Optimal. Leaf size=45 \[ \frac{5}{162} (3 x+2)^8-\frac{16}{63} (3 x+2)^7+\frac{91}{162} (3 x+2)^6-\frac{49}{405} (3 x+2)^5 \]
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Rubi [A] time = 0.0202908, 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} \[ \frac{5}{162} (3 x+2)^8-\frac{16}{63} (3 x+2)^7+\frac{91}{162} (3 x+2)^6-\frac{49}{405} (3 x+2)^5 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx &=\int \left (-\frac{49}{27} (2+3 x)^4+\frac{91}{9} (2+3 x)^5-\frac{16}{3} (2+3 x)^6+\frac{20}{27} (2+3 x)^7\right ) \, dx\\ &=-\frac{49}{405} (2+3 x)^5+\frac{91}{162} (2+3 x)^6-\frac{16}{63} (2+3 x)^7+\frac{5}{162} (2+3 x)^8\\ \end{align*}
Mathematica [A] time = 0.0011661, size = 49, normalized size = 1.09 \[ \frac{405 x^8}{2}+\frac{3672 x^7}{7}+\frac{675 x^6}{2}-\frac{1077 x^5}{5}-328 x^4-\frac{152 x^3}{3}+88 x^2+48 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 40, normalized size = 0.9 \begin{align*}{\frac{405\,{x}^{8}}{2}}+{\frac{3672\,{x}^{7}}{7}}+{\frac{675\,{x}^{6}}{2}}-{\frac{1077\,{x}^{5}}{5}}-328\,{x}^{4}-{\frac{152\,{x}^{3}}{3}}+88\,{x}^{2}+48\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.3948, size = 53, normalized size = 1.18 \begin{align*} \frac{405}{2} \, x^{8} + \frac{3672}{7} \, x^{7} + \frac{675}{2} \, x^{6} - \frac{1077}{5} \, x^{5} - 328 \, x^{4} - \frac{152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35805, size = 117, normalized size = 2.6 \begin{align*} \frac{405}{2} x^{8} + \frac{3672}{7} x^{7} + \frac{675}{2} x^{6} - \frac{1077}{5} x^{5} - 328 x^{4} - \frac{152}{3} x^{3} + 88 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063909, size = 46, normalized size = 1.02 \begin{align*} \frac{405 x^{8}}{2} + \frac{3672 x^{7}}{7} + \frac{675 x^{6}}{2} - \frac{1077 x^{5}}{5} - 328 x^{4} - \frac{152 x^{3}}{3} + 88 x^{2} + 48 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.78927, size = 53, normalized size = 1.18 \begin{align*} \frac{405}{2} \, x^{8} + \frac{3672}{7} \, x^{7} + \frac{675}{2} \, x^{6} - \frac{1077}{5} \, x^{5} - 328 \, x^{4} - \frac{152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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