Optimal. Leaf size=45 \[ -\frac {7}{81} (2+3 x)^7+\frac {91}{216} (2+3 x)^8-\frac {16}{81} (2+3 x)^9+\frac {2}{81} (2+3 x)^{10} \]
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Rubi [A]
time = 0.02, antiderivative size = 45, 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 {2}{81} (3 x+2)^{10}-\frac {16}{81} (3 x+2)^9+\frac {91}{216} (3 x+2)^8-\frac {7}{81} (3 x+2)^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^6 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^6+\frac {91}{9} (2+3 x)^7-\frac {16}{3} (2+3 x)^8+\frac {20}{27} (2+3 x)^9\right ) \, dx\\ &=-\frac {7}{81} (2+3 x)^7+\frac {91}{216} (2+3 x)^8-\frac {16}{81} (2+3 x)^9+\frac {2}{81} (2+3 x)^{10}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 53, normalized size = 1.18 \begin {gather*} 192 x+640 x^2+\frac {1936 x^3}{3}-1372 x^4-4284 x^5-2772 x^6+4185 x^7+\frac {68769 x^8}{8}+5832 x^9+1458 x^{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 50, normalized size = 1.11
method | result | size |
gosper | \(\frac {x \left (34992 x^{9}+139968 x^{8}+206307 x^{7}+100440 x^{6}-66528 x^{5}-102816 x^{4}-32928 x^{3}+15488 x^{2}+15360 x +4608\right )}{24}\) | \(49\) |
default | \(1458 x^{10}+5832 x^{9}+\frac {68769}{8} x^{8}+4185 x^{7}-2772 x^{6}-4284 x^{5}-1372 x^{4}+\frac {1936}{3} x^{3}+640 x^{2}+192 x\) | \(50\) |
norman | \(1458 x^{10}+5832 x^{9}+\frac {68769}{8} x^{8}+4185 x^{7}-2772 x^{6}-4284 x^{5}-1372 x^{4}+\frac {1936}{3} x^{3}+640 x^{2}+192 x\) | \(50\) |
risch | \(1458 x^{10}+5832 x^{9}+\frac {68769}{8} x^{8}+4185 x^{7}-2772 x^{6}-4284 x^{5}-1372 x^{4}+\frac {1936}{3} x^{3}+640 x^{2}+192 x\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 49, normalized size = 1.09 \begin {gather*} 1458 \, x^{10} + 5832 \, x^{9} + \frac {68769}{8} \, x^{8} + 4185 \, x^{7} - 2772 \, x^{6} - 4284 \, x^{5} - 1372 \, x^{4} + \frac {1936}{3} \, x^{3} + 640 \, x^{2} + 192 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.70, size = 49, normalized size = 1.09 \begin {gather*} 1458 \, x^{10} + 5832 \, x^{9} + \frac {68769}{8} \, x^{8} + 4185 \, x^{7} - 2772 \, x^{6} - 4284 \, x^{5} - 1372 \, x^{4} + \frac {1936}{3} \, x^{3} + 640 \, x^{2} + 192 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 51, normalized size = 1.13 \begin {gather*} 1458 x^{10} + 5832 x^{9} + \frac {68769 x^{8}}{8} + 4185 x^{7} - 2772 x^{6} - 4284 x^{5} - 1372 x^{4} + \frac {1936 x^{3}}{3} + 640 x^{2} + 192 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.56, size = 49, normalized size = 1.09 \begin {gather*} 1458 \, x^{10} + 5832 \, x^{9} + \frac {68769}{8} \, x^{8} + 4185 \, x^{7} - 2772 \, x^{6} - 4284 \, x^{5} - 1372 \, x^{4} + \frac {1936}{3} \, x^{3} + 640 \, x^{2} + 192 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 49, normalized size = 1.09 \begin {gather*} 1458\,x^{10}+5832\,x^9+\frac {68769\,x^8}{8}+4185\,x^7-2772\,x^6-4284\,x^5-1372\,x^4+\frac {1936\,x^3}{3}+640\,x^2+192\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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