Optimal. Leaf size=80 \[ 144 x+384 x^2+\frac {3016 x^3}{3}+1838 x^4+\frac {14801 x^5}{5}+\frac {10771 x^6}{3}+\frac {27763 x^7}{7}+3315 x^8+\frac {24859 x^9}{9}+1571 x^{10}+\frac {11525 x^{11}}{11}+\frac {875 x^{12}}{3}+\frac {2500 x^{13}}{13} \]
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Rubi [A]
time = 0.04, antiderivative size = 80, 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 {2500 x^{13}}{13}+\frac {875 x^{12}}{3}+\frac {11525 x^{11}}{11}+1571 x^{10}+\frac {24859 x^9}{9}+3315 x^8+\frac {27763 x^7}{7}+\frac {10771 x^6}{3}+\frac {14801 x^5}{5}+1838 x^4+\frac {3016 x^3}{3}+384 x^2+144 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 )^4 \, dx &=\int \left (144+768 x+3016 x^2+7352 x^3+14801 x^4+21542 x^5+27763 x^6+26520 x^7+24859 x^8+15710 x^9+11525 x^{10}+3500 x^{11}+2500 x^{12}\right ) \, dx\\ &=144 x+384 x^2+\frac {3016 x^3}{3}+1838 x^4+\frac {14801 x^5}{5}+\frac {10771 x^6}{3}+\frac {27763 x^7}{7}+3315 x^8+\frac {24859 x^9}{9}+1571 x^{10}+\frac {11525 x^{11}}{11}+\frac {875 x^{12}}{3}+\frac {2500 x^{13}}{13}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 80, normalized size = 1.00 \begin {gather*} 144 x+384 x^2+\frac {3016 x^3}{3}+1838 x^4+\frac {14801 x^5}{5}+\frac {10771 x^6}{3}+\frac {27763 x^7}{7}+3315 x^8+\frac {24859 x^9}{9}+1571 x^{10}+\frac {11525 x^{11}}{11}+\frac {875 x^{12}}{3}+\frac {2500 x^{13}}{13} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 65, normalized size = 0.81
method | result | size |
gosper | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
default | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
norman | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
risch | \(144 x +384 x^{2}+\frac {3016}{3} x^{3}+1838 x^{4}+\frac {14801}{5} x^{5}+\frac {10771}{3} x^{6}+\frac {27763}{7} x^{7}+3315 x^{8}+\frac {24859}{9} x^{9}+1571 x^{10}+\frac {11525}{11} x^{11}+\frac {875}{3} x^{12}+\frac {2500}{13} x^{13}\) | \(65\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 64, normalized size = 0.80 \begin {gather*} \frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.70, size = 64, normalized size = 0.80 \begin {gather*} \frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 76, normalized size = 0.95 \begin {gather*} \frac {2500 x^{13}}{13} + \frac {875 x^{12}}{3} + \frac {11525 x^{11}}{11} + 1571 x^{10} + \frac {24859 x^{9}}{9} + 3315 x^{8} + \frac {27763 x^{7}}{7} + \frac {10771 x^{6}}{3} + \frac {14801 x^{5}}{5} + 1838 x^{4} + \frac {3016 x^{3}}{3} + 384 x^{2} + 144 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.55, size = 64, normalized size = 0.80 \begin {gather*} \frac {2500}{13} \, x^{13} + \frac {875}{3} \, x^{12} + \frac {11525}{11} \, x^{11} + 1571 \, x^{10} + \frac {24859}{9} \, x^{9} + 3315 \, x^{8} + \frac {27763}{7} \, x^{7} + \frac {10771}{3} \, x^{6} + \frac {14801}{5} \, x^{5} + 1838 \, x^{4} + \frac {3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 64, normalized size = 0.80 \begin {gather*} \frac {2500\,x^{13}}{13}+\frac {875\,x^{12}}{3}+\frac {11525\,x^{11}}{11}+1571\,x^{10}+\frac {24859\,x^9}{9}+3315\,x^8+\frac {27763\,x^7}{7}+\frac {10771\,x^6}{3}+\frac {14801\,x^5}{5}+1838\,x^4+\frac {3016\,x^3}{3}+384\,x^2+144\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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