Optimal. Leaf size=45 \[ -135 x^8-\frac{1188 x^7}{7}+111 x^6+\frac{949 x^5}{5}-\frac{117 x^4}{4}-86 x^3+2 x^2+24 x \]
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Rubi [A] time = 0.0185275, antiderivative size = 45, 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} \[ -135 x^8-\frac{1188 x^7}{7}+111 x^6+\frac{949 x^5}{5}-\frac{117 x^4}{4}-86 x^3+2 x^2+24 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx &=\int \left (24+4 x-258 x^2-117 x^3+949 x^4+666 x^5-1188 x^6-1080 x^7\right ) \, dx\\ &=24 x+2 x^2-86 x^3-\frac{117 x^4}{4}+\frac{949 x^5}{5}+111 x^6-\frac{1188 x^7}{7}-135 x^8\\ \end{align*}
Mathematica [A] time = 0.0013432, size = 45, normalized size = 1. \[ -135 x^8-\frac{1188 x^7}{7}+111 x^6+\frac{949 x^5}{5}-\frac{117 x^4}{4}-86 x^3+2 x^2+24 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 40, normalized size = 0.9 \begin{align*} 24\,x+2\,{x}^{2}-86\,{x}^{3}-{\frac{117\,{x}^{4}}{4}}+{\frac{949\,{x}^{5}}{5}}+111\,{x}^{6}-{\frac{1188\,{x}^{7}}{7}}-135\,{x}^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00307, size = 53, normalized size = 1.18 \begin{align*} -135 \, x^{8} - \frac{1188}{7} \, x^{7} + 111 \, x^{6} + \frac{949}{5} \, x^{5} - \frac{117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.12778, size = 109, normalized size = 2.42 \begin{align*} -135 x^{8} - \frac{1188}{7} x^{7} + 111 x^{6} + \frac{949}{5} x^{5} - \frac{117}{4} x^{4} - 86 x^{3} + 2 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063556, size = 42, normalized size = 0.93 \begin{align*} - 135 x^{8} - \frac{1188 x^{7}}{7} + 111 x^{6} + \frac{949 x^{5}}{5} - \frac{117 x^{4}}{4} - 86 x^{3} + 2 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.89353, size = 53, normalized size = 1.18 \begin{align*} -135 \, x^{8} - \frac{1188}{7} \, x^{7} + 111 \, x^{6} + \frac{949}{5} \, x^{5} - \frac{117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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