Optimal. Leaf size=34 \[ -\frac {10}{243} (3 x+2)^9+\frac {37}{216} (3 x+2)^8-\frac {1}{27} (3 x+2)^7 \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \[ -\frac {10}{243} (3 x+2)^9+\frac {37}{216} (3 x+2)^8-\frac {1}{27} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^6+\frac {37}{9} (2+3 x)^7-\frac {10}{9} (2+3 x)^8\right ) \, dx\\ &=-\frac {1}{27} (2+3 x)^7+\frac {37}{216} (2+3 x)^8-\frac {10}{243} (2+3 x)^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 48, normalized size = 1.41 \[ -810 x^9-\frac {29889 x^8}{8}-7047 x^7-6552 x^6-2268 x^5+1260 x^4+\frac {5264 x^3}{3}+832 x^2+192 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 44, normalized size = 1.29 \[ -810 x^{9} - \frac {29889}{8} x^{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac {5264}{3} x^{3} + 832 x^{2} + 192 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 44, normalized size = 1.29 \[ -810 \, x^{9} - \frac {29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac {5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 1.32 \[ -810 x^{9}-\frac {29889}{8} x^{8}-7047 x^{7}-6552 x^{6}-2268 x^{5}+1260 x^{4}+\frac {5264}{3} x^{3}+832 x^{2}+192 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 44, normalized size = 1.29 \[ -810 \, x^{9} - \frac {29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac {5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 44, normalized size = 1.29 \[ -810\,x^9-\frac {29889\,x^8}{8}-7047\,x^7-6552\,x^6-2268\,x^5+1260\,x^4+\frac {5264\,x^3}{3}+832\,x^2+192\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 46, normalized size = 1.35 \[ - 810 x^{9} - \frac {29889 x^{8}}{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac {5264 x^{3}}{3} + 832 x^{2} + 192 x \]
Verification of antiderivative is not currently implemented for this CAS.
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