Optimal. Leaf size=47 \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]
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Rubi [A] time = 0.0181664, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx &=\int \left (54+27 x-603 x^2-425 x^3+2277 x^4+2010 x^5-2900 x^6-3000 x^7\right ) \, dx\\ &=54 x+\frac{27 x^2}{2}-201 x^3-\frac{425 x^4}{4}+\frac{2277 x^5}{5}+335 x^6-\frac{2900 x^7}{7}-375 x^8\\ \end{align*}
Mathematica [A] time = 0.0010069, size = 47, normalized size = 1. \[ -375 x^8-\frac{2900 x^7}{7}+335 x^6+\frac{2277 x^5}{5}-\frac{425 x^4}{4}-201 x^3+\frac{27 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 40, normalized size = 0.9 \begin{align*} 54\,x+{\frac{27\,{x}^{2}}{2}}-201\,{x}^{3}-{\frac{425\,{x}^{4}}{4}}+{\frac{2277\,{x}^{5}}{5}}+335\,{x}^{6}-{\frac{2900\,{x}^{7}}{7}}-375\,{x}^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03634, size = 53, normalized size = 1.13 \begin{align*} -375 \, x^{8} - \frac{2900}{7} \, x^{7} + 335 \, x^{6} + \frac{2277}{5} \, x^{5} - \frac{425}{4} \, x^{4} - 201 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.00643, size = 116, normalized size = 2.47 \begin{align*} -375 x^{8} - \frac{2900}{7} x^{7} + 335 x^{6} + \frac{2277}{5} x^{5} - \frac{425}{4} x^{4} - 201 x^{3} + \frac{27}{2} x^{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063234, size = 44, normalized size = 0.94 \begin{align*} - 375 x^{8} - \frac{2900 x^{7}}{7} + 335 x^{6} + \frac{2277 x^{5}}{5} - \frac{425 x^{4}}{4} - 201 x^{3} + \frac{27 x^{2}}{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.46492, size = 53, normalized size = 1.13 \begin{align*} -375 \, x^{8} - \frac{2900}{7} \, x^{7} + 335 \, x^{6} + \frac{2277}{5} \, x^{5} - \frac{425}{4} \, x^{4} - 201 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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