Optimal. Leaf size=69 \[ \frac {1382328 x}{390625}-\frac {507023 x^2}{156250}-\frac {26594 x^3}{3125}+\frac {108387 x^4}{12500}+\frac {44982 x^5}{3125}-\frac {1026 x^6}{125}-\frac {1944 x^7}{175}-\frac {1331}{1953125 (3+5 x)}+\frac {19239 \log (3+5 x)}{1953125} \]
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Rubi [A]
time = 0.02, antiderivative size = 69, 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 {1944 x^7}{175}-\frac {1026 x^6}{125}+\frac {44982 x^5}{3125}+\frac {108387 x^4}{12500}-\frac {26594 x^3}{3125}-\frac {507023 x^2}{156250}+\frac {1382328 x}{390625}-\frac {1331}{1953125 (5 x+3)}+\frac {19239 \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)^2} \, dx &=\int \left (\frac {1382328}{390625}-\frac {507023 x}{78125}-\frac {79782 x^2}{3125}+\frac {108387 x^3}{3125}+\frac {44982 x^4}{625}-\frac {6156 x^5}{125}-\frac {1944 x^6}{25}+\frac {1331}{390625 (3+5 x)^2}+\frac {19239}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {1382328 x}{390625}-\frac {507023 x^2}{156250}-\frac {26594 x^3}{3125}+\frac {108387 x^4}{12500}+\frac {44982 x^5}{3125}-\frac {1026 x^6}{125}-\frac {1944 x^7}{175}-\frac {1331}{1953125 (3+5 x)}+\frac {19239 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 66, normalized size = 0.96 \begin {gather*} \frac {1247330759+4982083965 x+2176277250 x^2-11417376250 x^3-4521978125 x^4+23662603125 x^5+12946500000 x^6-20334375000 x^7-15187500000 x^8+2693460 (3+5 x) \log (6 (3+5 x))}{273437500 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 52, normalized size = 0.75
method | result | size |
risch | \(-\frac {1944 x^{7}}{175}-\frac {1026 x^{6}}{125}+\frac {44982 x^{5}}{3125}+\frac {108387 x^{4}}{12500}-\frac {26594 x^{3}}{3125}-\frac {507023 x^{2}}{156250}+\frac {1382328 x}{390625}-\frac {1331}{9765625 \left (x +\frac {3}{5}\right )}+\frac {19239 \ln \left (3+5 x \right )}{1953125}\) | \(50\) |
default | \(\frac {1382328 x}{390625}-\frac {507023 x^{2}}{156250}-\frac {26594 x^{3}}{3125}+\frac {108387 x^{4}}{12500}+\frac {44982 x^{5}}{3125}-\frac {1026 x^{6}}{125}-\frac {1944 x^{7}}{175}-\frac {1331}{1953125 \left (3+5 x \right )}+\frac {19239 \ln \left (3+5 x \right )}{1953125}\) | \(52\) |
norman | \(\frac {\frac {12442283}{1171875} x +\frac {1243587}{156250} x^{2}-\frac {1304843}{31250} x^{3}-\frac {206719}{12500} x^{4}+\frac {1081719}{12500} x^{5}+\frac {29592}{625} x^{6}-\frac {13014}{175} x^{7}-\frac {1944}{35} x^{8}}{3+5 x}+\frac {19239 \ln \left (3+5 x \right )}{1953125}\) | \(57\) |
meijerg | \(\frac {16 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {19239 \ln \left (1+\frac {5 x}{3}\right )}{1953125}-\frac {112 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}+\frac {462 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}+\frac {126 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{125 \left (1+\frac {5 x}{3}\right )}-\frac {23247 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{12500 \left (1+\frac {5 x}{3}\right )}-\frac {2187 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{78125 \left (1+\frac {5 x}{3}\right )}+\frac {72171 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{781250 \left (1+\frac {5 x}{3}\right )}-\frac {157464 x \left (\frac {390625}{243} x^{7}-\frac {312500}{243} x^{6}+\frac {87500}{81} x^{5}-\frac {8750}{9} x^{4}+\frac {8750}{9} x^{3}-\frac {3500}{3} x^{2}+2100 x +2520\right )}{13671875 \left (1+\frac {5 x}{3}\right )}\) | \(230\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 51, normalized size = 0.74 \begin {gather*} -\frac {1944}{175} \, x^{7} - \frac {1026}{125} \, x^{6} + \frac {44982}{3125} \, x^{5} + \frac {108387}{12500} \, x^{4} - \frac {26594}{3125} \, x^{3} - \frac {507023}{156250} \, x^{2} + \frac {1382328}{390625} \, x - \frac {1331}{1953125 \, {\left (5 \, x + 3\right )}} + \frac {19239}{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 = 0.43, size = 62, normalized size = 0.90 \begin {gather*} -\frac {3037500000 \, x^{8} + 4066875000 \, x^{7} - 2589300000 \, x^{6} - 4732520625 \, x^{5} + 904395625 \, x^{4} + 2283475250 \, x^{3} - 435255450 \, x^{2} - 538692 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 580577760 \, x + 37268}{54687500 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 61, normalized size = 0.88 \begin {gather*} - \frac {1944 x^{7}}{175} - \frac {1026 x^{6}}{125} + \frac {44982 x^{5}}{3125} + \frac {108387 x^{4}}{12500} - \frac {26594 x^{3}}{3125} - \frac {507023 x^{2}}{156250} + \frac {1382328 x}{390625} + \frac {19239 \log {\left (5 x + 3 \right )}}{1953125} - \frac {1331}{9765625 x + 5859375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.87, size = 93, normalized size = 1.35 \begin {gather*} \frac {1}{273437500} \, {\left (5 \, x + 3\right )}^{7} {\left (\frac {672840}{5 \, x + 3} - \frac {3503304}{{\left (5 \, x + 3\right )}^{2}} + \frac {2251305}{{\left (5 \, x + 3\right )}^{3}} + \frac {16557100}{{\left (5 \, x + 3\right )}^{4}} + \frac {20720140}{{\left (5 \, x + 3\right )}^{5}} + \frac {15264480}{{\left (5 \, x + 3\right )}^{6}} - 38880\right )} - \frac {1331}{1953125 \, {\left (5 \, x + 3\right )}} - \frac {19239}{1953125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 49, normalized size = 0.71 \begin {gather*} \frac {1382328\,x}{390625}+\frac {19239\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {1331}{9765625\,\left (x+\frac {3}{5}\right )}-\frac {507023\,x^2}{156250}-\frac {26594\,x^3}{3125}+\frac {108387\,x^4}{12500}+\frac {44982\,x^5}{3125}-\frac {1026\,x^6}{125}-\frac {1944\,x^7}{175} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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