Optimal. Leaf size=41 \[ \frac {45 x^3}{4}+\frac {243 x^2}{4}+\frac {3177 x}{16}+\frac {3773}{32 (1-2 x)}+\frac {3283}{16} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {45 x^3}{4}+\frac {243 x^2}{4}+\frac {3177 x}{16}+\frac {3773}{32 (1-2 x)}+\frac {3283}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac {3177}{16}+\frac {243 x}{2}+\frac {135 x^2}{4}+\frac {3773}{16 (-1+2 x)^2}+\frac {3283}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {3773}{32 (1-2 x)}+\frac {3177 x}{16}+\frac {243 x^2}{4}+\frac {45 x^3}{4}+\frac {3283}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 41, normalized size = 1.00 \[ \frac {720 x^4+3528 x^3+10764 x^2-13770 x+6566 (2 x-1) \log (1-2 x)-65}{64 x-32} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 42, normalized size = 1.02 \[ \frac {720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 6354 \, x - 3773}{32 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 57, normalized size = 1.39 \[ \frac {9}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {69}{2 \, x - 1} + \frac {476}{{\left (2 \, x - 1\right )}^{2}} + 5\right )} - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} - \frac {3283}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 32, normalized size = 0.78 \[ \frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}+\frac {3283 \ln \left (2 x -1\right )}{16}-\frac {3773}{32 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 31, normalized size = 0.76 \[ \frac {45}{4} \, x^{3} + \frac {243}{4} \, x^{2} + \frac {3177}{16} \, x - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} + \frac {3283}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.71 \[ \frac {3177\,x}{16}+\frac {3283\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {3773}{64\,\left (x-\frac {1}{2}\right )}+\frac {243\,x^2}{4}+\frac {45\,x^3}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 34, normalized size = 0.83 \[ \frac {45 x^{3}}{4} + \frac {243 x^{2}}{4} + \frac {3177 x}{16} + \frac {3283 \log {\left (2 x - 1 \right )}}{16} - \frac {3773}{64 x - 32} \]
Verification of antiderivative is not currently implemented for this CAS.
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