Optimal. Leaf size=56 \[ -\frac {10}{729} (3 x+2)^{12}+\frac {428 (3 x+2)^{11}}{2673}-\frac {259}{405} (3 x+2)^{10}+\frac {2009 (3 x+2)^9}{2187}-\frac {343 (3 x+2)^8}{1944} \]
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Rubi [A] time = 0.03, antiderivative size = 56, 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} \[ -\frac {10}{729} (3 x+2)^{12}+\frac {428 (3 x+2)^{11}}{2673}-\frac {259}{405} (3 x+2)^{10}+\frac {2009 (3 x+2)^9}{2187}-\frac {343 (3 x+2)^8}{1944} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx &=\int \left (-\frac {343}{81} (2+3 x)^7+\frac {2009}{81} (2+3 x)^8-\frac {518}{27} (2+3 x)^9+\frac {428}{81} (2+3 x)^{10}-\frac {40}{81} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {343 (2+3 x)^8}{1944}+\frac {2009 (2+3 x)^9}{2187}-\frac {259}{405} (2+3 x)^{10}+\frac {428 (2+3 x)^{11}}{2673}-\frac {10}{729} (2+3 x)^{12}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 67, normalized size = 1.20 \[ -7290 x^{12}-\frac {329508 x^{11}}{11}-\frac {217971 x^{10}}{5}-15507 x^9+\frac {208035 x^8}{8}+29106 x^7+3514 x^6-\frac {48968 x^5}{5}-5148 x^4+480 x^3+1184 x^2+384 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 59, normalized size = 1.05 \[ -7290 x^{12} - \frac {329508}{11} x^{11} - \frac {217971}{5} x^{10} - 15507 x^{9} + \frac {208035}{8} x^{8} + 29106 x^{7} + 3514 x^{6} - \frac {48968}{5} x^{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 59, normalized size = 1.05 \[ -7290 \, x^{12} - \frac {329508}{11} \, x^{11} - \frac {217971}{5} \, x^{10} - 15507 \, x^{9} + \frac {208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac {48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 60, normalized size = 1.07 \[ -7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 59, normalized size = 1.05 \[ -7290 \, x^{12} - \frac {329508}{11} \, x^{11} - \frac {217971}{5} \, x^{10} - 15507 \, x^{9} + \frac {208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac {48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 59, normalized size = 1.05 \[ -7290\,x^{12}-\frac {329508\,x^{11}}{11}-\frac {217971\,x^{10}}{5}-15507\,x^9+\frac {208035\,x^8}{8}+29106\,x^7+3514\,x^6-\frac {48968\,x^5}{5}-5148\,x^4+480\,x^3+1184\,x^2+384\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 1.16 \[ - 7290 x^{12} - \frac {329508 x^{11}}{11} - \frac {217971 x^{10}}{5} - 15507 x^{9} + \frac {208035 x^{8}}{8} + 29106 x^{7} + 3514 x^{6} - \frac {48968 x^{5}}{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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