Optimal. Leaf size=44 \[ \frac {108 x^5}{25}+\frac {54 x^4}{25}-\frac {591 x^3}{125}-\frac {1931 x^2}{1250}+\frac {8293 x}{3125}+\frac {121 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {108 x^5}{25}+\frac {54 x^4}{25}-\frac {591 x^3}{125}-\frac {1931 x^2}{1250}+\frac {8293 x}{3125}+\frac {121 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^3}{3+5 x} \, dx &=\int \left (\frac {8293}{3125}-\frac {1931 x}{625}-\frac {1773 x^2}{125}+\frac {216 x^3}{25}+\frac {108 x^4}{5}+\frac {121}{3125 (3+5 x)}\right ) \, dx\\ &=\frac {8293 x}{3125}-\frac {1931 x^2}{1250}-\frac {591 x^3}{125}+\frac {54 x^4}{25}+\frac {108 x^5}{25}+\frac {121 \log (3+5 x)}{15625}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 37, normalized size = 0.84 \[ \frac {675000 x^5+337500 x^4-738750 x^3-241375 x^2+414650 x+1210 \log (5 x+3)+184863}{156250} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 32, normalized size = 0.73 \[ \frac {108}{25} \, x^{5} + \frac {54}{25} \, x^{4} - \frac {591}{125} \, x^{3} - \frac {1931}{1250} \, x^{2} + \frac {8293}{3125} \, x + \frac {121}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 33, normalized size = 0.75 \[ \frac {108}{25} \, x^{5} + \frac {54}{25} \, x^{4} - \frac {591}{125} \, x^{3} - \frac {1931}{1250} \, x^{2} + \frac {8293}{3125} \, x + \frac {121}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.75 \[ \frac {108 x^{5}}{25}+\frac {54 x^{4}}{25}-\frac {591 x^{3}}{125}-\frac {1931 x^{2}}{1250}+\frac {8293 x}{3125}+\frac {121 \ln \left (5 x +3\right )}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 32, normalized size = 0.73 \[ \frac {108}{25} \, x^{5} + \frac {54}{25} \, x^{4} - \frac {591}{125} \, x^{3} - \frac {1931}{1250} \, x^{2} + \frac {8293}{3125} \, x + \frac {121}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 30, normalized size = 0.68 \[ \frac {8293\,x}{3125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{15625}-\frac {1931\,x^2}{1250}-\frac {591\,x^3}{125}+\frac {54\,x^4}{25}+\frac {108\,x^5}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 41, normalized size = 0.93 \[ \frac {108 x^{5}}{25} + \frac {54 x^{4}}{25} - \frac {591 x^{3}}{125} - \frac {1931 x^{2}}{1250} + \frac {8293 x}{3125} + \frac {121 \log {\left (5 x + 3 \right )}}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
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