Optimal. Leaf size=23 \[ -\frac {25 x^2}{4}-\frac {85 x}{4}-\frac {121}{8} \log (1-2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 23, 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 {25 x^2}{4}-\frac {85 x}{4}-\frac {121}{8} \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)^2}{1-2 x} \, dx &=\int \left (-\frac {85}{4}-\frac {25 x}{2}-\frac {121}{4 (-1+2 x)}\right ) \, dx\\ &=-\frac {85 x}{4}-\frac {25 x^2}{4}-\frac {121}{8} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{16} \left (-5 \left (20 x^2+68 x-39\right )-242 \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)^2}{1-2 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.21, size = 17, normalized size = 0.74 \begin {gather*} -\frac {25}{4} \, x^{2} - \frac {85}{4} \, x - \frac {121}{8} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 18, normalized size = 0.78 \begin {gather*} -\frac {25}{4} \, x^{2} - \frac {85}{4} \, x - \frac {121}{8} \, \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 = 0.00, size = 18, normalized size = 0.78 \begin {gather*} -\frac {25 x^{2}}{4}-\frac {85 x}{4}-\frac {121 \ln \left (2 x -1\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 17, normalized size = 0.74 \begin {gather*} -\frac {25}{4} \, x^{2} - \frac {85}{4} \, x - \frac {121}{8} \, \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 = 0.02, size = 15, normalized size = 0.65 \begin {gather*} -\frac {85\,x}{4}-\frac {121\,\ln \left (x-\frac {1}{2}\right )}{8}-\frac {25\,x^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 22, normalized size = 0.96 \begin {gather*} - \frac {25 x^{2}}{4} - \frac {85 x}{4} - \frac {121 \log {\left (2 x - 1 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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