Optimal. Leaf size=41 \[ \frac {125 x^3}{4}+\frac {325 x^2}{2}+\frac {8245 x}{16}+\frac {9317}{32 (1-2 x)}+\frac {8349}{16} \log (1-2 x) \]
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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} \begin {gather*} \frac {125 x^3}{4}+\frac {325 x^2}{2}+\frac {8245 x}{16}+\frac {9317}{32 (1-2 x)}+\frac {8349}{16} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {8245}{16}+325 x+\frac {375 x^2}{4}+\frac {9317}{16 (-1+2 x)^2}+\frac {8349}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {9317}{32 (1-2 x)}+\frac {8245 x}{16}+\frac {325 x^2}{2}+\frac {125 x^3}{4}+\frac {8349}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 41, normalized size = 1.00 \begin {gather*} \frac {2000 x^4+9400 x^3+27780 x^2-35830 x+16698 (2 x-1) \log (1-2 x)+353}{64 x-32} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.78, size = 42, normalized size = 1.02 \begin {gather*} \frac {2000 \, x^{4} + 9400 \, x^{3} + 27780 \, x^{2} + 16698 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 16490 \, x - 9317}{32 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 57, normalized size = 1.39 \begin {gather*} \frac {5}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {335}{2 \, x - 1} + \frac {2244}{{\left (2 \, x - 1\right )}^{2}} + 25\right )} - \frac {9317}{32 \, {\left (2 \, x - 1\right )}} - \frac {8349}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}
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 \begin {gather*} \frac {125 x^{3}}{4}+\frac {325 x^{2}}{2}+\frac {8245 x}{16}+\frac {8349 \ln \left (2 x -1\right )}{16}-\frac {9317}{32 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 31, normalized size = 0.76 \begin {gather*} \frac {125}{4} \, x^{3} + \frac {325}{2} \, x^{2} + \frac {8245}{16} \, x - \frac {9317}{32 \, {\left (2 \, x - 1\right )}} + \frac {8349}{16} \, \log \left (2 \, x - 1\right ) \end {gather*}
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 \begin {gather*} \frac {8245\,x}{16}+\frac {8349\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {9317}{64\,\left (x-\frac {1}{2}\right )}+\frac {325\,x^2}{2}+\frac {125\,x^3}{4} \end {gather*}
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 \begin {gather*} \frac {125 x^{3}}{4} + \frac {325 x^{2}}{2} + \frac {8245 x}{16} + \frac {8349 \log {\left (2 x - 1 \right )}}{16} - \frac {9317}{64 x - 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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