Optimal. Leaf size=41 \[ -\frac {286 x}{27}+\frac {134 x^2}{27}-\frac {40 x^3}{27}+\frac {343}{243 (2+3 x)}+\frac {2009}{243} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {40 x^3}{27}+\frac {134 x^2}{27}-\frac {286 x}{27}+\frac {343}{243 (3 x+2)}+\frac {2009}{243} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac {286}{27}+\frac {268 x}{27}-\frac {40 x^2}{9}-\frac {343}{81 (2+3 x)^2}+\frac {2009}{81 (2+3 x)}\right ) \, dx\\ &=-\frac {286 x}{27}+\frac {134 x^2}{27}-\frac {40 x^3}{27}+\frac {343}{243 (2+3 x)}+\frac {2009}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 44, normalized size = 1.07 \begin {gather*} \frac {4808-4113 x-10620 x^2+5796 x^3-2160 x^4+4018 (2+3 x) \log (4+6 x)}{486 (2+3 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 32, normalized size = 0.78
method | result | size |
risch | \(-\frac {40 x^{3}}{27}+\frac {134 x^{2}}{27}-\frac {286 x}{27}+\frac {343}{729 \left (\frac {2}{3}+x \right )}+\frac {2009 \ln \left (2+3 x \right )}{243}\) | \(30\) |
default | \(-\frac {286 x}{27}+\frac {134 x^{2}}{27}-\frac {40 x^{3}}{27}+\frac {343}{243 \left (2+3 x \right )}+\frac {2009 \ln \left (2+3 x \right )}{243}\) | \(32\) |
norman | \(\frac {-\frac {3775}{162} x -\frac {590}{27} x^{2}+\frac {322}{27} x^{3}-\frac {40}{9} x^{4}}{2+3 x}+\frac {2009 \ln \left (2+3 x \right )}{243}\) | \(37\) |
meijerg | \(\frac {35 x}{12 \left (1+\frac {3 x}{2}\right )}+\frac {2009 \ln \left (1+\frac {3 x}{2}\right )}{243}+\frac {2 x \left (\frac {9 x}{2}+6\right )}{9 \left (1+\frac {3 x}{2}\right )}-\frac {2 x \left (-\frac {9}{2} x^{2}+9 x +12\right )}{3 \left (1+\frac {3 x}{2}\right )}-\frac {32 x \left (\frac {135}{8} x^{3}-\frac {45}{2} x^{2}+45 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 31, normalized size = 0.76 \begin {gather*} -\frac {40}{27} \, x^{3} + \frac {134}{27} \, x^{2} - \frac {286}{27} \, x + \frac {343}{243 \, {\left (3 \, x + 2\right )}} + \frac {2009}{243} \, \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 = 0.45, size = 42, normalized size = 1.02 \begin {gather*} -\frac {1080 \, x^{4} - 2898 \, x^{3} + 5310 \, x^{2} - 2009 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 5148 \, x - 343}{243 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 34, normalized size = 0.83 \begin {gather*} - \frac {40 x^{3}}{27} + \frac {134 x^{2}}{27} - \frac {286 x}{27} + \frac {2009 \log {\left (3 x + 2 \right )}}{243} + \frac {343}{729 x + 486} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.46, size = 57, normalized size = 1.39 \begin {gather*} \frac {2}{729} \, {\left (3 \, x + 2\right )}^{3} {\left (\frac {321}{3 \, x + 2} - \frac {2331}{{\left (3 \, x + 2\right )}^{2}} - 20\right )} + \frac {343}{243 \, {\left (3 \, x + 2\right )}} - \frac {2009}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\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 = 29, normalized size = 0.71 \begin {gather*} \frac {2009\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {286\,x}{27}+\frac {343}{729\,\left (x+\frac {2}{3}\right )}+\frac {134\,x^2}{27}-\frac {40\,x^3}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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