Optimal. Leaf size=51 \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]
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Rubi [A] time = 0.0201723, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+276 x-202 x^2-2045 x^3-1828 x^4+3087 x^5+5940 x^6+2700 x^7\right ) \, dx\\ &=72 x+138 x^2-\frac{202 x^3}{3}-\frac{2045 x^4}{4}-\frac{1828 x^5}{5}+\frac{1029 x^6}{2}+\frac{5940 x^7}{7}+\frac{675 x^8}{2}\\ \end{align*}
Mathematica [A] time = 0.0021384, size = 51, normalized size = 1. \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 40, normalized size = 0.8 \begin{align*} 72\,x+138\,{x}^{2}-{\frac{202\,{x}^{3}}{3}}-{\frac{2045\,{x}^{4}}{4}}-{\frac{1828\,{x}^{5}}{5}}+{\frac{1029\,{x}^{6}}{2}}+{\frac{5940\,{x}^{7}}{7}}+{\frac{675\,{x}^{8}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10531, size = 53, normalized size = 1.04 \begin{align*} \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33593, size = 124, normalized size = 2.43 \begin{align*} \frac{675}{2} x^{8} + \frac{5940}{7} x^{7} + \frac{1029}{2} x^{6} - \frac{1828}{5} x^{5} - \frac{2045}{4} x^{4} - \frac{202}{3} x^{3} + 138 x^{2} + 72 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.064331, size = 48, normalized size = 0.94 \begin{align*} \frac{675 x^{8}}{2} + \frac{5940 x^{7}}{7} + \frac{1029 x^{6}}{2} - \frac{1828 x^{5}}{5} - \frac{2045 x^{4}}{4} - \frac{202 x^{3}}{3} + 138 x^{2} + 72 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.38317, size = 53, normalized size = 1.04 \begin{align*} \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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