Optimal. Leaf size=45 \[ -\frac{12 x^2}{125}+\frac{316 x}{625}-\frac{3267}{3125 (5 x+3)}-\frac{1331}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0210411, antiderivative size = 45, 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} \[ -\frac{12 x^2}{125}+\frac{316 x}{625}-\frac{3267}{3125 (5 x+3)}-\frac{1331}{6250 (5 x+3)^2}-\frac{2046 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^3} \, dx &=\int \left (\frac{316}{625}-\frac{24 x}{125}+\frac{1331}{625 (3+5 x)^3}+\frac{3267}{625 (3+5 x)^2}-\frac{2046}{625 (3+5 x)}\right ) \, dx\\ &=\frac{316 x}{625}-\frac{12 x^2}{125}-\frac{1331}{6250 (3+5 x)^2}-\frac{3267}{3125 (3+5 x)}-\frac{2046 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0187059, size = 46, normalized size = 1.02 \[ -\frac{15000 x^4-61000 x^3-53650 x^2+47130 x+4092 (5 x+3)^2 \log (10 x+6)+33803}{6250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*}{\frac{316\,x}{625}}-{\frac{12\,{x}^{2}}{125}}-{\frac{1331}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{3267}{9375+15625\,x}}-{\frac{2046\,\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 = 1.01657, size = 49, normalized size = 1.09 \begin{align*} -\frac{12}{125} \, x^{2} + \frac{316}{625} \, x - \frac{121 \,{\left (270 \, x + 173\right )}}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{2046}{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 = 1.33372, size = 165, normalized size = 3.67 \begin{align*} -\frac{15000 \, x^{4} - 61000 \, x^{3} - 89400 \, x^{2} + 4092 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 4230 \, x + 20933}{6250 \,{\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 = 0.117702, size = 36, normalized size = 0.8 \begin{align*} - \frac{12 x^{2}}{125} + \frac{316 x}{625} - \frac{32670 x + 20933}{156250 x^{2} + 187500 x + 56250} - \frac{2046 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.07504, size = 43, normalized size = 0.96 \begin{align*} -\frac{12}{125} \, x^{2} + \frac{316}{625} \, x - \frac{121 \,{\left (270 \, x + 173\right )}}{6250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{2046}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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