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 = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 0.57, size = 49, normalized size = 0.88 \[ -972 x^{10} - 2628 x^{9} - \frac {6291}{4} x^{8} + 1683 x^{7} + \frac {4333}{2} x^{6} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 49, normalized size = 0.88 \[ -972 \, x^{10} - 2628 \, x^{9} - \frac {6291}{4} \, x^{8} + 1683 \, x^{7} + \frac {4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 50, normalized size = 0.89 \[ -972 x^{10}-2628 x^{9}-\frac {6291}{4} x^{8}+1683 x^{7}+\frac {4333}{2} x^{6}+14 x^{5}-882 x^{4}-256 x^{3}+152 x^{2}+96 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 49, normalized size = 0.88 \[ -972 \, x^{10} - 2628 \, x^{9} - \frac {6291}{4} \, x^{8} + 1683 \, x^{7} + \frac {4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 0.88 \[ -972\,x^{10}-2628\,x^9-\frac {6291\,x^8}{4}+1683\,x^7+\frac {4333\,x^6}{2}+14\,x^5-882\,x^4-256\,x^3+152\,x^2+96\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 51, normalized size = 0.91 \[ - 972 x^{10} - 2628 x^{9} - \frac {6291 x^{8}}{4} + 1683 x^{7} + \frac {4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \]
Verification of antiderivative is not currently implemented for this CAS.
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