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 = {45}
\begin {gather*} \frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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 \begin {gather*} \frac {11}{4 (1-2 x)}+\frac {5}{4} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 19, normalized size = 0.86
method | result | size |
risch | \(-\frac {11}{8 \left (-\frac {1}{2}+x \right )}+\frac {5 \ln \left (-1+2 x \right )}{4}\) | \(17\) |
default | \(-\frac {11}{4 \left (-1+2 x \right )}+\frac {5 \ln \left (-1+2 x \right )}{4}\) | \(19\) |
norman | \(-\frac {11 x}{2 \left (-1+2 x \right )}+\frac {5 \ln \left (-1+2 x \right )}{4}\) | \(20\) |
meijerg | \(\frac {11 x}{2 \left (1-2 x \right )}+\frac {5 \ln \left (1-2 x \right )}{4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 18, normalized size = 0.82 \begin {gather*} -\frac {11}{4 \, {\left (2 \, x - 1\right )}} + \frac {5}{4} \, \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 = 0.89, size = 24, normalized size = 1.09 \begin {gather*} \frac {5 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{4 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.68 \begin {gather*} \frac {5 \log {\left (2 x - 1 \right )}}{4} - \frac {11}{8 x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.27, size = 28, normalized size = 1.27 \begin {gather*} -\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 ) \end {gather*}
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 \begin {gather*} \frac {5\,\ln \left (x-\frac {1}{2}\right )}{4}-\frac {11}{8\,\left (x-\frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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