Optimal. Leaf size=28 \[ \frac{7}{3 (3 x+2)}-11 \log (3 x+2)+11 \log (5 x+3) \]
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Rubi [A] time = 0.0135171, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{7}{3 (3 x+2)}-11 \log (3 x+2)+11 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac{7}{(2+3 x)^2}-\frac{33}{2+3 x}+\frac{55}{3+5 x}\right ) \, dx\\ &=\frac{7}{3 (2+3 x)}-11 \log (2+3 x)+11 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0133397, size = 38, normalized size = 1.36 \[ \frac{-33 (3 x+2) \log (3 x+2)+33 (3 x+2) \log (-3 (5 x+3))+7}{9 x+6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 1. \begin{align*}{\frac{7}{6+9\,x}}-11\,\ln \left ( 2+3\,x \right ) +11\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.40898, size = 35, normalized size = 1.25 \begin{align*} \frac{7}{3 \,{\left (3 \, x + 2\right )}} + 11 \, \log \left (5 \, x + 3\right ) - 11 \, \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 = 1.78787, size = 101, normalized size = 3.61 \begin{align*} \frac{33 \,{\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 33 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 7}{3 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.109632, size = 22, normalized size = 0.79 \begin{align*} 11 \log{\left (x + \frac{3}{5} \right )} - 11 \log{\left (x + \frac{2}{3} \right )} + \frac{7}{9 x + 6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.75867, size = 34, normalized size = 1.21 \begin{align*} \frac{7}{3 \,{\left (3 \, x + 2\right )}} + 11 \, \log \left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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