Optimal. Leaf size=30 \[ \frac {118 x}{27}-\frac {5 x^2}{18}-\frac {50 x^3}{9}+\frac {7}{81} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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 {50 x^3}{9}-\frac {5 x^2}{18}+\frac {118 x}{27}+\frac {7}{81} \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+5 x)^2}{2+3 x} \, dx &=\int \left (\frac {118}{27}-\frac {5 x}{9}-\frac {50 x^2}{3}+\frac {7}{27 (2+3 x)}\right ) \, dx\\ &=\frac {118 x}{27}-\frac {5 x^2}{18}-\frac {50 x^3}{9}+\frac {7}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {1}{486} \left (676+2124 x-135 x^2-2700 x^3+42 \log (2+3 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 23, normalized size = 0.77
method | result | size |
default | \(\frac {118 x}{27}-\frac {5 x^{2}}{18}-\frac {50 x^{3}}{9}+\frac {7 \ln \left (2+3 x \right )}{81}\) | \(23\) |
norman | \(\frac {118 x}{27}-\frac {5 x^{2}}{18}-\frac {50 x^{3}}{9}+\frac {7 \ln \left (2+3 x \right )}{81}\) | \(23\) |
risch | \(\frac {118 x}{27}-\frac {5 x^{2}}{18}-\frac {50 x^{3}}{9}+\frac {7 \ln \left (2+3 x \right )}{81}\) | \(23\) |
meijerg | \(\frac {7 \ln \left (1+\frac {3 x}{2}\right )}{81}+4 x +\frac {35 x \left (-\frac {9 x}{2}+6\right )}{27}-\frac {50 x \left (9 x^{2}-9 x +12\right )}{81}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 22, normalized size = 0.73 \begin {gather*} -\frac {50}{9} \, x^{3} - \frac {5}{18} \, x^{2} + \frac {118}{27} \, x + \frac {7}{81} \, \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 = 0.70, size = 22, normalized size = 0.73 \begin {gather*} -\frac {50}{9} \, x^{3} - \frac {5}{18} \, x^{2} + \frac {118}{27} \, x + \frac {7}{81} \, \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 = 0.03, size = 27, normalized size = 0.90 \begin {gather*} - \frac {50 x^{3}}{9} - \frac {5 x^{2}}{18} + \frac {118 x}{27} + \frac {7 \log {\left (3 x + 2 \right )}}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.18, size = 23, normalized size = 0.77 \begin {gather*} -\frac {50}{9} \, x^{3} - \frac {5}{18} \, x^{2} + \frac {118}{27} \, x + \frac {7}{81} \, \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 = 20, normalized size = 0.67 \begin {gather*} \frac {118\,x}{27}+\frac {7\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {5\,x^2}{18}-\frac {50\,x^3}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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