Optimal. Leaf size=54 \[ -\frac{22}{343 (3 x+2)}-\frac{11}{98 (3 x+2)^2}+\frac{1}{63 (3 x+2)^3}-\frac{44 \log (1-2 x)}{2401}+\frac{44 \log (3 x+2)}{2401} \]
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Rubi [A] time = 0.0210959, antiderivative size = 54, 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} \[ -\frac{22}{343 (3 x+2)}-\frac{11}{98 (3 x+2)^2}+\frac{1}{63 (3 x+2)^3}-\frac{44 \log (1-2 x)}{2401}+\frac{44 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x) (2+3 x)^4} \, dx &=\int \left (-\frac{88}{2401 (-1+2 x)}-\frac{1}{7 (2+3 x)^4}+\frac{33}{49 (2+3 x)^3}+\frac{66}{343 (2+3 x)^2}+\frac{132}{2401 (2+3 x)}\right ) \, dx\\ &=\frac{1}{63 (2+3 x)^3}-\frac{11}{98 (2+3 x)^2}-\frac{22}{343 (2+3 x)}-\frac{44 \log (1-2 x)}{2401}+\frac{44 \log (2+3 x)}{2401}\\ \end{align*}
Mathematica [A] time = 0.02141, size = 40, normalized size = 0.74 \[ \frac{-\frac{7 \left (3564 x^2+6831 x+2872\right )}{(3 x+2)^3}-792 \log (3-6 x)+792 \log (3 x+2)}{43218} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 45, normalized size = 0.8 \begin{align*} -{\frac{44\,\ln \left ( 2\,x-1 \right ) }{2401}}+{\frac{1}{63\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{11}{98\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{22}{686+1029\,x}}+{\frac{44\,\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 = 1.06565, size = 62, normalized size = 1.15 \begin{align*} -\frac{3564 \, x^{2} + 6831 \, x + 2872}{6174 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{44}{2401} \, \log \left (3 \, x + 2\right ) - \frac{44}{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 = 1.32163, size = 223, normalized size = 4.13 \begin{align*} -\frac{24948 \, x^{2} - 792 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 792 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 47817 \, x + 20104}{43218 \,{\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 = 0.151297, size = 44, normalized size = 0.81 \begin{align*} - \frac{3564 x^{2} + 6831 x + 2872}{166698 x^{3} + 333396 x^{2} + 222264 x + 49392} - \frac{44 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{44 \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 = 1.94863, size = 51, normalized size = 0.94 \begin{align*} -\frac{3564 \, x^{2} + 6831 \, x + 2872}{6174 \,{\left (3 \, x + 2\right )}^{3}} + \frac{44}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{44}{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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