Optimal. Leaf size=26 \[ -\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {72} \[ -\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {9}{10}-\frac {49}{22 (-1+2 x)}+\frac {1}{55 (3+5 x)}\right ) \, dx\\ &=-\frac {9 x}{10}-\frac {49}{44} \log (1-2 x)+\frac {1}{275} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 31, normalized size = 1.19 \[ -\frac {9 x}{10}-\frac {49}{44} \log (3-6 x)+\frac {1}{275} \log (-3 (5 x+3))-\frac {3}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 20, normalized size = 0.77 \[ -\frac {9}{10} \, x + \frac {1}{275} \, \log \left (5 \, x + 3\right ) - \frac {49}{44} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 22, normalized size = 0.85 \[ -\frac {9}{10} \, x + \frac {1}{275} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {49}{44} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 21, normalized size = 0.81 \[ -\frac {9 x}{10}-\frac {49 \ln \left (2 x -1\right )}{44}+\frac {\ln \left (5 x +3\right )}{275} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 20, normalized size = 0.77 \[ -\frac {9}{10} \, x + \frac {1}{275} \, \log \left (5 \, x + 3\right ) - \frac {49}{44} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 16, normalized size = 0.62 \[ \frac {\ln \left (x+\frac {3}{5}\right )}{275}-\frac {49\,\ln \left (x-\frac {1}{2}\right )}{44}-\frac {9\,x}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.85 \[ - \frac {9 x}{10} - \frac {49 \log {\left (x - \frac {1}{2} \right )}}{44} + \frac {\log {\left (x + \frac {3}{5} \right )}}{275} \]
Verification of antiderivative is not currently implemented for this CAS.
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