Optimal. Leaf size=47 \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]
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Rubi [A] time = 0.0213267, antiderivative size = 47, 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} \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+12 x-395 x^2-228 x^3+1473 x^4+1162 x^5-1860 x^6-1800 x^7\right ) \, dx\\ &=36 x+6 x^2-\frac{395 x^3}{3}-57 x^4+\frac{1473 x^5}{5}+\frac{581 x^6}{3}-\frac{1860 x^7}{7}-225 x^8\\ \end{align*}
Mathematica [A] time = 0.0013372, size = 47, normalized size = 1. \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 40, normalized size = 0.9 \begin{align*} 36\,x+6\,{x}^{2}-{\frac{395\,{x}^{3}}{3}}-57\,{x}^{4}+{\frac{1473\,{x}^{5}}{5}}+{\frac{581\,{x}^{6}}{3}}-{\frac{1860\,{x}^{7}}{7}}-225\,{x}^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01445, size = 53, normalized size = 1.13 \begin{align*} -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.09715, size = 113, normalized size = 2.4 \begin{align*} -225 x^{8} - \frac{1860}{7} x^{7} + \frac{581}{3} x^{6} + \frac{1473}{5} x^{5} - 57 x^{4} - \frac{395}{3} x^{3} + 6 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06397, size = 44, normalized size = 0.94 \begin{align*} - 225 x^{8} - \frac{1860 x^{7}}{7} + \frac{581 x^{6}}{3} + \frac{1473 x^{5}}{5} - 57 x^{4} - \frac{395 x^{3}}{3} + 6 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.66295, size = 53, normalized size = 1.13 \begin{align*} -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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