Optimal. Leaf size=43 \[ \frac {1}{42 (2+3 x)^2}-\frac {11}{49 (2+3 x)}-\frac {22}{343} \log (1-2 x)+\frac {22}{343} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {11}{49 (3 x+2)}+\frac {1}{42 (3 x+2)^2}-\frac {22}{343} \log (1-2 x)+\frac {22}{343} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x) (2+3 x)^3} \, dx &=\int \left (-\frac {44}{343 (-1+2 x)}-\frac {1}{7 (2+3 x)^3}+\frac {33}{49 (2+3 x)^2}+\frac {66}{343 (2+3 x)}\right ) \, dx\\ &=\frac {1}{42 (2+3 x)^2}-\frac {11}{49 (2+3 x)}-\frac {22}{343} \log (1-2 x)+\frac {22}{343} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {-\frac {7 (125+198 x)}{(2+3 x)^2}-132 \log (3-6 x)+132 \log (2+3 x)}{2058} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {-\frac {33 x}{49}-\frac {125}{294}}{\left (2+3 x \right )^{2}}-\frac {22 \ln \left (-1+2 x \right )}{343}+\frac {22 \ln \left (2+3 x \right )}{343}\) | \(32\) |
norman | \(\frac {\frac {59}{98} x +\frac {375}{392} x^{2}}{\left (2+3 x \right )^{2}}-\frac {22 \ln \left (-1+2 x \right )}{343}+\frac {22 \ln \left (2+3 x \right )}{343}\) | \(35\) |
default | \(-\frac {22 \ln \left (-1+2 x \right )}{343}+\frac {1}{42 \left (2+3 x \right )^{2}}-\frac {11}{49 \left (2+3 x \right )}+\frac {22 \ln \left (2+3 x \right )}{343}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 36, normalized size = 0.84 \begin {gather*} -\frac {198 \, x + 125}{294 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {22}{343} \, \log \left (3 \, x + 2\right ) - \frac {22}{343} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.80, size = 55, normalized size = 1.28 \begin {gather*} \frac {132 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 132 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 1386 \, x - 875}{2058 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 34, normalized size = 0.79 \begin {gather*} - \frac {198 x + 125}{2646 x^{2} + 3528 x + 1176} - \frac {22 \log {\left (x - \frac {1}{2} \right )}}{343} + \frac {22 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.63, size = 33, normalized size = 0.77 \begin {gather*} -\frac {198 \, x + 125}{294 \, {\left (3 \, x + 2\right )}^{2}} + \frac {22}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {22}{343} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 26, normalized size = 0.60 \begin {gather*} \frac {44\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{343}-\frac {\frac {11\,x}{147}+\frac {125}{2646}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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