Optimal. Leaf size=68 \[ 108 x+108 x^2+237 x^3+\frac {635 x^4}{4}+\frac {1416 x^5}{5}+\frac {299 x^6}{3}+\frac {1571 x^7}{7}+\frac {83 x^8}{8}+\frac {922 x^9}{9}-6 x^{10}+\frac {200 x^{11}}{11} \]
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Rubi [A]
time = 0.03, antiderivative size = 68, 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 {200 x^{11}}{11}-6 x^{10}+\frac {922 x^9}{9}+\frac {83 x^8}{8}+\frac {1571 x^7}{7}+\frac {299 x^6}{3}+\frac {1416 x^5}{5}+\frac {635 x^4}{4}+237 x^3+108 x^2+108 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 )^2 \, dx &=\int \left (108+216 x+711 x^2+635 x^3+1416 x^4+598 x^5+1571 x^6+83 x^7+922 x^8-60 x^9+200 x^{10}\right ) \, dx\\ &=108 x+108 x^2+237 x^3+\frac {635 x^4}{4}+\frac {1416 x^5}{5}+\frac {299 x^6}{3}+\frac {1571 x^7}{7}+\frac {83 x^8}{8}+\frac {922 x^9}{9}-6 x^{10}+\frac {200 x^{11}}{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 68, normalized size = 1.00 \begin {gather*} 108 x+108 x^2+237 x^3+\frac {635 x^4}{4}+\frac {1416 x^5}{5}+\frac {299 x^6}{3}+\frac {1571 x^7}{7}+\frac {83 x^8}{8}+\frac {922 x^9}{9}-6 x^{10}+\frac {200 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 55, normalized size = 0.81
method | result | size |
gosper | \(108 x +108 x^{2}+237 x^{3}+\frac {635}{4} x^{4}+\frac {1416}{5} x^{5}+\frac {299}{3} x^{6}+\frac {1571}{7} x^{7}+\frac {83}{8} x^{8}+\frac {922}{9} x^{9}-6 x^{10}+\frac {200}{11} x^{11}\) | \(55\) |
default | \(108 x +108 x^{2}+237 x^{3}+\frac {635}{4} x^{4}+\frac {1416}{5} x^{5}+\frac {299}{3} x^{6}+\frac {1571}{7} x^{7}+\frac {83}{8} x^{8}+\frac {922}{9} x^{9}-6 x^{10}+\frac {200}{11} x^{11}\) | \(55\) |
norman | \(108 x +108 x^{2}+237 x^{3}+\frac {635}{4} x^{4}+\frac {1416}{5} x^{5}+\frac {299}{3} x^{6}+\frac {1571}{7} x^{7}+\frac {83}{8} x^{8}+\frac {922}{9} x^{9}-6 x^{10}+\frac {200}{11} x^{11}\) | \(55\) |
risch | \(108 x +108 x^{2}+237 x^{3}+\frac {635}{4} x^{4}+\frac {1416}{5} x^{5}+\frac {299}{3} x^{6}+\frac {1571}{7} x^{7}+\frac {83}{8} x^{8}+\frac {922}{9} x^{9}-6 x^{10}+\frac {200}{11} x^{11}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 54, normalized size = 0.79 \begin {gather*} \frac {200}{11} \, x^{11} - 6 \, x^{10} + \frac {922}{9} \, x^{9} + \frac {83}{8} \, x^{8} + \frac {1571}{7} \, x^{7} + \frac {299}{3} \, x^{6} + \frac {1416}{5} \, x^{5} + \frac {635}{4} \, x^{4} + 237 \, x^{3} + 108 \, x^{2} + 108 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.04, size = 54, normalized size = 0.79 \begin {gather*} \frac {200}{11} \, x^{11} - 6 \, x^{10} + \frac {922}{9} \, x^{9} + \frac {83}{8} \, x^{8} + \frac {1571}{7} \, x^{7} + \frac {299}{3} \, x^{6} + \frac {1416}{5} \, x^{5} + \frac {635}{4} \, x^{4} + 237 \, x^{3} + 108 \, x^{2} + 108 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 65, normalized size = 0.96 \begin {gather*} \frac {200 x^{11}}{11} - 6 x^{10} + \frac {922 x^{9}}{9} + \frac {83 x^{8}}{8} + \frac {1571 x^{7}}{7} + \frac {299 x^{6}}{3} + \frac {1416 x^{5}}{5} + \frac {635 x^{4}}{4} + 237 x^{3} + 108 x^{2} + 108 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.63, size = 54, normalized size = 0.79 \begin {gather*} \frac {200}{11} \, x^{11} - 6 \, x^{10} + \frac {922}{9} \, x^{9} + \frac {83}{8} \, x^{8} + \frac {1571}{7} \, x^{7} + \frac {299}{3} \, x^{6} + \frac {1416}{5} \, x^{5} + \frac {635}{4} \, x^{4} + 237 \, x^{3} + 108 \, x^{2} + 108 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 54, normalized size = 0.79 \begin {gather*} \frac {200\,x^{11}}{11}-6\,x^{10}+\frac {922\,x^9}{9}+\frac {83\,x^8}{8}+\frac {1571\,x^7}{7}+\frac {299\,x^6}{3}+\frac {1416\,x^5}{5}+\frac {635\,x^4}{4}+237\,x^3+108\,x^2+108\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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