Optimal. Leaf size=65 \[ \frac {729 x^8}{10}+\frac {34992 x^7}{175}+\frac {35883 x^6}{250}-\frac {228447 x^5}{3125}-\frac {1677159 x^4}{12500}-\frac {422841 x^3}{15625}+\frac {5555569 x^2}{156250}+\frac {8333293 x}{390625}+\frac {121 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.03, antiderivative size = 65, 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} \begin {gather*} \frac {729 x^8}{10}+\frac {34992 x^7}{175}+\frac {35883 x^6}{250}-\frac {228447 x^5}{3125}-\frac {1677159 x^4}{12500}-\frac {422841 x^3}{15625}+\frac {5555569 x^2}{156250}+\frac {8333293 x}{390625}+\frac {121 \log (5 x+3)}{1953125} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx &=\int \left (\frac {8333293}{390625}+\frac {5555569 x}{78125}-\frac {1268523 x^2}{15625}-\frac {1677159 x^3}{3125}-\frac {228447 x^4}{625}+\frac {107649 x^5}{125}+\frac {34992 x^6}{25}+\frac {2916 x^7}{5}+\frac {121}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {8333293 x}{390625}+\frac {5555569 x^2}{156250}-\frac {422841 x^3}{15625}-\frac {1677159 x^4}{12500}-\frac {228447 x^5}{3125}+\frac {35883 x^6}{250}+\frac {34992 x^7}{175}+\frac {729 x^8}{10}+\frac {121 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 52, normalized size = 0.80 \begin {gather*} \frac {19933593750 x^8+54675000000 x^7+39247031250 x^6-19989112500 x^5-36687853125 x^4-7399717500 x^3+9722245750 x^2+5833305100 x+16940 \log (5 x+3)+966660747}{273437500} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.58, size = 47, normalized size = 0.72 \begin {gather*} \frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 48, normalized size = 0.74 \begin {gather*} \frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 48, normalized size = 0.74 \begin {gather*} \frac {729 x^{8}}{10}+\frac {34992 x^{7}}{175}+\frac {35883 x^{6}}{250}-\frac {228447 x^{5}}{3125}-\frac {1677159 x^{4}}{12500}-\frac {422841 x^{3}}{15625}+\frac {5555569 x^{2}}{156250}+\frac {8333293 x}{390625}+\frac {121 \ln \left (5 x +3\right )}{1953125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 47, normalized size = 0.72 \begin {gather*} \frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 45, normalized size = 0.69 \begin {gather*} \frac {8333293\,x}{390625}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{1953125}+\frac {5555569\,x^2}{156250}-\frac {422841\,x^3}{15625}-\frac {1677159\,x^4}{12500}-\frac {228447\,x^5}{3125}+\frac {35883\,x^6}{250}+\frac {34992\,x^7}{175}+\frac {729\,x^8}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 61, normalized size = 0.94 \begin {gather*} \frac {729 x^{8}}{10} + \frac {34992 x^{7}}{175} + \frac {35883 x^{6}}{250} - \frac {228447 x^{5}}{3125} - \frac {1677159 x^{4}}{12500} - \frac {422841 x^{3}}{15625} + \frac {5555569 x^{2}}{156250} + \frac {8333293 x}{390625} + \frac {121 \log {\left (5 x + 3 \right )}}{1953125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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