Optimal. Leaf size=44 \[ \frac{50 x^7}{7}+\frac{35 x^6}{6}+\frac{103 x^5}{5}+\frac{85 x^4}{4}+\frac{83 x^3}{3}+16 x^2+12 x \]
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Rubi [A] time = 0.0285789, antiderivative size = 44, normalized size of antiderivative = 1., 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} \[ \frac{50 x^7}{7}+\frac{35 x^6}{6}+\frac{103 x^5}{5}+\frac{85 x^4}{4}+\frac{83 x^3}{3}+16 x^2+12 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right )^2 \, dx &=\int \left (12+32 x+83 x^2+85 x^3+103 x^4+35 x^5+50 x^6\right ) \, dx\\ &=12 x+16 x^2+\frac{83 x^3}{3}+\frac{85 x^4}{4}+\frac{103 x^5}{5}+\frac{35 x^6}{6}+\frac{50 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.001421, size = 44, normalized size = 1. \[ \frac{50 x^7}{7}+\frac{35 x^6}{6}+\frac{103 x^5}{5}+\frac{85 x^4}{4}+\frac{83 x^3}{3}+16 x^2+12 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 35, normalized size = 0.8 \begin{align*} 12\,x+16\,{x}^{2}+{\frac{83\,{x}^{3}}{3}}+{\frac{85\,{x}^{4}}{4}}+{\frac{103\,{x}^{5}}{5}}+{\frac{35\,{x}^{6}}{6}}+{\frac{50\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960582, size = 46, normalized size = 1.05 \begin{align*} \frac{50}{7} \, x^{7} + \frac{35}{6} \, x^{6} + \frac{103}{5} \, x^{5} + \frac{85}{4} \, x^{4} + \frac{83}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.711843, size = 96, normalized size = 2.18 \begin{align*} \frac{50}{7} x^{7} + \frac{35}{6} x^{6} + \frac{103}{5} x^{5} + \frac{85}{4} x^{4} + \frac{83}{3} x^{3} + 16 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079116, size = 41, normalized size = 0.93 \begin{align*} \frac{50 x^{7}}{7} + \frac{35 x^{6}}{6} + \frac{103 x^{5}}{5} + \frac{85 x^{4}}{4} + \frac{83 x^{3}}{3} + 16 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18458, size = 46, normalized size = 1.05 \begin{align*} \frac{50}{7} \, x^{7} + \frac{35}{6} \, x^{6} + \frac{103}{5} \, x^{5} + \frac{85}{4} \, x^{4} + \frac{83}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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