Optimal. Leaf size=56 \[ -\frac {343 (2+3 x)^8}{1944}+\frac {2009 (2+3 x)^9}{2187}-\frac {259}{405} (2+3 x)^{10}+\frac {428 (2+3 x)^{11}}{2673}-\frac {10}{729} (2+3 x)^{12} \]
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Rubi [A]
time = 0.02, 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 = {78}
\begin {gather*} -\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} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
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 \begin {gather*} 384 x+1184 x^2+480 x^3-5148 x^4-\frac {48968 x^5}{5}+3514 x^6+29106 x^7+\frac {208035 x^8}{8}-15507 x^9-\frac {217971 x^{10}}{5}-\frac {329508 x^{11}}{11}-7290 x^{12} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 60, normalized size = 1.07
method | result | size |
gosper | \(-\frac {x \left (3207600 x^{11}+13180320 x^{10}+19181448 x^{9}+6823080 x^{8}-11441925 x^{7}-12806640 x^{6}-1546160 x^{5}+4309184 x^{4}+2265120 x^{3}-211200 x^{2}-520960 x -168960\right )}{440}\) | \(59\) |
default | \(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\) | \(60\) |
norman | \(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\) | \(60\) |
risch | \(-7290 x^{12}-\frac {329508}{11} x^{11}-\frac {217971}{5} x^{10}-15507 x^{9}+\frac {208035}{8} x^{8}+29106 x^{7}+3514 x^{6}-\frac {48968}{5} x^{5}-5148 x^{4}+480 x^{3}+1184 x^{2}+384 x\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 59, normalized size = 1.05 \begin {gather*} -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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 59, normalized size = 1.05 \begin {gather*} -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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 65, normalized size = 1.16 \begin {gather*} - 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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.00, size = 59, normalized size = 1.05 \begin {gather*} -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 \end {gather*}
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 \begin {gather*} -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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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