Optimal. Leaf size=30 \[ -\frac {8 x^3}{15}+\frac {42 x^2}{25}-\frac {402 x}{125}+\frac {1331}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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} \[ -\frac {8 x^3}{15}+\frac {42 x^2}{25}-\frac {402 x}{125}+\frac {1331}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{3+5 x} \, dx &=\int \left (-\frac {402}{125}+\frac {84 x}{25}-\frac {8 x^2}{5}+\frac {1331}{125 (3+5 x)}\right ) \, dx\\ &=-\frac {402 x}{125}+\frac {42 x^2}{25}-\frac {8 x^3}{15}+\frac {1331}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.90 \[ \frac {-1000 x^3+3150 x^2-6030 x+3993 \log (5 x+3)-4968}{1875} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 22, normalized size = 0.73 \[ -\frac {8}{15} \, x^{3} + \frac {42}{25} \, x^{2} - \frac {402}{125} \, x + \frac {1331}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 23, normalized size = 0.77 \[ -\frac {8}{15} \, x^{3} + \frac {42}{25} \, x^{2} - \frac {402}{125} \, x + \frac {1331}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.77 \[ -\frac {8 x^{3}}{15}+\frac {42 x^{2}}{25}-\frac {402 x}{125}+\frac {1331 \ln \left (5 x +3\right )}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 22, normalized size = 0.73 \[ -\frac {8}{15} \, x^{3} + \frac {42}{25} \, x^{2} - \frac {402}{125} \, x + \frac {1331}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.67 \[ \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {402\,x}{125}+\frac {42\,x^2}{25}-\frac {8\,x^3}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 27, normalized size = 0.90 \[ - \frac {8 x^{3}}{15} + \frac {42 x^{2}}{25} - \frac {402 x}{125} + \frac {1331 \log {\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
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