-\frac {1703753 x^3}{46875}-\frac {138741 x^2}{156250}+\frac {4166223 x}{390625}+\frac {1331 \log (5 x+3)}{1953125} \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)^5}{3+5 x} \, dx &=\int \left (\frac {4166223}{390625}-\frac {138741 x}{78125}-\frac {1703753 x^2}{15625}-\frac {73749 x^3}{3125}+\frac {243333 x^4}{625}+\frac {26514 x^5}{125}-\frac {11988 x^6}{25}-\frac {1944 x^7}{5}+\frac {1331}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {4166223 x}{390625}-\frac {138741 x^2}{156250}-\frac {1703753 x^3}{46875}-\frac {73749 x^4}{12500}+\frac {243333 x^5}{3125}+\frac {4419 x^6}{125}-\frac {11988 x^7}{175}-\frac {243 x^8}{5}+\frac {1331 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 52, normalized size = 0.80 \begin {gather*} \frac {2409164451+8749068300 x-728390250 x^2-29815677500 x^3-4839778125 x^4+63874912500 x^5+28999687500 x^6-56193750000 x^7-39867187500 x^8+559020 \log (3+5 x)}{820312500} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 48, normalized size = 0.74
method | result | size |
default | \(\frac {4166223 x}{390625}-\frac {138741 x^{2}}{156250}-\frac {1703753 x^{3}}{46875}-\frac {73749 x^{4}}{12500}+\frac {243333 x^{5}}{3125}+\frac {4419 x^{6}}{125}-\frac {11988 x^{7}}{175}-\frac {243 x^{8}}{5}+\frac {1331 \ln \left (3+5 x \right )}{1953125}\) | \(48\) |
norman | \(\frac {4166223 x}{390625}-\frac {138741 x^{2}}{156250}-\frac {1703753 x^{3}}{46875}-\frac {73749 x^{4}}{12500}+\frac {243333 x^{5}}{3125}+\frac {4419 x^{6}}{125}-\frac {11988 x^{7}}{175}-\frac {243 x^{8}}{5}+\frac {1331 \ln \left (3+5 x \right )}{1953125}\) | \(48\) |
risch | \(\frac {4166223 x}{390625}-\frac {138741 x^{2}}{156250}-\frac {1703753 x^{3}}{46875}-\frac {73749 x^{4}}{12500}+\frac {243333 x^{5}}{3125}+\frac {4419 x^{6}}{125}-\frac {11988 x^{7}}{175}-\frac {243 x^{8}}{5}+\frac {1331 \ln \left (3+5 x \right )}{1953125}\) | \(48\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{1953125}+\frac {48 x}{5}+\frac {168 x \left (-5 x +6\right )}{25}-\frac {462 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}-\frac {189 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{250}+\frac {69741 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{62500}+\frac {2187 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{156250}-\frac {216513 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{5468750}+\frac {59049 x \left (-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{13671875}\) | \(174\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 47, normalized size = 0.72 \begin {gather*} -\frac {243}{5} \, x^{8} - \frac {11988}{175} \, x^{7} + \frac {4419}{125} \, x^{6} + \frac {243333}{3125} \, x^{5} - \frac {73749}{12500} \, x^{4} - \frac {1703753}{46875} \, x^{3} - \frac {138741}{156250} \, x^{2} + \frac {4166223}{390625} \, x + \frac {1331}{1953125} \, \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 = 0.42, size = 47, normalized size = 0.72 \begin {gather*} -\frac {243}{5} \, x^{8} - \frac {11988}{175} \, x^{7} + \frac {4419}{125} \, x^{6} + \frac {243333}{3125} \, x^{5} - \frac {73749}{12500} \, x^{4} - \frac {1703753}{46875} \, x^{3} - \frac {138741}{156250} \, x^{2} + \frac {4166223}{390625} \, x + \frac {1331}{1953125} \, \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 = 61, normalized size = 0.94 \begin {gather*} - \frac {243 x^{8}}{5} - \frac {11988 x^{7}}{175} + \frac {4419 x^{6}}{125} + \frac {243333 x^{5}}{3125} - \frac {73749 x^{4}}{12500} - \frac {1703753 x^{3}}{46875} - \frac {138741 x^{2}}{156250} + \frac {4166223 x}{390625} + \frac {1331 \log {\left (5 x + 3 \right )}}{1953125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.28, size = 48, normalized size = 0.74 \begin {gather*} -\frac {243}{5} \, x^{8} - \frac {11988}{175} \, x^{7} + \frac {4419}{125} \, x^{6} + \frac {243333}{3125} \, x^{5} - \frac {73749}{12500} \, x^{4} - \frac {1703753}{46875} \, x^{3} - \frac {138741}{156250} \, x^{2} + \frac {4166223}{390625} \, x + \frac {1331}{1953125} \, \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 = 0.04, size = 45, normalized size = 0.69 \begin {gather*} \frac {4166223\,x}{390625}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {138741\,x^2}{156250}-\frac {1703753\,x^3}{46875}-\frac {73749\,x^4}{12500}+\frac {243333\,x^5}{3125}+\frac {4419\,x^6}{125}-\frac {11988\,x^7}{175}-\frac {243\,x^8}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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