Optimal. Leaf size=33 \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0125276, antiderivative size = 33, 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} \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
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)^3} \, dx &=\int \left (\frac{11}{25 (3+5 x)^3}+\frac{31}{25 (3+5 x)^2}-\frac{6}{25 (3+5 x)}\right ) \, dx\\ &=-\frac{11}{250 (3+5 x)^2}-\frac{31}{125 (3+5 x)}-\frac{6}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0079225, size = 33, normalized size = 1. \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 28, normalized size = 0.9 \begin{align*} -{\frac{11}{250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{31}{375+625\,x}}-{\frac{6\,\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 = 2.07221, size = 38, normalized size = 1.15 \begin{align*} -\frac{310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{6}{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 = 1.49881, size = 108, normalized size = 3.27 \begin{align*} -\frac{12 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.106527, size = 26, normalized size = 0.79 \begin{align*} - \frac{310 x + 197}{6250 x^{2} + 7500 x + 2250} - \frac{6 \log{\left (5 x + 3 \right )}}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.60364, size = 32, normalized size = 0.97 \begin{align*} -\frac{310 \, x + 197}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{6}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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