Optimal. Leaf size=32 \[ \frac{7}{22 (1-2 x)}-\frac{1}{121} \log (1-2 x)+\frac{1}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0137954, antiderivative size = 32, 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} \[ \frac{7}{22 (1-2 x)}-\frac{1}{121} \log (1-2 x)+\frac{1}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac{7}{11 (-1+2 x)^2}-\frac{2}{121 (-1+2 x)}+\frac{5}{121 (3+5 x)}\right ) \, dx\\ &=\frac{7}{22 (1-2 x)}-\frac{1}{121} \log (1-2 x)+\frac{1}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0126048, size = 37, normalized size = 1.16 \[ \frac{(2-4 x) \log (1-2 x)+(4 x-2) \log (10 x+6)-77}{242 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*} -{\frac{7}{44\,x-22}}-{\frac{\ln \left ( 2\,x-1 \right ) }{121}}+{\frac{\ln \left ( 3+5\,x \right ) }{121}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02438, size = 35, normalized size = 1.09 \begin{align*} -\frac{7}{22 \,{\left (2 \, x - 1\right )}} + \frac{1}{121} \, \log \left (5 \, x + 3\right ) - \frac{1}{121} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32093, size = 103, normalized size = 3.22 \begin{align*} \frac{2 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 2 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 77}{242 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.109386, size = 22, normalized size = 0.69 \begin{align*} - \frac{\log{\left (x - \frac{1}{2} \right )}}{121} + \frac{\log{\left (x + \frac{3}{5} \right )}}{121} - \frac{7}{44 x - 22} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.1449, size = 34, normalized size = 1.06 \begin{align*} -\frac{7}{22 \,{\left (2 \, x - 1\right )}} + \frac{1}{121} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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