Optimal. Leaf size=55 \[ \frac {1998 x}{3125}-\frac {12077 x^2}{6250}+\frac {786 x^3}{625}+\frac {189 x^4}{125}-\frac {216 x^5}{125}-\frac {1331}{78125 (3+5 x)}+\frac {11253 \log (3+5 x)}{78125} \]
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Rubi [A]
time = 0.02, antiderivative size = 55, 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 {216 x^5}{125}+\frac {189 x^4}{125}+\frac {786 x^3}{625}-\frac {12077 x^2}{6250}+\frac {1998 x}{3125}-\frac {1331}{78125 (5 x+3)}+\frac {11253 \log (5 x+3)}{78125} \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)^3}{(3+5 x)^2} \, dx &=\int \left (\frac {1998}{3125}-\frac {12077 x}{3125}+\frac {2358 x^2}{625}+\frac {756 x^3}{125}-\frac {216 x^4}{25}+\frac {1331}{15625 (3+5 x)^2}+\frac {11253}{15625 (3+5 x)}\right ) \, dx\\ &=\frac {1998 x}{3125}-\frac {12077 x^2}{6250}+\frac {786 x^3}{625}+\frac {189 x^4}{125}-\frac {216 x^5}{125}-\frac {1331}{78125 (3+5 x)}+\frac {11253 \log (3+5 x)}{78125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 54, normalized size = 0.98 \begin {gather*} \frac {2378647+5485095 x-2031375 x^2-4600625 x^3+8456250 x^4+1856250 x^5-6750000 x^6+112530 (3+5 x) \log (3+5 x)}{781250 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 42, normalized size = 0.76
method | result | size |
risch | \(-\frac {216 x^{5}}{125}+\frac {189 x^{4}}{125}+\frac {786 x^{3}}{625}-\frac {12077 x^{2}}{6250}+\frac {1998 x}{3125}-\frac {1331}{390625 \left (x +\frac {3}{5}\right )}+\frac {11253 \ln \left (3+5 x \right )}{78125}\) | \(40\) |
default | \(\frac {1998 x}{3125}-\frac {12077 x^{2}}{6250}+\frac {786 x^{3}}{625}+\frac {189 x^{4}}{125}-\frac {216 x^{5}}{125}-\frac {1331}{78125 \left (3+5 x \right )}+\frac {11253 \ln \left (3+5 x \right )}{78125}\) | \(42\) |
norman | \(\frac {\frac {91241}{46875} x -\frac {16251}{6250} x^{2}-\frac {7361}{1250} x^{3}+\frac {1353}{125} x^{4}+\frac {297}{125} x^{5}-\frac {216}{25} x^{6}}{3+5 x}+\frac {11253 \ln \left (3+5 x \right )}{78125}\) | \(47\) |
meijerg | \(\frac {76 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {11253 \ln \left (1+\frac {5 x}{3}\right )}{78125}-\frac {22 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}-\frac {213 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{500 \left (1+\frac {5 x}{3}\right )}+\frac {594 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}+\frac {243 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {8748 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{546875 \left (1+\frac {5 x}{3}\right )}\) | \(145\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 41, normalized size = 0.75 \begin {gather*} -\frac {216}{125} \, x^{5} + \frac {189}{125} \, x^{4} + \frac {786}{625} \, x^{3} - \frac {12077}{6250} \, x^{2} + \frac {1998}{3125} \, x - \frac {1331}{78125 \, {\left (5 \, x + 3\right )}} + \frac {11253}{78125} \, \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 = 52, normalized size = 0.95 \begin {gather*} -\frac {1350000 \, x^{6} - 371250 \, x^{5} - 1691250 \, x^{4} + 920125 \, x^{3} + 406275 \, x^{2} - 22506 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 299700 \, x + 2662}{156250 \, {\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 = 48, normalized size = 0.87 \begin {gather*} - \frac {216 x^{5}}{125} + \frac {189 x^{4}}{125} + \frac {786 x^{3}}{625} - \frac {12077 x^{2}}{6250} + \frac {1998 x}{3125} + \frac {11253 \log {\left (5 x + 3 \right )}}{78125} - \frac {1331}{390625 x + 234375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.57, size = 75, normalized size = 1.36 \begin {gather*} \frac {1}{781250} \, {\left (5 \, x + 3\right )}^{5} {\left (\frac {8370}{5 \, x + 3} - \frac {53700}{{\left (5 \, x + 3\right )}^{2}} + \frac {87575}{{\left (5 \, x + 3\right )}^{3}} + \frac {295350}{{\left (5 \, x + 3\right )}^{4}} - 432\right )} - \frac {1331}{78125 \, {\left (5 \, x + 3\right )}} - \frac {11253}{78125} \, \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 = 0.03, size = 39, normalized size = 0.71 \begin {gather*} \frac {1998\,x}{3125}+\frac {11253\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {1331}{390625\,\left (x+\frac {3}{5}\right )}-\frac {12077\,x^2}{6250}+\frac {786\,x^3}{625}+\frac {189\,x^4}{125}-\frac {216\,x^5}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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