Optimal. Leaf size=32 \[ -\frac {1}{55 (5 x+3)}-\frac {7}{121} \log (1-2 x)+\frac {7}{121} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 32, 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 = {77} \[ -\frac {1}{55 (5 x+3)}-\frac {7}{121} \log (1-2 x)+\frac {7}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {14}{121 (-1+2 x)}+\frac {1}{11 (3+5 x)^2}+\frac {35}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {1}{55 (3+5 x)}-\frac {7}{121} \log (1-2 x)+\frac {7}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 30, normalized size = 0.94 \[ \frac {1}{605} \left (-\frac {11}{5 x+3}-35 \log (5-10 x)+35 \log (5 x+3)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 37, normalized size = 1.16 \[ \frac {35 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 35 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 11}{605 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 25, normalized size = 0.78 \[ -\frac {1}{55 \, {\left (5 \, x + 3\right )}} - \frac {7}{121} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ -\frac {7 \ln \left (2 x -1\right )}{121}+\frac {7 \ln \left (5 x +3\right )}{121}-\frac {1}{55 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 26, normalized size = 0.81 \[ -\frac {1}{55 \, {\left (5 \, x + 3\right )}} + \frac {7}{121} \, \log \left (5 \, x + 3\right ) - \frac {7}{121} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 18, normalized size = 0.56 \[ \frac {14\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{121}-\frac {1}{275\,\left (x+\frac {3}{5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 26, normalized size = 0.81 \[ - \frac {7 \log {\left (x - \frac {1}{2} \right )}}{121} + \frac {7 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {1}{275 x + 165} \]
Verification of antiderivative is not currently implemented for this CAS.
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