Optimal. Leaf size=46 \[ \frac {20 x^7}{7}-\frac {4 x^6}{3}+\frac {61 x^5}{5}+\frac {x^4}{4}+\frac {53 x^3}{3}+\frac {15 x^2}{2}+18 x \]
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Rubi [A] time = 0.03, antiderivative size = 46, 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 = {1657} \[ \frac {20 x^7}{7}-\frac {4 x^6}{3}+\frac {61 x^5}{5}+\frac {x^4}{4}+\frac {53 x^3}{3}+\frac {15 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right ) \, dx &=\int \left (18+15 x+53 x^2+x^3+61 x^4-8 x^5+20 x^6\right ) \, dx\\ &=18 x+\frac {15 x^2}{2}+\frac {53 x^3}{3}+\frac {x^4}{4}+\frac {61 x^5}{5}-\frac {4 x^6}{3}+\frac {20 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 46, normalized size = 1.00 \[ \frac {20 x^7}{7}-\frac {4 x^6}{3}+\frac {61 x^5}{5}+\frac {x^4}{4}+\frac {53 x^3}{3}+\frac {15 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 34, normalized size = 0.74 \[ \frac {20}{7} x^{7} - \frac {4}{3} x^{6} + \frac {61}{5} x^{5} + \frac {1}{4} x^{4} + \frac {53}{3} x^{3} + \frac {15}{2} x^{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 34, normalized size = 0.74 \[ \frac {20}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {61}{5} \, x^{5} + \frac {1}{4} \, x^{4} + \frac {53}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.76 \[ \frac {20}{7} x^{7}-\frac {4}{3} x^{6}+\frac {61}{5} x^{5}+\frac {1}{4} x^{4}+\frac {53}{3} x^{3}+\frac {15}{2} x^{2}+18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 34, normalized size = 0.74 \[ \frac {20}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {61}{5} \, x^{5} + \frac {1}{4} \, x^{4} + \frac {53}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.74 \[ \frac {20\,x^7}{7}-\frac {4\,x^6}{3}+\frac {61\,x^5}{5}+\frac {x^4}{4}+\frac {53\,x^3}{3}+\frac {15\,x^2}{2}+18\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 41, normalized size = 0.89 \[ \frac {20 x^{7}}{7} - \frac {4 x^{6}}{3} + \frac {61 x^{5}}{5} + \frac {x^{4}}{4} + \frac {53 x^{3}}{3} + \frac {15 x^{2}}{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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