Optimal. Leaf size=34 \[ -\frac {4 x^2}{25}+\frac {108 x}{125}-\frac {1331}{625 (5 x+3)}-\frac {726}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 34, 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} \[ -\frac {4 x^2}{25}+\frac {108 x}{125}-\frac {1331}{625 (5 x+3)}-\frac {726}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac {108}{125}-\frac {8 x}{25}+\frac {1331}{125 (3+5 x)^2}-\frac {726}{125 (3+5 x)}\right ) \, dx\\ &=\frac {108 x}{125}-\frac {4 x^2}{25}-\frac {1331}{625 (3+5 x)}-\frac {726}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 39, normalized size = 1.15 \[ \frac {-500 x^3+2400 x^2+395 x-726 (5 x+3) \log (10 x+6)-2066}{625 (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 37, normalized size = 1.09 \[ -\frac {500 \, x^{3} - 2400 \, x^{2} + 726 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1620 \, x + 1331}{625 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 48, normalized size = 1.41 \[ \frac {4}{625} \, {\left (5 \, x + 3\right )}^{2} {\left (\frac {33}{5 \, x + 3} - 1\right )} - \frac {1331}{625 \, {\left (5 \, x + 3\right )}} + \frac {726}{625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.79 \[ -\frac {4 x^{2}}{25}+\frac {108 x}{125}-\frac {726 \ln \left (5 x +3\right )}{625}-\frac {1331}{625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 26, normalized size = 0.76 \[ -\frac {4}{25} \, x^{2} + \frac {108}{125} \, x - \frac {1331}{625 \, {\left (5 \, x + 3\right )}} - \frac {726}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.71 \[ \frac {108\,x}{125}-\frac {726\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {1331}{3125\,\left (x+\frac {3}{5}\right )}-\frac {4\,x^2}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 27, normalized size = 0.79 \[ - \frac {4 x^{2}}{25} + \frac {108 x}{125} - \frac {726 \log {\left (5 x + 3 \right )}}{625} - \frac {1331}{3125 x + 1875} \]
Verification of antiderivative is not currently implemented for this CAS.
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