Optimal. Leaf size=54 \[ \frac{1331}{686 (1-2 x)}-\frac{101}{3087 (3 x+2)}+\frac{1}{882 (3 x+2)^2}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (3 x+2)}{2401} \]
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Rubi [A] time = 0.0233992, antiderivative size = 54, 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} \[ \frac{1331}{686 (1-2 x)}-\frac{101}{3087 (3 x+2)}+\frac{1}{882 (3 x+2)^2}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^3} \, dx &=\int \left (\frac{1331}{343 (-1+2 x)^2}+\frac{726}{2401 (-1+2 x)}-\frac{1}{147 (2+3 x)^3}+\frac{101}{1029 (2+3 x)^2}-\frac{1089}{2401 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{686 (1-2 x)}+\frac{1}{882 (2+3 x)^2}-\frac{101}{3087 (2+3 x)}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (2+3 x)}{2401}\\ \end{align*}
Mathematica [A] time = 0.0294321, size = 48, normalized size = 0.89 \[ \frac{\frac{83853}{1-2 x}-\frac{1414}{3 x+2}+\frac{49}{(3 x+2)^2}+6534 \log (1-2 x)-6534 \log (6 x+4)}{43218} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 45, normalized size = 0.8 \begin{align*} -{\frac{1331}{1372\,x-686}}+{\frac{363\,\ln \left ( 2\,x-1 \right ) }{2401}}+{\frac{1}{882\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{101}{6174+9261\,x}}-{\frac{363\,\ln \left ( 2+3\,x \right ) }{2401}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10034, size = 62, normalized size = 1.15 \begin{align*} -\frac{109023 \, x^{2} + 143936 \, x + 47519}{6174 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} - \frac{363}{2401} \, \log \left (3 \, x + 2\right ) + \frac{363}{2401} \, \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 = 1.46515, size = 227, normalized size = 4.2 \begin{align*} -\frac{763161 \, x^{2} + 6534 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 6534 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 1007552 \, x + 332633}{43218 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.153694, size = 44, normalized size = 0.81 \begin{align*} - \frac{109023 x^{2} + 143936 x + 47519}{111132 x^{3} + 92610 x^{2} - 24696 x - 24696} + \frac{363 \log{\left (x - \frac{1}{2} \right )}}{2401} - \frac{363 \log{\left (x + \frac{2}{3} \right )}}{2401} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.12242, size = 69, normalized size = 1.28 \begin{align*} -\frac{1331}{686 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{231}{2 \, x - 1} + 100\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} - \frac{363}{2401} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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