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 = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.70, size = 37, normalized size = 1.12 \[ -\frac {20 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 222 \, x + 141}{54 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 24, normalized size = 0.73 \[ -\frac {74 \, x + 47}{18 \, {\left (3 \, x + 2\right )}^{2}} - \frac {10}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.85 \[ -\frac {10 \ln \left (3 x +2\right )}{27}+\frac {7}{54 \left (3 x +2\right )^{2}}-\frac {37}{27 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 28, normalized size = 0.85 \[ -\frac {74 \, x + 47}{18 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {10}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 24, normalized size = 0.73 \[ -\frac {10\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {\frac {37\,x}{81}+\frac {47}{162}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 26, normalized size = 0.79 \[ - \frac {74 x + 47}{162 x^{2} + 216 x + 72} - \frac {10 \log {\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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