Optimal. Leaf size=45 \[ -\frac{25}{324} (3 x+2)^8+\frac{65}{189} (3 x+2)^7-\frac{4}{27} (3 x+2)^6+\frac{7}{405} (3 x+2)^5 \]
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Rubi [A] time = 0.0201711, 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} \[ -\frac{25}{324} (3 x+2)^8+\frac{65}{189} (3 x+2)^7-\frac{4}{27} (3 x+2)^6+\frac{7}{405} (3 x+2)^5 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac{7}{27} (2+3 x)^4-\frac{8}{3} (2+3 x)^5+\frac{65}{9} (2+3 x)^6-\frac{50}{27} (2+3 x)^7\right ) \, dx\\ &=\frac{7}{405} (2+3 x)^5-\frac{4}{27} (2+3 x)^6+\frac{65}{189} (2+3 x)^7-\frac{25}{324} (2+3 x)^8\\ \end{align*}
Mathematica [A] time = 0.0011451, size = 47, normalized size = 1.04 \[ -\frac{2025 x^8}{4}-\frac{13635 x^7}{7}-2898 x^6-\frac{9039 x^5}{5}+94 x^4+\frac{2536 x^3}{3}+528 x^2+144 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 40, normalized size = 0.9 \begin{align*} -{\frac{2025\,{x}^{8}}{4}}-{\frac{13635\,{x}^{7}}{7}}-2898\,{x}^{6}-{\frac{9039\,{x}^{5}}{5}}+94\,{x}^{4}+{\frac{2536\,{x}^{3}}{3}}+528\,{x}^{2}+144\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14081, size = 53, normalized size = 1.18 \begin{align*} -\frac{2025}{4} \, x^{8} - \frac{13635}{7} \, x^{7} - 2898 \, x^{6} - \frac{9039}{5} \, x^{5} + 94 \, x^{4} + \frac{2536}{3} \, x^{3} + 528 \, x^{2} + 144 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29925, size = 123, normalized size = 2.73 \begin{align*} -\frac{2025}{4} x^{8} - \frac{13635}{7} x^{7} - 2898 x^{6} - \frac{9039}{5} x^{5} + 94 x^{4} + \frac{2536}{3} x^{3} + 528 x^{2} + 144 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06363, size = 44, normalized size = 0.98 \begin{align*} - \frac{2025 x^{8}}{4} - \frac{13635 x^{7}}{7} - 2898 x^{6} - \frac{9039 x^{5}}{5} + 94 x^{4} + \frac{2536 x^{3}}{3} + 528 x^{2} + 144 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.77101, size = 53, normalized size = 1.18 \begin{align*} -\frac{2025}{4} \, x^{8} - \frac{13635}{7} \, x^{7} - 2898 \, x^{6} - \frac{9039}{5} \, x^{5} + 94 \, x^{4} + \frac{2536}{3} \, x^{3} + 528 \, x^{2} + 144 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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