Optimal. Leaf size=54 \[ -\frac{121}{343 (3 x+2)}+\frac{34}{441 (3 x+2)^2}-\frac{1}{189 (3 x+2)^3}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (3 x+2)}{2401} \]
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Rubi [A] time = 0.021555, 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} \[ -\frac{121}{343 (3 x+2)}+\frac{34}{441 (3 x+2)^2}-\frac{1}{189 (3 x+2)^3}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^4} \, dx &=\int \left (-\frac{484}{2401 (-1+2 x)}+\frac{1}{21 (2+3 x)^4}-\frac{68}{147 (2+3 x)^3}+\frac{363}{343 (2+3 x)^2}+\frac{726}{2401 (2+3 x)}\right ) \, dx\\ &=-\frac{1}{189 (2+3 x)^3}+\frac{34}{441 (2+3 x)^2}-\frac{121}{343 (2+3 x)}-\frac{242 \log (1-2 x)}{2401}+\frac{242 \log (2+3 x)}{2401}\\ \end{align*}
Mathematica [A] time = 0.022006, size = 40, normalized size = 0.74 \[ \frac{-\frac{7 \left (29403 x^2+37062 x+11689\right )}{(3 x+2)^3}-6534 \log (1-2 x)+6534 \log (6 x+4)}{64827} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 45, normalized size = 0.8 \begin{align*} -{\frac{242\,\ln \left ( 2\,x-1 \right ) }{2401}}-{\frac{1}{189\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{34}{441\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{121}{686+1029\,x}}+{\frac{242\,\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 = 1.06188, size = 62, normalized size = 1.15 \begin{align*} -\frac{29403 \, x^{2} + 37062 \, x + 11689}{9261 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{242}{2401} \, \log \left (3 \, x + 2\right ) - \frac{242}{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 = 1.32705, size = 228, normalized size = 4.22 \begin{align*} -\frac{205821 \, x^{2} - 6534 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 6534 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 259434 \, x + 81823}{64827 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.16002, size = 44, normalized size = 0.81 \begin{align*} - \frac{29403 x^{2} + 37062 x + 11689}{250047 x^{3} + 500094 x^{2} + 333396 x + 74088} - \frac{242 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{242 \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 = 1.22196, size = 51, normalized size = 0.94 \begin{align*} -\frac{29403 \, x^{2} + 37062 \, x + 11689}{9261 \,{\left (3 \, x + 2\right )}^{3}} + \frac{242}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{242}{2401} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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