Optimal. Leaf size=43 \[ -\frac {407}{196 (1-2 x)}+\frac {121}{56 (1-2 x)^2}-\frac {1}{343} \log (1-2 x)+\frac {1}{343} \log (3 x+2) \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} -\frac {407}{196 (1-2 x)}+\frac {121}{56 (1-2 x)^2}-\frac {1}{343} \log (1-2 x)+\frac {1}{343} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac {121}{14 (-1+2 x)^3}-\frac {407}{98 (-1+2 x)^2}-\frac {2}{343 (-1+2 x)}+\frac {3}{343 (2+3 x)}\right ) \, dx\\ &=\frac {121}{56 (1-2 x)^2}-\frac {407}{196 (1-2 x)}-\frac {1}{343} \log (1-2 x)+\frac {1}{343} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 35, normalized size = 0.81 \begin {gather*} \frac {\frac {77 (148 x+3)}{(1-2 x)^2}-8 \log (3-6 x)+8 \log (3 x+2)}{2744} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(3+5 x)^2}{(1-2 x)^3 (2+3 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.55, size = 55, normalized size = 1.28 \begin {gather*} \frac {8 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 8 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 11396 \, x + 231}{2744 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 33, normalized size = 0.77 \begin {gather*} \frac {11 \, {\left (148 \, x + 3\right )}}{392 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1}{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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maple [A] time = 0.01, size = 36, normalized size = 0.84 \begin {gather*} -\frac {\ln \left (2 x -1\right )}{343}+\frac {\ln \left (3 x +2\right )}{343}+\frac {121}{56 \left (2 x -1\right )^{2}}+\frac {407}{196 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 36, normalized size = 0.84 \begin {gather*} \frac {11 \, {\left (148 \, x + 3\right )}}{392 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{343} \, \log \left (3 \, x + 2\right ) - \frac {1}{343} \, \log \left (2 \, x - 1\right ) \end {gather*}
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 \begin {gather*} \frac {2\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{343}+\frac {\frac {407\,x}{392}+\frac {33}{1568}}{x^2-x+\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 32, normalized size = 0.74 \begin {gather*} - \frac {- 1628 x - 33}{1568 x^{2} - 1568 x + 392} - \frac {\log {\left (x - \frac {1}{2} \right )}}{343} + \frac {\log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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