Optimal. Leaf size=62 \[ \frac {133659 x}{78125}-\frac {1816 x^2}{625}-\frac {4217 x^3}{3125}+\frac {7317 x^4}{1250}+\frac {108 x^5}{625}-\frac {108 x^6}{25}-\frac {1331}{390625 (3+5 x)}+\frac {15246 \log (3+5 x)}{390625} \]
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Rubi [A]
time = 0.02, antiderivative size = 62, 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 {108 x^6}{25}+\frac {108 x^5}{625}+\frac {7317 x^4}{1250}-\frac {4217 x^3}{3125}-\frac {1816 x^2}{625}+\frac {133659 x}{78125}-\frac {1331}{390625 (5 x+3)}+\frac {15246 \log (5 x+3)}{390625} \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)^4}{(3+5 x)^2} \, dx &=\int \left (\frac {133659}{78125}-\frac {3632 x}{625}-\frac {12651 x^2}{3125}+\frac {14634 x^3}{625}+\frac {108 x^4}{125}-\frac {648 x^5}{25}+\frac {1331}{78125 (3+5 x)^2}+\frac {15246}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {133659 x}{78125}-\frac {1816 x^2}{625}-\frac {4217 x^3}{3125}+\frac {7317 x^4}{1250}+\frac {108 x^5}{625}-\frac {108 x^6}{25}-\frac {1331}{390625 (3+5 x)}+\frac {15246 \log (3+5 x)}{390625}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 61, normalized size = 0.98 \begin {gather*} \frac {14487499+44216865 x-635250 x^2-72563750 x^3+42240625 x^4+116353125 x^5-47250000 x^6-84375000 x^7+152460 (3+5 x) \log (6 (3+5 x))}{3906250 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 47, normalized size = 0.76
method | result | size |
risch | \(-\frac {108 x^{6}}{25}+\frac {108 x^{5}}{625}+\frac {7317 x^{4}}{1250}-\frac {4217 x^{3}}{3125}-\frac {1816 x^{2}}{625}+\frac {133659 x}{78125}-\frac {1331}{1953125 \left (x +\frac {3}{5}\right )}+\frac {15246 \ln \left (3+5 x \right )}{390625}\) | \(45\) |
default | \(\frac {133659 x}{78125}-\frac {1816 x^{2}}{625}-\frac {4217 x^{3}}{3125}+\frac {7317 x^{4}}{1250}+\frac {108 x^{5}}{625}-\frac {108 x^{6}}{25}-\frac {1331}{390625 \left (3+5 x \right )}+\frac {15246 \ln \left (3+5 x \right )}{390625}\) | \(47\) |
norman | \(\frac {\frac {1204262}{234375} x -\frac {2541}{15625} x^{2}-\frac {58051}{3125} x^{3}+\frac {13517}{1250} x^{4}+\frac {37233}{1250} x^{5}-\frac {1512}{125} x^{6}-\frac {108}{5} x^{7}}{3+5 x}+\frac {15246 \ln \left (3+5 x \right )}{390625}\) | \(52\) |
meijerg | \(\frac {16 x}{9 \left (1+\frac {5 x}{3}\right )}-\frac {56 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}+\frac {15246 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {42 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}+\frac {1827 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {1701 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{6250 \left (1+\frac {5 x}{3}\right )}-\frac {4374 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{78125 \left (1+\frac {5 x}{3}\right )}+\frac {6561 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{390625 \left (1+\frac {5 x}{3}\right )}\) | \(185\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 46, normalized size = 0.74 \begin {gather*} -\frac {108}{25} \, x^{6} + \frac {108}{625} \, x^{5} + \frac {7317}{1250} \, x^{4} - \frac {4217}{3125} \, x^{3} - \frac {1816}{625} \, x^{2} + \frac {133659}{78125} \, x - \frac {1331}{390625 \, {\left (5 \, x + 3\right )}} + \frac {15246}{390625} \, \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 = 57, normalized size = 0.92 \begin {gather*} -\frac {16875000 \, x^{7} + 9450000 \, x^{6} - 23270625 \, x^{5} - 8448125 \, x^{4} + 14512750 \, x^{3} + 127050 \, x^{2} - 30492 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 4009770 \, x + 2662}{781250 \, {\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 = 54, normalized size = 0.87 \begin {gather*} - \frac {108 x^{6}}{25} + \frac {108 x^{5}}{625} + \frac {7317 x^{4}}{1250} - \frac {4217 x^{3}}{3125} - \frac {1816 x^{2}}{625} + \frac {133659 x}{78125} + \frac {15246 \log {\left (5 x + 3 \right )}}{390625} - \frac {1331}{1953125 x + 1171875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 84, normalized size = 1.35 \begin {gather*} \frac {1}{3906250} \, {\left (5 \, x + 3\right )}^{6} {\left (\frac {19656}{5 \, x + 3} - \frac {112455}{{\left (5 \, x + 3\right )}^{2}} + \frac {121450}{{\left (5 \, x + 3\right )}^{3}} + \frac {530600}{{\left (5 \, x + 3\right )}^{4}} + \frac {632940}{{\left (5 \, x + 3\right )}^{5}} - 1080\right )} - \frac {1331}{390625 \, {\left (5 \, x + 3\right )}} - \frac {15246}{390625} \, \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 = 44, normalized size = 0.71 \begin {gather*} \frac {133659\,x}{78125}+\frac {15246\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {1331}{1953125\,\left (x+\frac {3}{5}\right )}-\frac {1816\,x^2}{625}-\frac {4217\,x^3}{3125}+\frac {7317\,x^4}{1250}+\frac {108\,x^5}{625}-\frac {108\,x^6}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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