Optimal. Leaf size=41 \[ -\frac{18 x^3}{25}-\frac{81 x^2}{250}+\frac{522 x}{625}-\frac{11}{3125 (5 x+3)}+\frac{97 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0186173, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{18 x^3}{25}-\frac{81 x^2}{250}+\frac{522 x}{625}-\frac{11}{3125 (5 x+3)}+\frac{97 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac{522}{625}-\frac{81 x}{125}-\frac{54 x^2}{25}+\frac{11}{625 (3+5 x)^2}+\frac{97}{625 (3+5 x)}\right ) \, dx\\ &=\frac{522 x}{625}-\frac{81 x^2}{250}-\frac{18 x^3}{25}-\frac{11}{3125 (3+5 x)}+\frac{97 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0131939, size = 46, normalized size = 1.12 \[ \frac{-67500 x^4-70875 x^3+60075 x^2+92680 x+582 (5 x+3) \log (-3 (5 x+3))+27354}{18750 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*}{\frac{522\,x}{625}}-{\frac{81\,{x}^{2}}{250}}-{\frac{18\,{x}^{3}}{25}}-{\frac{11}{9375+15625\,x}}+{\frac{97\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04108, size = 42, normalized size = 1.02 \begin{align*} -\frac{18}{25} \, x^{3} - \frac{81}{250} \, x^{2} + \frac{522}{625} \, x - \frac{11}{3125 \,{\left (5 \, x + 3\right )}} + \frac{97}{3125} \, \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 = 1.47549, size = 134, normalized size = 3.27 \begin{align*} -\frac{22500 \, x^{4} + 23625 \, x^{3} - 20025 \, x^{2} - 194 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 15660 \, x + 22}{6250 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.099436, size = 34, normalized size = 0.83 \begin{align*} - \frac{18 x^{3}}{25} - \frac{81 x^{2}}{250} + \frac{522 x}{625} + \frac{97 \log{\left (5 x + 3 \right )}}{3125} - \frac{11}{15625 x + 9375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.69013, size = 77, normalized size = 1.88 \begin{align*} \frac{9}{6250} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{27}{5 \, x + 3} + \frac{62}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac{11}{3125 \,{\left (5 \, x + 3\right )}} - \frac{97}{3125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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