Optimal. Leaf size=56 \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]
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Rubi [A] time = 0.0230412, antiderivative size = 56, 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} \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+132 x-754 x^2-1641 x^3+2262 x^4+6743 x^5-234 x^6-9180 x^7-5400 x^8\right ) \, dx\\ &=72 x+66 x^2-\frac{754 x^3}{3}-\frac{1641 x^4}{4}+\frac{2262 x^5}{5}+\frac{6743 x^6}{6}-\frac{234 x^7}{7}-\frac{2295 x^8}{2}-600 x^9\\ \end{align*}
Mathematica [A] time = 0.0022935, size = 56, normalized size = 1. \[ -600 x^9-\frac{2295 x^8}{2}-\frac{234 x^7}{7}+\frac{6743 x^6}{6}+\frac{2262 x^5}{5}-\frac{1641 x^4}{4}-\frac{754 x^3}{3}+66 x^2+72 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 0.8 \begin{align*} 72\,x+66\,{x}^{2}-{\frac{754\,{x}^{3}}{3}}-{\frac{1641\,{x}^{4}}{4}}+{\frac{2262\,{x}^{5}}{5}}+{\frac{6743\,{x}^{6}}{6}}-{\frac{234\,{x}^{7}}{7}}-{\frac{2295\,{x}^{8}}{2}}-600\,{x}^{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01818, size = 59, normalized size = 1.05 \begin{align*} -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.18955, size = 138, normalized size = 2.46 \begin{align*} -600 x^{9} - \frac{2295}{2} x^{8} - \frac{234}{7} x^{7} + \frac{6743}{6} x^{6} + \frac{2262}{5} x^{5} - \frac{1641}{4} x^{4} - \frac{754}{3} x^{3} + 66 x^{2} + 72 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06655, size = 53, normalized size = 0.95 \begin{align*} - 600 x^{9} - \frac{2295 x^{8}}{2} - \frac{234 x^{7}}{7} + \frac{6743 x^{6}}{6} + \frac{2262 x^{5}}{5} - \frac{1641 x^{4}}{4} - \frac{754 x^{3}}{3} + 66 x^{2} + 72 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.98643, size = 59, normalized size = 1.05 \begin{align*} -600 \, x^{9} - \frac{2295}{2} \, x^{8} - \frac{234}{7} \, x^{7} + \frac{6743}{6} \, x^{6} + \frac{2262}{5} \, x^{5} - \frac{1641}{4} \, x^{4} - \frac{754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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