Optimal. Leaf size=21 \[ \frac {1}{55} \log (5 x+3)-\frac {7}{22} \log (1-2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 21, 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 = {72} \begin {gather*} \frac {1}{55} \log (5 x+3)-\frac {7}{22} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {7}{11 (-1+2 x)}+\frac {1}{11 (3+5 x)}\right ) \, dx\\ &=-\frac {7}{22} \log (1-2 x)+\frac {1}{55} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {1}{55} \log (5 x+3)-\frac {7}{22} \log (1-2 x) \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 {2+3 x}{(1-2 x) (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.45, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{55} \, \log \left (5 \, x + 3\right ) - \frac {7}{22} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 19, normalized size = 0.90 \begin {gather*} \frac {1}{55} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {7}{22} \, \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 = 18, normalized size = 0.86 \begin {gather*} -\frac {7 \ln \left (2 x -1\right )}{22}+\frac {\ln \left (5 x +3\right )}{55} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{55} \, \log \left (5 \, x + 3\right ) - \frac {7}{22} \, \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 = 1.15, size = 13, normalized size = 0.62 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{55}-\frac {7\,\ln \left (x-\frac {1}{2}\right )}{22} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.81 \begin {gather*} - \frac {7 \log {\left (x - \frac {1}{2} \right )}}{22} + \frac {\log {\left (x + \frac {3}{5} \right )}}{55} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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