Optimal. Leaf size=56 \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]
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Rubi [A] time = 0.0377753, antiderivative size = 56, 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} \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]
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 )^3 \, dx &=\int \left (24+100 x+322 x^2+579 x^3+876 x^4+804 x^5+720 x^6+325 x^7+250 x^8\right ) \, dx\\ &=24 x+50 x^2+\frac{322 x^3}{3}+\frac{579 x^4}{4}+\frac{876 x^5}{5}+134 x^6+\frac{720 x^7}{7}+\frac{325 x^8}{8}+\frac{250 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0017287, size = 56, normalized size = 1. \[ \frac{250 x^9}{9}+\frac{325 x^8}{8}+\frac{720 x^7}{7}+134 x^6+\frac{876 x^5}{5}+\frac{579 x^4}{4}+\frac{322 x^3}{3}+50 x^2+24 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 45, normalized size = 0.8 \begin{align*} 24\,x+50\,{x}^{2}+{\frac{322\,{x}^{3}}{3}}+{\frac{579\,{x}^{4}}{4}}+{\frac{876\,{x}^{5}}{5}}+134\,{x}^{6}+{\frac{720\,{x}^{7}}{7}}+{\frac{325\,{x}^{8}}{8}}+{\frac{250\,{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983348, size = 59, normalized size = 1.05 \begin{align*} \frac{250}{9} \, x^{9} + \frac{325}{8} \, x^{8} + \frac{720}{7} \, x^{7} + 134 \, x^{6} + \frac{876}{5} \, x^{5} + \frac{579}{4} \, x^{4} + \frac{322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.716507, size = 131, normalized size = 2.34 \begin{align*} \frac{250}{9} x^{9} + \frac{325}{8} x^{8} + \frac{720}{7} x^{7} + 134 x^{6} + \frac{876}{5} x^{5} + \frac{579}{4} x^{4} + \frac{322}{3} x^{3} + 50 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.084274, size = 53, normalized size = 0.95 \begin{align*} \frac{250 x^{9}}{9} + \frac{325 x^{8}}{8} + \frac{720 x^{7}}{7} + 134 x^{6} + \frac{876 x^{5}}{5} + \frac{579 x^{4}}{4} + \frac{322 x^{3}}{3} + 50 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17455, size = 59, normalized size = 1.05 \begin{align*} \frac{250}{9} \, x^{9} + \frac{325}{8} \, x^{8} + \frac{720}{7} \, x^{7} + 134 \, x^{6} + \frac{876}{5} \, x^{5} + \frac{579}{4} \, x^{4} + \frac{322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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