Optimal. Leaf size=38 \[ -\frac {125 x}{8}-\frac {1815}{16 (1-2 x)}+\frac {1331}{32 (1-2 x)^2}-\frac {825}{16} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} -\frac {125 x}{8}-\frac {1815}{16 (1-2 x)}+\frac {1331}{32 (1-2 x)^2}-\frac {825}{16} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {125}{8}-\frac {1331}{8 (-1+2 x)^3}-\frac {1815}{8 (-1+2 x)^2}-\frac {825}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {1331}{32 (1-2 x)^2}-\frac {1815}{16 (1-2 x)}-\frac {125 x}{8}-\frac {825}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 34, normalized size = 0.89 \begin {gather*} \frac {1}{32} \left (\frac {1000 x^2+6260 x-2049}{(1-2 x)^2}-500 x-1650 \log (1-2 x)\right ) \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 {(3+5 x)^3}{(1-2 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.75, size = 47, normalized size = 1.24 \begin {gather*} -\frac {2000 \, x^{3} - 2000 \, x^{2} + 1650 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 6760 \, x + 2299}{32 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 27, normalized size = 0.71 \begin {gather*} -\frac {125}{8} \, x + \frac {121 \, {\left (60 \, x - 19\right )}}{32 \, {\left (2 \, x - 1\right )}^{2}} - \frac {825}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 0.82 \begin {gather*} -\frac {125 x}{8}-\frac {825 \ln \left (2 x -1\right )}{16}+\frac {1331}{32 \left (2 x -1\right )^{2}}+\frac {1815}{16 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 31, normalized size = 0.82 \begin {gather*} -\frac {125}{8} \, x + \frac {121 \, {\left (60 \, x - 19\right )}}{32 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {825}{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 = 1.05, size = 26, normalized size = 0.68 \begin {gather*} \frac {\frac {1815\,x}{32}-\frac {2299}{128}}{x^2-x+\frac {1}{4}}-\frac {825\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {125\,x}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 31, normalized size = 0.82 \begin {gather*} - \frac {125 x}{8} - \frac {2299 - 7260 x}{128 x^{2} - 128 x + 32} - \frac {825 \log {\left (2 x - 1 \right )}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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