Optimal. Leaf size=58 \[ \frac {972 x^7}{35}+\frac {1404 x^6}{25}+\frac {7803 x^5}{625}-\frac {102159 x^4}{2500}-\frac {72841 x^3}{3125}+\frac {305569 x^2}{31250}+\frac {833293 x}{78125}+\frac {121 \log (5 x+3)}{390625} \]
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Rubi [A] time = 0.03, antiderivative size = 58, 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} \[ \frac {972 x^7}{35}+\frac {1404 x^6}{25}+\frac {7803 x^5}{625}-\frac {102159 x^4}{2500}-\frac {72841 x^3}{3125}+\frac {305569 x^2}{31250}+\frac {833293 x}{78125}+\frac {121 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx &=\int \left (\frac {833293}{78125}+\frac {305569 x}{15625}-\frac {218523 x^2}{3125}-\frac {102159 x^3}{625}+\frac {7803 x^4}{125}+\frac {8424 x^5}{25}+\frac {972 x^6}{5}+\frac {121}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {833293 x}{78125}+\frac {305569 x^2}{31250}-\frac {72841 x^3}{3125}-\frac {102159 x^4}{2500}+\frac {7803 x^5}{625}+\frac {1404 x^6}{25}+\frac {972 x^7}{35}+\frac {121 \log (3+5 x)}{390625}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 47, normalized size = 0.81 \[ \frac {1518750000 x^7+3071250000 x^6+682762500 x^5-2234728125 x^4-1274717500 x^3+534745750 x^2+583305100 x+16940 \log (5 x+3)+124071027}{54687500} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 42, normalized size = 0.72 \[ \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 43, normalized size = 0.74 \[ \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 43, normalized size = 0.74 \[ \frac {972 x^{7}}{35}+\frac {1404 x^{6}}{25}+\frac {7803 x^{5}}{625}-\frac {102159 x^{4}}{2500}-\frac {72841 x^{3}}{3125}+\frac {305569 x^{2}}{31250}+\frac {833293 x}{78125}+\frac {121 \ln \left (5 x +3\right )}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 42, normalized size = 0.72 \[ \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 40, normalized size = 0.69 \[ \frac {833293\,x}{78125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{390625}+\frac {305569\,x^2}{31250}-\frac {72841\,x^3}{3125}-\frac {102159\,x^4}{2500}+\frac {7803\,x^5}{625}+\frac {1404\,x^6}{25}+\frac {972\,x^7}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 54, normalized size = 0.93 \[ \frac {972 x^{7}}{35} + \frac {1404 x^{6}}{25} + \frac {7803 x^{5}}{625} - \frac {102159 x^{4}}{2500} - \frac {72841 x^{3}}{3125} + \frac {305569 x^{2}}{31250} + \frac {833293 x}{78125} + \frac {121 \log {\left (5 x + 3 \right )}}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
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