Optimal. Leaf size=56 \[ 54 x+\frac {27 x^2}{2}+60 x^3-5 x^4+\frac {288 x^5}{5}-\frac {83 x^6}{6}+\frac {190 x^7}{7}-\frac {9 x^8}{2}+\frac {40 x^9}{9} \]
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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 = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1671}
\begin {gather*} \frac {40 x^9}{9}-\frac {9 x^8}{2}+\frac {190 x^7}{7}-\frac {83 x^6}{6}+\frac {288 x^5}{5}-5 x^4+60 x^3+\frac {27 x^2}{2}+54 x \end {gather*}
Antiderivative was successfully verified.
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Rule 1671
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right ) \, dx &=\int \left (54+27 x+180 x^2-20 x^3+288 x^4-83 x^5+190 x^6-36 x^7+40 x^8\right ) \, dx\\ &=54 x+\frac {27 x^2}{2}+60 x^3-5 x^4+\frac {288 x^5}{5}-\frac {83 x^6}{6}+\frac {190 x^7}{7}-\frac {9 x^8}{2}+\frac {40 x^9}{9}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 56, normalized size = 1.00 \begin {gather*} 54 x+\frac {27 x^2}{2}+60 x^3-5 x^4+\frac {288 x^5}{5}-\frac {83 x^6}{6}+\frac {190 x^7}{7}-\frac {9 x^8}{2}+\frac {40 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.80
method | result | size |
gosper | \(54 x +\frac {27}{2} x^{2}+60 x^{3}-5 x^{4}+\frac {288}{5} x^{5}-\frac {83}{6} x^{6}+\frac {190}{7} x^{7}-\frac {9}{2} x^{8}+\frac {40}{9} x^{9}\) | \(45\) |
default | \(54 x +\frac {27}{2} x^{2}+60 x^{3}-5 x^{4}+\frac {288}{5} x^{5}-\frac {83}{6} x^{6}+\frac {190}{7} x^{7}-\frac {9}{2} x^{8}+\frac {40}{9} x^{9}\) | \(45\) |
norman | \(54 x +\frac {27}{2} x^{2}+60 x^{3}-5 x^{4}+\frac {288}{5} x^{5}-\frac {83}{6} x^{6}+\frac {190}{7} x^{7}-\frac {9}{2} x^{8}+\frac {40}{9} x^{9}\) | \(45\) |
risch | \(54 x +\frac {27}{2} x^{2}+60 x^{3}-5 x^{4}+\frac {288}{5} x^{5}-\frac {83}{6} x^{6}+\frac {190}{7} x^{7}-\frac {9}{2} x^{8}+\frac {40}{9} x^{9}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 44, normalized size = 0.79 \begin {gather*} \frac {40}{9} \, x^{9} - \frac {9}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {83}{6} \, x^{6} + \frac {288}{5} \, x^{5} - 5 \, x^{4} + 60 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.05, size = 44, normalized size = 0.79 \begin {gather*} \frac {40}{9} \, x^{9} - \frac {9}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {83}{6} \, x^{6} + \frac {288}{5} \, x^{5} - 5 \, x^{4} + 60 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, 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*} \frac {40 x^{9}}{9} - \frac {9 x^{8}}{2} + \frac {190 x^{7}}{7} - \frac {83 x^{6}}{6} + \frac {288 x^{5}}{5} - 5 x^{4} + 60 x^{3} + \frac {27 x^{2}}{2} + 54 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.85, size = 44, normalized size = 0.79 \begin {gather*} \frac {40}{9} \, x^{9} - \frac {9}{2} \, x^{8} + \frac {190}{7} \, x^{7} - \frac {83}{6} \, x^{6} + \frac {288}{5} \, x^{5} - 5 \, x^{4} + 60 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 44, normalized size = 0.79 \begin {gather*} \frac {40\,x^9}{9}-\frac {9\,x^8}{2}+\frac {190\,x^7}{7}-\frac {83\,x^6}{6}+\frac {288\,x^5}{5}-5\,x^4+60\,x^3+\frac {27\,x^2}{2}+54\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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