Optimal. Leaf size=56 \[ 72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9 \]
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Rubi [A]
time = 0.01, antiderivative size = 56, 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 = {90}
\begin {gather*} -600 x^9-\frac {2295 x^8}{2}-\frac {234 x^7}{7}+\frac {6743 x^6}{6}+\frac {2262 x^5}{5}-\frac {1641 x^4}{4}-\frac {754 x^3}{3}+66 x^2+72 x \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+132 x-754 x^2-1641 x^3+2262 x^4+6743 x^5-234 x^6-9180 x^7-5400 x^8\right ) \, dx\\ &=72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 56, normalized size = 1.00 \begin {gather*} 72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 45, normalized size = 0.80
method | result | size |
gosper | \(-\frac {x \left (252000 x^{8}+481950 x^{7}+14040 x^{6}-472010 x^{5}-190008 x^{4}+172305 x^{3}+105560 x^{2}-27720 x -30240\right )}{420}\) | \(44\) |
default | \(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\) | \(45\) |
norman | \(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\) | \(45\) |
risch | \(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 44, normalized size = 0.79 \begin {gather*} -600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 44, normalized size = 0.79 \begin {gather*} -600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 53, normalized size = 0.95 \begin {gather*} - 600 x^{9} - \frac {2295 x^{8}}{2} - \frac {234 x^{7}}{7} + \frac {6743 x^{6}}{6} + \frac {2262 x^{5}}{5} - \frac {1641 x^{4}}{4} - \frac {754 x^{3}}{3} + 66 x^{2} + 72 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.25, size = 44, normalized size = 0.79 \begin {gather*} -600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 44, normalized size = 0.79 \begin {gather*} -600\,x^9-\frac {2295\,x^8}{2}-\frac {234\,x^7}{7}+\frac {6743\,x^6}{6}+\frac {2262\,x^5}{5}-\frac {1641\,x^4}{4}-\frac {754\,x^3}{3}+66\,x^2+72\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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