Optimal. Leaf size=60 \[ \frac {100 x^9}{9}-\frac {45 x^8}{8}+\frac {111 x^7}{7}-\frac {37 x^6}{6}+\frac {148 x^5}{5}+\frac {65 x^4}{4}+\frac {107 x^3}{3}+\frac {33 x^2}{2}+18 x \]
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Rubi [A] time = 0.04, antiderivative size = 60, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {1657} \[ \frac {100 x^9}{9}-\frac {45 x^8}{8}+\frac {111 x^7}{7}-\frac {37 x^6}{6}+\frac {148 x^5}{5}+\frac {65 x^4}{4}+\frac {107 x^3}{3}+\frac {33 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin {align*} \int \left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (18+33 x+107 x^2+65 x^3+148 x^4-37 x^5+111 x^6-45 x^7+100 x^8\right ) \, dx\\ &=18 x+\frac {33 x^2}{2}+\frac {107 x^3}{3}+\frac {65 x^4}{4}+\frac {148 x^5}{5}-\frac {37 x^6}{6}+\frac {111 x^7}{7}-\frac {45 x^8}{8}+\frac {100 x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 60, normalized size = 1.00 \[ \frac {100 x^9}{9}-\frac {45 x^8}{8}+\frac {111 x^7}{7}-\frac {37 x^6}{6}+\frac {148 x^5}{5}+\frac {65 x^4}{4}+\frac {107 x^3}{3}+\frac {33 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 44, normalized size = 0.73 \[ \frac {100}{9} x^{9} - \frac {45}{8} x^{8} + \frac {111}{7} x^{7} - \frac {37}{6} x^{6} + \frac {148}{5} x^{5} + \frac {65}{4} x^{4} + \frac {107}{3} x^{3} + \frac {33}{2} x^{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 44, normalized size = 0.73 \[ \frac {100}{9} \, x^{9} - \frac {45}{8} \, x^{8} + \frac {111}{7} \, x^{7} - \frac {37}{6} \, x^{6} + \frac {148}{5} \, x^{5} + \frac {65}{4} \, x^{4} + \frac {107}{3} \, x^{3} + \frac {33}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 0.75 \[ \frac {100}{9} x^{9}-\frac {45}{8} x^{8}+\frac {111}{7} x^{7}-\frac {37}{6} x^{6}+\frac {148}{5} x^{5}+\frac {65}{4} x^{4}+\frac {107}{3} x^{3}+\frac {33}{2} x^{2}+18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 44, normalized size = 0.73 \[ \frac {100}{9} \, x^{9} - \frac {45}{8} \, x^{8} + \frac {111}{7} \, x^{7} - \frac {37}{6} \, x^{6} + \frac {148}{5} \, x^{5} + \frac {65}{4} \, x^{4} + \frac {107}{3} \, x^{3} + \frac {33}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 44, normalized size = 0.73 \[ \frac {100\,x^9}{9}-\frac {45\,x^8}{8}+\frac {111\,x^7}{7}-\frac {37\,x^6}{6}+\frac {148\,x^5}{5}+\frac {65\,x^4}{4}+\frac {107\,x^3}{3}+\frac {33\,x^2}{2}+18\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 56, normalized size = 0.93 \[ \frac {100 x^{9}}{9} - \frac {45 x^{8}}{8} + \frac {111 x^{7}}{7} - \frac {37 x^{6}}{6} + \frac {148 x^{5}}{5} + \frac {65 x^{4}}{4} + \frac {107 x^{3}}{3} + \frac {33 x^{2}}{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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