Optimal. Leaf size=33 \[ -\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2) \]
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Rubi [A] time = 0.0137995, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{37}{27 (3 x+2)}+\frac{7}{54 (3 x+2)^2}-\frac{10}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)}{(2+3 x)^3} \, dx &=\int \left (-\frac{7}{9 (2+3 x)^3}+\frac{37}{9 (2+3 x)^2}-\frac{10}{9 (2+3 x)}\right ) \, dx\\ &=\frac{7}{54 (2+3 x)^2}-\frac{37}{27 (2+3 x)}-\frac{10}{27} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0094619, size = 27, normalized size = 0.82 \[ \frac{1}{54} \left (-\frac{3 (74 x+47)}{(3 x+2)^2}-20 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \begin{align*}{\frac{7}{54\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{37}{54+81\,x}}-{\frac{10\,\ln \left ( 2+3\,x \right ) }{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15818, size = 38, normalized size = 1.15 \begin{align*} -\frac{74 \, x + 47}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{10}{27} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55005, size = 104, normalized size = 3.15 \begin{align*} -\frac{20 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 222 \, x + 141}{54 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.108, size = 26, normalized size = 0.79 \begin{align*} - \frac{74 x + 47}{162 x^{2} + 216 x + 72} - \frac{10 \log{\left (3 x + 2 \right )}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.74514, size = 32, normalized size = 0.97 \begin{align*} -\frac{74 \, x + 47}{18 \,{\left (3 \, x + 2\right )}^{2}} - \frac{10}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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