Optimal. Leaf size=54 \[ 36 x+42 x^2+\frac {241 x^3}{3}+59 x^4+78 x^5+\frac {86 x^6}{3}+\frac {321 x^7}{7}+\frac {5 x^8}{2}+\frac {100 x^9}{9} \]
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Rubi [A]
time = 0.03, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {1671}
\begin {gather*} \frac {100 x^9}{9}+\frac {5 x^8}{2}+\frac {321 x^7}{7}+\frac {86 x^6}{3}+78 x^5+59 x^4+\frac {241 x^3}{3}+42 x^2+36 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 )^2 \left (2+3 x+5 x^2\right )^2 \, dx &=\int \left (36+84 x+241 x^2+236 x^3+390 x^4+172 x^5+321 x^6+20 x^7+100 x^8\right ) \, dx\\ &=36 x+42 x^2+\frac {241 x^3}{3}+59 x^4+78 x^5+\frac {86 x^6}{3}+\frac {321 x^7}{7}+\frac {5 x^8}{2}+\frac {100 x^9}{9}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 54, normalized size = 1.00 \begin {gather*} 36 x+42 x^2+\frac {241 x^3}{3}+59 x^4+78 x^5+\frac {86 x^6}{3}+\frac {321 x^7}{7}+\frac {5 x^8}{2}+\frac {100 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 45, normalized size = 0.83
method | result | size |
gosper | \(36 x +42 x^{2}+\frac {241}{3} x^{3}+59 x^{4}+78 x^{5}+\frac {86}{3} x^{6}+\frac {321}{7} x^{7}+\frac {5}{2} x^{8}+\frac {100}{9} x^{9}\) | \(45\) |
default | \(36 x +42 x^{2}+\frac {241}{3} x^{3}+59 x^{4}+78 x^{5}+\frac {86}{3} x^{6}+\frac {321}{7} x^{7}+\frac {5}{2} x^{8}+\frac {100}{9} x^{9}\) | \(45\) |
norman | \(36 x +42 x^{2}+\frac {241}{3} x^{3}+59 x^{4}+78 x^{5}+\frac {86}{3} x^{6}+\frac {321}{7} x^{7}+\frac {5}{2} x^{8}+\frac {100}{9} x^{9}\) | \(45\) |
risch | \(36 x +42 x^{2}+\frac {241}{3} x^{3}+59 x^{4}+78 x^{5}+\frac {86}{3} x^{6}+\frac {321}{7} x^{7}+\frac {5}{2} x^{8}+\frac {100}{9} x^{9}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 44, normalized size = 0.81 \begin {gather*} \frac {100}{9} \, x^{9} + \frac {5}{2} \, x^{8} + \frac {321}{7} \, x^{7} + \frac {86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac {241}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.76, size = 44, normalized size = 0.81 \begin {gather*} \frac {100}{9} \, x^{9} + \frac {5}{2} \, x^{8} + \frac {321}{7} \, x^{7} + \frac {86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac {241}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 51, normalized size = 0.94 \begin {gather*} \frac {100 x^{9}}{9} + \frac {5 x^{8}}{2} + \frac {321 x^{7}}{7} + \frac {86 x^{6}}{3} + 78 x^{5} + 59 x^{4} + \frac {241 x^{3}}{3} + 42 x^{2} + 36 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.34, size = 44, normalized size = 0.81 \begin {gather*} \frac {100}{9} \, x^{9} + \frac {5}{2} \, x^{8} + \frac {321}{7} \, x^{7} + \frac {86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac {241}{3} \, x^{3} + 42 \, x^{2} + 36 \, 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 = 0.81 \begin {gather*} \frac {100\,x^9}{9}+\frac {5\,x^8}{2}+\frac {321\,x^7}{7}+\frac {86\,x^6}{3}+78\,x^5+59\,x^4+\frac {241\,x^3}{3}+42\,x^2+36\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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