Optimal. Leaf size=27 \[ -\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0116215, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{6 x}{25}-\frac{11}{125 (5 x+3)}+\frac{31}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)}{(3+5 x)^2} \, dx &=\int \left (-\frac{6}{25}+\frac{11}{25 (3+5 x)^2}+\frac{31}{25 (3+5 x)}\right ) \, dx\\ &=-\frac{6 x}{25}-\frac{11}{125 (3+5 x)}+\frac{31}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0091958, size = 26, normalized size = 0.96 \[ \frac{1}{125} \left (-30 x-\frac{11}{5 x+3}+31 \log (5 x+3)-18\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 22, normalized size = 0.8 \begin{align*} -{\frac{6\,x}{25}}-{\frac{11}{375+625\,x}}+{\frac{31\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.18226, size = 28, normalized size = 1.04 \begin{align*} -\frac{6}{25} \, x - \frac{11}{125 \,{\left (5 \, x + 3\right )}} + \frac{31}{125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47497, size = 92, normalized size = 3.41 \begin{align*} -\frac{150 \, x^{2} - 31 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 90 \, x + 11}{125 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091536, size = 20, normalized size = 0.74 \begin{align*} - \frac{6 x}{25} + \frac{31 \log{\left (5 x + 3 \right )}}{125} - \frac{11}{625 x + 375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.95158, size = 43, normalized size = 1.59 \begin{align*} -\frac{6}{25} \, x - \frac{11}{125 \,{\left (5 \, x + 3\right )}} - \frac{31}{125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{18}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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