Optimal. Leaf size=39 \[ \frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3) \]
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Rubi [A] time = 0.0181024, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac{147}{2+3 x}+\frac{121}{5 (3+5 x)^3}-\frac{407}{5 (3+5 x)^2}+\frac{245}{3+5 x}\right ) \, dx\\ &=-\frac{121}{50 (3+5 x)^2}+\frac{407}{25 (3+5 x)}-49 \log (2+3 x)+49 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0178352, size = 48, normalized size = 1.23 \[ \frac{4070 x-2450 (5 x+3)^2 \log (3 x+2)+2450 (5 x+3)^2 \log (-3 (5 x+3))+2321}{50 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.9 \begin{align*} -{\frac{121}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{407}{75+125\,x}}-49\,\ln \left ( 2+3\,x \right ) +49\,\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 = 1.11537, size = 49, normalized size = 1.26 \begin{align*} \frac{11 \,{\left (370 \, x + 211\right )}}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + 49 \, \log \left (5 \, x + 3\right ) - 49 \, \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 = 1.34134, size = 165, normalized size = 4.23 \begin{align*} \frac{2450 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2450 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 4070 \, x + 2321}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.135583, size = 31, normalized size = 0.79 \begin{align*} \frac{4070 x + 2321}{1250 x^{2} + 1500 x + 450} + 49 \log{\left (x + \frac{3}{5} \right )} - 49 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.71257, size = 45, normalized size = 1.15 \begin{align*} \frac{11 \,{\left (370 \, x + 211\right )}}{50 \,{\left (5 \, x + 3\right )}^{2}} + 49 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 49 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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