Optimal. Leaf size=55 \[ -\frac {486 x^5}{125}-\frac {3969 x^4}{500}-\frac {1854 x^3}{625}+\frac {24093 x^2}{6250}+\frac {444 x}{125}-\frac {11}{78125 (5 x+3)}+\frac {163 \log (5 x+3)}{78125} \]
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Rubi [A] time = 0.03, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {486 x^5}{125}-\frac {3969 x^4}{500}-\frac {1854 x^3}{625}+\frac {24093 x^2}{6250}+\frac {444 x}{125}-\frac {11}{78125 (5 x+3)}+\frac {163 \log (5 x+3)}{78125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^5}{(3+5 x)^2} \, dx &=\int \left (\frac {444}{125}+\frac {24093 x}{3125}-\frac {5562 x^2}{625}-\frac {3969 x^3}{125}-\frac {486 x^4}{25}+\frac {11}{15625 (3+5 x)^2}+\frac {163}{15625 (3+5 x)}\right ) \, dx\\ &=\frac {444 x}{125}+\frac {24093 x^2}{6250}-\frac {1854 x^3}{625}-\frac {3969 x^4}{500}-\frac {486 x^5}{125}-\frac {11}{78125 (3+5 x)}+\frac {163 \log (3+5 x)}{78125}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 0.87 \[ \frac {-3645000 x^5-7441875 x^4-2781000 x^3+3613950 x^2+3330000 x-\frac {132}{5 x+3}+1956 \log (-3 (5 x+3))+779800}{937500} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 52, normalized size = 0.95 \[ -\frac {6075000 \, x^{6} + 16048125 \, x^{5} + 12076875 \, x^{4} - 3242250 \, x^{3} - 9163950 \, x^{2} - 652 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 3330000 \, x + 44}{312500 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 75, normalized size = 1.36 \[ \frac {3}{1562500} \, {\left (5 \, x + 3\right )}^{5} {\left (\frac {3105}{5 \, x + 3} + \frac {8700}{{\left (5 \, x + 3\right )}^{2}} + \frac {9300}{{\left (5 \, x + 3\right )}^{3}} + \frac {6400}{{\left (5 \, x + 3\right )}^{4}} - 648\right )} - \frac {11}{78125 \, {\left (5 \, x + 3\right )}} - \frac {163}{78125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 42, normalized size = 0.76 \[ -\frac {486 x^{5}}{125}-\frac {3969 x^{4}}{500}-\frac {1854 x^{3}}{625}+\frac {24093 x^{2}}{6250}+\frac {444 x}{125}+\frac {163 \ln \left (5 x +3\right )}{78125}-\frac {11}{78125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 41, normalized size = 0.75 \[ -\frac {486}{125} \, x^{5} - \frac {3969}{500} \, x^{4} - \frac {1854}{625} \, x^{3} + \frac {24093}{6250} \, x^{2} + \frac {444}{125} \, x - \frac {11}{78125 \, {\left (5 \, x + 3\right )}} + \frac {163}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 39, normalized size = 0.71 \[ \frac {444\,x}{125}+\frac {163\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {11}{390625\,\left (x+\frac {3}{5}\right )}+\frac {24093\,x^2}{6250}-\frac {1854\,x^3}{625}-\frac {3969\,x^4}{500}-\frac {486\,x^5}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 48, normalized size = 0.87 \[ - \frac {486 x^{5}}{125} - \frac {3969 x^{4}}{500} - \frac {1854 x^{3}}{625} + \frac {24093 x^{2}}{6250} + \frac {444 x}{125} + \frac {163 \log {\left (5 x + 3 \right )}}{78125} - \frac {11}{390625 x + 234375} \]
Verification of antiderivative is not currently implemented for this CAS.
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