Optimal. Leaf size=56 \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]
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Rubi [A] time = 0.0237418, antiderivative size = 56, 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} \[ -\frac{4}{243} (3 x+2)^{10}+\frac{428 (3 x+2)^9}{2187}-\frac{259}{324} (3 x+2)^8+\frac{287}{243} (3 x+2)^7-\frac{343 (3 x+2)^6}{1458} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^5+\frac{2009}{81} (2+3 x)^6-\frac{518}{27} (2+3 x)^7+\frac{428}{81} (2+3 x)^8-\frac{40}{81} (2+3 x)^9\right ) \, dx\\ &=-\frac{343 (2+3 x)^6}{1458}+\frac{287}{243} (2+3 x)^7-\frac{259}{324} (2+3 x)^8+\frac{428 (2+3 x)^9}{2187}-\frac{4}{243} (2+3 x)^{10}\\ \end{align*}
Mathematica [A] time = 0.0021923, size = 53, normalized size = 0.95 \[ -972 x^{10}-2628 x^9-\frac{6291 x^8}{4}+1683 x^7+\frac{4333 x^6}{2}+14 x^5-882 x^4-256 x^3+152 x^2+96 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 50, normalized size = 0.9 \begin{align*} -972\,{x}^{10}-2628\,{x}^{9}-{\frac{6291\,{x}^{8}}{4}}+1683\,{x}^{7}+{\frac{4333\,{x}^{6}}{2}}+14\,{x}^{5}-882\,{x}^{4}-256\,{x}^{3}+152\,{x}^{2}+96\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.18748, size = 66, normalized size = 1.18 \begin{align*} -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.16307, size = 142, normalized size = 2.54 \begin{align*} -972 x^{10} - 2628 x^{9} - \frac{6291}{4} x^{8} + 1683 x^{7} + \frac{4333}{2} x^{6} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067272, size = 51, normalized size = 0.91 \begin{align*} - 972 x^{10} - 2628 x^{9} - \frac{6291 x^{8}}{4} + 1683 x^{7} + \frac{4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.56065, size = 66, normalized size = 1.18 \begin{align*} -972 \, x^{10} - 2628 \, x^{9} - \frac{6291}{4} \, x^{8} + 1683 \, x^{7} + \frac{4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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