Optimal. Leaf size=44 \[ \frac {922 x}{243}-\frac {1433 x^2}{162}+\frac {82 x^3}{81}+\frac {145 x^4}{9}-\frac {40 x^5}{3}+\frac {343}{729} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 44, 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 {40 x^5}{3}+\frac {145 x^4}{9}+\frac {82 x^3}{81}-\frac {1433 x^2}{162}+\frac {922 x}{243}+\frac {343}{729} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac {922}{243}-\frac {1433 x}{81}+\frac {82 x^2}{27}+\frac {580 x^3}{9}-\frac {200 x^4}{3}+\frac {343}{243 (2+3 x)}\right ) \, dx\\ &=\frac {922 x}{243}-\frac {1433 x^2}{162}+\frac {82 x^3}{81}+\frac {145 x^4}{9}-\frac {40 x^5}{3}+\frac {343}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {7972+16596 x-38691 x^2+4428 x^3+70470 x^4-58320 x^5+2058 \log (2+3 x)}{4374} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 33, normalized size = 0.75
method | result | size |
default | \(\frac {922 x}{243}-\frac {1433 x^{2}}{162}+\frac {82 x^{3}}{81}+\frac {145 x^{4}}{9}-\frac {40 x^{5}}{3}+\frac {343 \ln \left (2+3 x \right )}{729}\) | \(33\) |
norman | \(\frac {922 x}{243}-\frac {1433 x^{2}}{162}+\frac {82 x^{3}}{81}+\frac {145 x^{4}}{9}-\frac {40 x^{5}}{3}+\frac {343 \ln \left (2+3 x \right )}{729}\) | \(33\) |
risch | \(\frac {922 x}{243}-\frac {1433 x^{2}}{162}+\frac {82 x^{3}}{81}+\frac {145 x^{4}}{9}-\frac {40 x^{5}}{3}+\frac {343 \ln \left (2+3 x \right )}{729}\) | \(33\) |
meijerg | \(\frac {343 \ln \left (1+\frac {3 x}{2}\right )}{729}-8 x +\frac {47 x \left (-\frac {9 x}{2}+6\right )}{27}+\frac {46 x \left (9 x^{2}-9 x +12\right )}{27}-\frac {8 x \left (-\frac {405}{8} x^{3}+45 x^{2}-45 x +60\right )}{81}-\frac {160 x \left (\frac {243}{4} x^{4}-\frac {405}{8} x^{3}+45 x^{2}-45 x +60\right )}{729}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 32, normalized size = 0.73 \begin {gather*} -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 32, normalized size = 0.73 \begin {gather*} -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 41, normalized size = 0.93 \begin {gather*} - \frac {40 x^{5}}{3} + \frac {145 x^{4}}{9} + \frac {82 x^{3}}{81} - \frac {1433 x^{2}}{162} + \frac {922 x}{243} + \frac {343 \log {\left (3 x + 2 \right )}}{729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 33, normalized size = 0.75 \begin {gather*} -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 30, normalized size = 0.68 \begin {gather*} \frac {922\,x}{243}+\frac {343\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1433\,x^2}{162}+\frac {82\,x^3}{81}+\frac {145\,x^4}{9}-\frac {40\,x^5}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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