Optimal. Leaf size=72 \[ \frac {972 x^9}{5}+\frac {16767 x^8}{25}+\frac {672867 x^7}{875}+\frac {130383 x^6}{1250}-\frac {7315947 x^5}{15625}-\frac {20577159 x^4}{62500}+\frac {1327159 x^3}{78125}+\frac {80555569 x^2}{781250}+\frac {83333293 x}{1953125}+\frac {121 \log (5 x+3)}{9765625} \]
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Rubi [A] time = 0.03, antiderivative size = 72, 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 {972 x^9}{5}+\frac {16767 x^8}{25}+\frac {672867 x^7}{875}+\frac {130383 x^6}{1250}-\frac {7315947 x^5}{15625}-\frac {20577159 x^4}{62500}+\frac {1327159 x^3}{78125}+\frac {80555569 x^2}{781250}+\frac {83333293 x}{1953125}+\frac {121 \log (5 x+3)}{9765625} \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)^7}{3+5 x} \, dx &=\int \left (\frac {83333293}{1953125}+\frac {80555569 x}{390625}+\frac {3981477 x^2}{78125}-\frac {20577159 x^3}{15625}-\frac {7315947 x^4}{3125}+\frac {391149 x^5}{625}+\frac {672867 x^6}{125}+\frac {134136 x^7}{25}+\frac {8748 x^8}{5}+\frac {121}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac {83333293 x}{1953125}+\frac {80555569 x^2}{781250}+\frac {1327159 x^3}{78125}-\frac {20577159 x^4}{62500}-\frac {7315947 x^5}{15625}+\frac {130383 x^6}{1250}+\frac {672867 x^7}{875}+\frac {16767 x^8}{25}+\frac {972 x^9}{5}+\frac {121 \log (3+5 x)}{9765625}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 57, normalized size = 0.79 \begin {gather*} \frac {265781250000 x^9+916945312500 x^8+1051354687500 x^7+142606406250 x^6-640145362500 x^5-450125353125 x^4+23225282500 x^3+140972245750 x^2+58333305100 x+16940 \log (5 x+3)+7880238537}{1367187500} \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)^7}{3+5 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.97, size = 52, normalized size = 0.72 \begin {gather*} \frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \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 = 0.89, size = 53, normalized size = 0.74 \begin {gather*} \frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \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 = 53, normalized size = 0.74 \begin {gather*} \frac {972 x^{9}}{5}+\frac {16767 x^{8}}{25}+\frac {672867 x^{7}}{875}+\frac {130383 x^{6}}{1250}-\frac {7315947 x^{5}}{15625}-\frac {20577159 x^{4}}{62500}+\frac {1327159 x^{3}}{78125}+\frac {80555569 x^{2}}{781250}+\frac {83333293 x}{1953125}+\frac {121 \ln \left (5 x +3\right )}{9765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 52, normalized size = 0.72 \begin {gather*} \frac {972}{5} \, x^{9} + \frac {16767}{25} \, x^{8} + \frac {672867}{875} \, x^{7} + \frac {130383}{1250} \, x^{6} - \frac {7315947}{15625} \, x^{5} - \frac {20577159}{62500} \, x^{4} + \frac {1327159}{78125} \, x^{3} + \frac {80555569}{781250} \, x^{2} + \frac {83333293}{1953125} \, x + \frac {121}{9765625} \, \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 = 0.05, size = 50, normalized size = 0.69 \begin {gather*} \frac {83333293\,x}{1953125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{9765625}+\frac {80555569\,x^2}{781250}+\frac {1327159\,x^3}{78125}-\frac {20577159\,x^4}{62500}-\frac {7315947\,x^5}{15625}+\frac {130383\,x^6}{1250}+\frac {672867\,x^7}{875}+\frac {16767\,x^8}{25}+\frac {972\,x^9}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 68, normalized size = 0.94 \begin {gather*} \frac {972 x^{9}}{5} + \frac {16767 x^{8}}{25} + \frac {672867 x^{7}}{875} + \frac {130383 x^{6}}{1250} - \frac {7315947 x^{5}}{15625} - \frac {20577159 x^{4}}{62500} + \frac {1327159 x^{3}}{78125} + \frac {80555569 x^{2}}{781250} + \frac {83333293 x}{1953125} + \frac {121 \log {\left (5 x + 3 \right )}}{9765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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