Optimal. Leaf size=44 \[ -\frac{162 x^5}{25}-\frac{1269 x^4}{100}-\frac{531 x^3}{125}+\frac{7779 x^2}{1250}+\frac{16663 x}{3125}+\frac{11 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.0168164, antiderivative size = 44, 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} \[ -\frac{162 x^5}{25}-\frac{1269 x^4}{100}-\frac{531 x^3}{125}+\frac{7779 x^2}{1250}+\frac{16663 x}{3125}+\frac{11 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^4}{3+5 x} \, dx &=\int \left (\frac{16663}{3125}+\frac{7779 x}{625}-\frac{1593 x^2}{125}-\frac{1269 x^3}{25}-\frac{162 x^4}{5}+\frac{11}{3125 (3+5 x)}\right ) \, dx\\ &=\frac{16663 x}{3125}+\frac{7779 x^2}{1250}-\frac{531 x^3}{125}-\frac{1269 x^4}{100}-\frac{162 x^5}{25}+\frac{11 \log (3+5 x)}{15625}\\ \end{align*}
Mathematica [A] time = 0.0127459, size = 37, normalized size = 0.84 \[ \frac{-2025000 x^5-3965625 x^4-1327500 x^3+1944750 x^2+1666300 x+220 \log (5 x+3)+369411}{312500} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 33, normalized size = 0.8 \begin{align*}{\frac{16663\,x}{3125}}+{\frac{7779\,{x}^{2}}{1250}}-{\frac{531\,{x}^{3}}{125}}-{\frac{1269\,{x}^{4}}{100}}-{\frac{162\,{x}^{5}}{25}}+{\frac{11\,\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 = 1.32061, size = 43, normalized size = 0.98 \begin{align*} -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{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 = 1.56556, size = 131, normalized size = 2.98 \begin{align*} -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{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 = 0.088346, size = 41, normalized size = 0.93 \begin{align*} - \frac{162 x^{5}}{25} - \frac{1269 x^{4}}{100} - \frac{531 x^{3}}{125} + \frac{7779 x^{2}}{1250} + \frac{16663 x}{3125} + \frac{11 \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 = 2.3878, size = 45, normalized size = 1.02 \begin{align*} -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{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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