Optimal. Leaf size=21 \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]
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Rubi [A] time = 0.0084839, antiderivative size = 21, 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 = {72} \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x) (3+5 x)} \, dx &=\int \left (-\frac{7}{2+3 x}+\frac{11}{3+5 x}\right ) \, dx\\ &=-\frac{7}{3} \log (2+3 x)+\frac{11}{5} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0046402, size = 21, normalized size = 1. \[ \frac{11}{5} \log (5 x+3)-\frac{7}{3} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*} -{\frac{7\,\ln \left ( 2+3\,x \right ) }{3}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28072, size = 23, normalized size = 1.1 \begin{align*} \frac{11}{5} \, \log \left (5 \, x + 3\right ) - \frac{7}{3} \, \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 = 1.52817, size = 51, normalized size = 2.43 \begin{align*} \frac{11}{5} \, \log \left (5 \, x + 3\right ) - \frac{7}{3} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.102219, size = 19, normalized size = 0.9 \begin{align*} \frac{11 \log{\left (x + \frac{3}{5} \right )}}{5} - \frac{7 \log{\left (x + \frac{2}{3} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.52308, size = 26, normalized size = 1.24 \begin{align*} \frac{11}{5} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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