Optimal. Leaf size=27 \[ -\frac {10 x}{9}+\frac {7}{27 (3 x+2)}+\frac {37}{27} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 27, 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} \begin {gather*} -\frac {10 x}{9}+\frac {7}{27 (3 x+2)}+\frac {37}{27} \log (3 x+2) \end {gather*}
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)^2} \, dx &=\int \left (-\frac {10}{9}-\frac {7}{9 (2+3 x)^2}+\frac {37}{9 (2+3 x)}\right ) \, dx\\ &=-\frac {10 x}{9}+\frac {7}{27 (2+3 x)}+\frac {37}{27} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.96 \begin {gather*} \frac {1}{27} \left (-30 x+\frac {7}{3 x+2}+37 \log (3 x+2)-20\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x) (3+5 x)}{(2+3 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.47, size = 32, normalized size = 1.19 \begin {gather*} -\frac {90 \, x^{2} - 37 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 60 \, x - 7}{27 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 32, normalized size = 1.19 \begin {gather*} -\frac {10}{9} \, x + \frac {7}{27 \, {\left (3 \, x + 2\right )}} - \frac {37}{27} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) - \frac {20}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} -\frac {10 x}{9}+\frac {37 \ln \left (3 x +2\right )}{27}+\frac {7}{27 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 21, normalized size = 0.78 \begin {gather*} -\frac {10}{9} \, x + \frac {7}{27 \, {\left (3 \, x + 2\right )}} + \frac {37}{27} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 19, normalized size = 0.70 \begin {gather*} \frac {37\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {10\,x}{9}+\frac {7}{81\,\left (x+\frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 20, normalized size = 0.74 \begin {gather*} - \frac {10 x}{9} + \frac {37 \log {\left (3 x + 2 \right )}}{27} + \frac {7}{81 x + 54} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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