Optimal. Leaf size=22 \[ \frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \[ \frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^2} \, dx &=\int \left (\frac {11}{2 (-1+2 x)^2}+\frac {5}{2 (-1+2 x)}\right ) \, dx\\ &=\frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ \frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 24, normalized size = 1.09 \[ \frac {5 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{4 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 28, normalized size = 1.27 \[ -\frac {11}{4 \, {\left (2 \, x - 1\right )}} - \frac {5}{4} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 0.86 \[ \frac {5 \ln \left (2 x -1\right )}{4}-\frac {11}{4 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 18, normalized size = 0.82 \[ -\frac {11}{4 \, {\left (2 \, x - 1\right )}} + \frac {5}{4} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 16, normalized size = 0.73 \[ \frac {5\,\ln \left (x-\frac {1}{2}\right )}{4}-\frac {11}{8\,\left (x-\frac {1}{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.68 \[ \frac {5 \log {\left (2 x - 1 \right )}}{4} - \frac {11}{8 x - 4} \]
Verification of antiderivative is not currently implemented for this CAS.
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