Optimal. Leaf size=44 \[ \frac{108 x^5}{25}+\frac{54 x^4}{25}-\frac{591 x^3}{125}-\frac{1931 x^2}{1250}+\frac{8293 x}{3125}+\frac{121 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.0189513, antiderivative size = 44, normalized size of antiderivative = 1., 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 = {88} \[ \frac{108 x^5}{25}+\frac{54 x^4}{25}-\frac{591 x^3}{125}-\frac{1931 x^2}{1250}+\frac{8293 x}{3125}+\frac{121 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^3}{3+5 x} \, dx &=\int \left (\frac{8293}{3125}-\frac{1931 x}{625}-\frac{1773 x^2}{125}+\frac{216 x^3}{25}+\frac{108 x^4}{5}+\frac{121}{3125 (3+5 x)}\right ) \, dx\\ &=\frac{8293 x}{3125}-\frac{1931 x^2}{1250}-\frac{591 x^3}{125}+\frac{54 x^4}{25}+\frac{108 x^5}{25}+\frac{121 \log (3+5 x)}{15625}\\ \end{align*}
Mathematica [A] time = 0.0107388, size = 37, normalized size = 0.84 \[ \frac{675000 x^5+337500 x^4-738750 x^3-241375 x^2+414650 x+1210 \log (5 x+3)+184863}{156250} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 33, normalized size = 0.8 \begin{align*}{\frac{8293\,x}{3125}}-{\frac{1931\,{x}^{2}}{1250}}-{\frac{591\,{x}^{3}}{125}}+{\frac{54\,{x}^{4}}{25}}+{\frac{108\,{x}^{5}}{25}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{15625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28447, size = 43, normalized size = 0.98 \begin{align*} \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \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 = 1.48363, size = 126, normalized size = 2.86 \begin{align*} \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086615, size = 41, normalized size = 0.93 \begin{align*} \frac{108 x^{5}}{25} + \frac{54 x^{4}}{25} - \frac{591 x^{3}}{125} - \frac{1931 x^{2}}{1250} + \frac{8293 x}{3125} + \frac{121 \log{\left (5 x + 3 \right )}}{15625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.90204, size = 45, normalized size = 1.02 \begin{align*} \frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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