Optimal. Leaf size=34 \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0155181, antiderivative size = 34, 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} \[ \frac{75 x^2}{8}+\frac{215 x}{4}+\frac{847}{16 (1-2 x)}+\frac{1133}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{215}{4}+\frac{75 x}{4}+\frac{847}{8 (-1+2 x)^2}+\frac{1133}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{847}{16 (1-2 x)}+\frac{215 x}{4}+\frac{75 x^2}{8}+\frac{1133}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.010032, size = 36, normalized size = 1.06 \[ \frac{600 x^3+3140 x^2-3590 x+2266 (2 x-1) \log (1-2 x)-759}{64 x-32} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*}{\frac{75\,{x}^{2}}{8}}+{\frac{215\,x}{4}}+{\frac{1133\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{847}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16079, size = 35, normalized size = 1.03 \begin{align*} \frac{75}{8} \, x^{2} + \frac{215}{4} \, x - \frac{847}{16 \,{\left (2 \, x - 1\right )}} + \frac{1133}{16} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31753, size = 109, normalized size = 3.21 \begin{align*} \frac{300 \, x^{3} + 1570 \, x^{2} + 1133 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 860 \, x - 847}{16 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097321, size = 27, normalized size = 0.79 \begin{align*} \frac{75 x^{2}}{8} + \frac{215 x}{4} + \frac{1133 \log{\left (2 x - 1 \right )}}{16} - \frac{847}{32 x - 16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.24092, size = 65, normalized size = 1.91 \begin{align*} \frac{5}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{202}{2 \, x - 1} + 15\right )} - \frac{847}{16 \,{\left (2 \, x - 1\right )}} - \frac{1133}{16} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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