Optimal. Leaf size=54 \[ \frac {22}{343 (1-2 x)}-\frac {31}{343 (3 x+2)}+\frac {1}{98 (3 x+2)^2}-\frac {128 \log (1-2 x)}{2401}+\frac {128 \log (3 x+2)}{2401} \]
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Rubi [A] time = 0.02, antiderivative size = 54, 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 = {77} \[ \frac {22}{343 (1-2 x)}-\frac {31}{343 (3 x+2)}+\frac {1}{98 (3 x+2)^2}-\frac {128 \log (1-2 x)}{2401}+\frac {128 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^2 (2+3 x)^3} \, dx &=\int \left (\frac {44}{343 (-1+2 x)^2}-\frac {256}{2401 (-1+2 x)}-\frac {3}{49 (2+3 x)^3}+\frac {93}{343 (2+3 x)^2}+\frac {384}{2401 (2+3 x)}\right ) \, dx\\ &=\frac {22}{343 (1-2 x)}+\frac {1}{98 (2+3 x)^2}-\frac {31}{343 (2+3 x)}-\frac {128 \log (1-2 x)}{2401}+\frac {128 \log (2+3 x)}{2401}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 47, normalized size = 0.87 \[ \frac {-\frac {7 \left (768 x^2+576 x+59\right )}{(2 x-1) (3 x+2)^2}-256 \log (1-2 x)+256 \log (6 x+4)}{4802} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 75, normalized size = 1.39 \[ -\frac {5376 \, x^{2} - 256 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) + 256 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 4032 \, x + 413}{4802 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 51, normalized size = 0.94 \[ -\frac {22}{343 \, {\left (2 \, x - 1\right )}} + \frac {6 \, {\left (\frac {203}{2 \, x - 1} + 90\right )}}{2401 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{2}} + \frac {128}{2401} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.83 \[ -\frac {128 \ln \left (2 x -1\right )}{2401}+\frac {128 \ln \left (3 x +2\right )}{2401}+\frac {1}{98 \left (3 x +2\right )^{2}}-\frac {31}{343 \left (3 x +2\right )}-\frac {22}{343 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 46, normalized size = 0.85 \[ -\frac {768 \, x^{2} + 576 \, x + 59}{686 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac {128}{2401} \, \log \left (3 \, x + 2\right ) - \frac {128}{2401} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 37, normalized size = 0.69 \[ \frac {256\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{2401}+\frac {\frac {64\,x^2}{1029}+\frac {16\,x}{343}+\frac {59}{12348}}{-x^3-\frac {5\,x^2}{6}+\frac {2\,x}{9}+\frac {2}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 46, normalized size = 0.85 \[ \frac {- 768 x^{2} - 576 x - 59}{12348 x^{3} + 10290 x^{2} - 2744 x - 2744} - \frac {128 \log {\left (x - \frac {1}{2} \right )}}{2401} + \frac {128 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
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