Optimal. Leaf size=16 \[ -\frac {5 x}{2}-\frac {11}{4} \log (1-2 x) \]
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Rubi [A]
time = 0.00, antiderivative size = 16, 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 {5 x}{2}-\frac {11}{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} \, dx &=\int \left (-\frac {5}{2}-\frac {11}{2 (-1+2 x)}\right ) \, dx\\ &=-\frac {5 x}{2}-\frac {11}{4} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.06 \begin {gather*} \frac {1}{4} (5-10 x-11 \log (1-2 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 13, normalized size = 0.81
method | result | size |
default | \(-\frac {5 x}{2}-\frac {11 \ln \left (-1+2 x \right )}{4}\) | \(13\) |
norman | \(-\frac {5 x}{2}-\frac {11 \ln \left (-1+2 x \right )}{4}\) | \(13\) |
meijerg | \(-\frac {5 x}{2}-\frac {11 \ln \left (1-2 x \right )}{4}\) | \(13\) |
risch | \(-\frac {5 x}{2}-\frac {11 \ln \left (-1+2 x \right )}{4}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 12, normalized size = 0.75 \begin {gather*} -\frac {5}{2} \, x - \frac {11}{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 = 0.47, size = 12, normalized size = 0.75 \begin {gather*} -\frac {5}{2} \, x - \frac {11}{4} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 15, normalized size = 0.94 \begin {gather*} - \frac {5 x}{2} - \frac {11 \log {\left (2 x - 1 \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 13, normalized size = 0.81 \begin {gather*} -\frac {5}{2} \, x - \frac {11}{4} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 10, normalized size = 0.62 \begin {gather*} -\frac {5\,x}{2}-\frac {11\,\ln \left (x-\frac {1}{2}\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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