Optimal. Leaf size=28 \[ -\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3) \]
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Rubi [A] time = 0.0127324, 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} \[ -\frac{11}{5 (5 x+3)}+7 \log (3 x+2)-7 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x) (3+5 x)^2} \, dx &=\int \left (\frac{21}{2+3 x}+\frac{11}{(3+5 x)^2}-\frac{35}{3+5 x}\right ) \, dx\\ &=-\frac{11}{5 (3+5 x)}+7 \log (2+3 x)-7 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0138742, size = 30, normalized size = 1.07 \[ -\frac{11}{5 (5 x+3)}+7 \log (5 (3 x+2))-7 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 1. \begin{align*} -{\frac{11}{15+25\,x}}+7\,\ln \left ( 2+3\,x \right ) -7\,\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 = 1.02682, size = 35, normalized size = 1.25 \begin{align*} -\frac{11}{5 \,{\left (5 \, x + 3\right )}} - 7 \, \log \left (5 \, x + 3\right ) + 7 \, \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 = 1.52058, size = 104, normalized size = 3.71 \begin{align*} -\frac{35 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 35 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 11}{5 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.109081, size = 22, normalized size = 0.79 \begin{align*} - 7 \log{\left (x + \frac{3}{5} \right )} + 7 \log{\left (x + \frac{2}{3} \right )} - \frac{11}{25 x + 15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.77144, size = 34, normalized size = 1.21 \begin{align*} -\frac{11}{5 \,{\left (5 \, x + 3\right )}} + 7 \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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