Optimal. Leaf size=58 \[ -\frac {1458 x^7}{35}-\frac {7047 x^6}{50}-\frac {106677 x^5}{625}-\frac {152469 x^4}{2500}+\frac {152469 x^3}{3125}+\frac {1777779 x^2}{31250}+\frac {1666663 x}{78125}+\frac {11 \log (5 x+3)}{390625} \]
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Rubi [A] time = 0.02, antiderivative size = 58, 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} \[ -\frac {1458 x^7}{35}-\frac {7047 x^6}{50}-\frac {106677 x^5}{625}-\frac {152469 x^4}{2500}+\frac {152469 x^3}{3125}+\frac {1777779 x^2}{31250}+\frac {1666663 x}{78125}+\frac {11 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^6}{3+5 x} \, dx &=\int \left (\frac {1666663}{78125}+\frac {1777779 x}{15625}+\frac {457407 x^2}{3125}-\frac {152469 x^3}{625}-\frac {106677 x^4}{125}-\frac {21141 x^5}{25}-\frac {1458 x^6}{5}+\frac {11}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {1666663 x}{78125}+\frac {1777779 x^2}{31250}+\frac {152469 x^3}{3125}-\frac {152469 x^4}{2500}-\frac {106677 x^5}{625}-\frac {7047 x^6}{50}-\frac {1458 x^7}{35}+\frac {11 \log (3+5 x)}{390625}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 47, normalized size = 0.81 \[ \frac {-2278125000 x^7-7707656250 x^6-9334237500 x^5-3335259375 x^4+2668207500 x^3+3111113250 x^2+1166664100 x+1540 \log (5 x+3)+158585307}{54687500} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 42, normalized size = 0.72 \[ -\frac {1458}{35} \, x^{7} - \frac {7047}{50} \, x^{6} - \frac {106677}{625} \, x^{5} - \frac {152469}{2500} \, x^{4} + \frac {152469}{3125} \, x^{3} + \frac {1777779}{31250} \, x^{2} + \frac {1666663}{78125} \, x + \frac {11}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 43, normalized size = 0.74 \[ -\frac {1458}{35} \, x^{7} - \frac {7047}{50} \, x^{6} - \frac {106677}{625} \, x^{5} - \frac {152469}{2500} \, x^{4} + \frac {152469}{3125} \, x^{3} + \frac {1777779}{31250} \, x^{2} + \frac {1666663}{78125} \, x + \frac {11}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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 \[ -\frac {1458 x^{7}}{35}-\frac {7047 x^{6}}{50}-\frac {106677 x^{5}}{625}-\frac {152469 x^{4}}{2500}+\frac {152469 x^{3}}{3125}+\frac {1777779 x^{2}}{31250}+\frac {1666663 x}{78125}+\frac {11 \ln \left (5 x +3\right )}{390625} \]
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 \[ -\frac {1458}{35} \, x^{7} - \frac {7047}{50} \, x^{6} - \frac {106677}{625} \, x^{5} - \frac {152469}{2500} \, x^{4} + \frac {152469}{3125} \, x^{3} + \frac {1777779}{31250} \, x^{2} + \frac {1666663}{78125} \, x + \frac {11}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 40, normalized size = 0.69 \[ \frac {1666663\,x}{78125}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{390625}+\frac {1777779\,x^2}{31250}+\frac {152469\,x^3}{3125}-\frac {152469\,x^4}{2500}-\frac {106677\,x^5}{625}-\frac {7047\,x^6}{50}-\frac {1458\,x^7}{35} \]
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 \[ - \frac {1458 x^{7}}{35} - \frac {7047 x^{6}}{50} - \frac {106677 x^{5}}{625} - \frac {152469 x^{4}}{2500} + \frac {152469 x^{3}}{3125} + \frac {1777779 x^{2}}{31250} + \frac {1666663 x}{78125} + \frac {11 \log {\left (5 x + 3 \right )}}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
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