Optimal. Leaf size=38 \[ -\frac {8 x}{125}+\frac {726}{625 (5 x+3)}-\frac {1331}{1250 (5 x+3)^2}+\frac {132}{625} \log (5 x+3) \]
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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} \[ -\frac {8 x}{125}+\frac {726}{625 (5 x+3)}-\frac {1331}{1250 (5 x+3)^2}+\frac {132}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(3+5 x)^3} \, dx &=\int \left (-\frac {8}{125}+\frac {1331}{125 (3+5 x)^3}-\frac {726}{125 (3+5 x)^2}+\frac {132}{125 (3+5 x)}\right ) \, dx\\ &=-\frac {8 x}{125}-\frac {1331}{1250 (3+5 x)^2}+\frac {726}{625 (3+5 x)}+\frac {132}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 37, normalized size = 0.97 \[ \frac {\frac {5 \left (-400 x^3-280 x^2+1548 x+677\right )}{(5 x+3)^2}+264 \log (10 x+6)}{1250} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 47, normalized size = 1.24 \[ -\frac {2000 \, x^{3} + 2400 \, x^{2} - 264 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 6540 \, x - 3025}{1250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 27, normalized size = 0.71 \[ -\frac {8}{125} \, x + \frac {121 \, {\left (12 \, x + 5\right )}}{250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {132}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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 \[ -\frac {8 x}{125}+\frac {132 \ln \left (5 x +3\right )}{625}-\frac {1331}{1250 \left (5 x +3\right )^{2}}+\frac {726}{625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 31, normalized size = 0.82 \[ -\frac {8}{125} \, x + \frac {121 \, {\left (12 \, x + 5\right )}}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {132}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 26, normalized size = 0.68 \[ \frac {132\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {8\,x}{125}+\frac {\frac {726\,x}{3125}+\frac {121}{1250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \]
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 \[ - \frac {8 x}{125} - \frac {- 1452 x - 605}{6250 x^{2} + 7500 x + 2250} + \frac {132 \log {\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
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