Optimal. Leaf size=43 \[ -\frac {1}{49 (1-2 x)}+\frac {11}{28 (1-2 x)^2}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (3 x+2) \]
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Rubi [A] time = 0.02, 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 = {77} \[ -\frac {1}{49 (1-2 x)}+\frac {11}{28 (1-2 x)^2}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac {11}{7 (-1+2 x)^3}-\frac {2}{49 (-1+2 x)^2}+\frac {6}{343 (-1+2 x)}-\frac {9}{343 (2+3 x)}\right ) \, dx\\ &=\frac {11}{28 (1-2 x)^2}-\frac {1}{49 (1-2 x)}+\frac {3}{343} \log (1-2 x)-\frac {3}{343} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 35, normalized size = 0.81 \[ \frac {\frac {7 (8 x+73)}{(1-2 x)^2}+12 \log (1-2 x)-12 \log (6 x+4)}{1372} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 55, normalized size = 1.28 \[ -\frac {12 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 12 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 56 \, x - 511}{1372 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 33, normalized size = 0.77 \[ \frac {8 \, x + 73}{196 \, {\left (2 \, x - 1\right )}^{2}} - \frac {3}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {3}{343} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \[ \frac {3 \ln \left (2 x -1\right )}{343}-\frac {3 \ln \left (3 x +2\right )}{343}+\frac {11}{28 \left (2 x -1\right )^{2}}+\frac {1}{98 x -49} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 36, normalized size = 0.84 \[ \frac {8 \, x + 73}{196 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {3}{343} \, \log \left (3 \, x + 2\right ) + \frac {3}{343} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 25, normalized size = 0.58 \[ \frac {\frac {x}{98}+\frac {73}{784}}{x^2-x+\frac {1}{4}}-\frac {6\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 36, normalized size = 0.84 \[ - \frac {- 8 x - 73}{784 x^{2} - 784 x + 196} + \frac {3 \log {\left (x - \frac {1}{2} \right )}}{343} - \frac {3 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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