Optimal. Leaf size=45 \[ -\frac {50}{729} (3 x+2)^9+\frac {65}{216} (3 x+2)^8-\frac {8}{63} (3 x+2)^7+\frac {7}{486} (3 x+2)^6 \]
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Rubi [A] time = 0.02, antiderivative size = 45, 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} \[ -\frac {50}{729} (3 x+2)^9+\frac {65}{216} (3 x+2)^8-\frac {8}{63} (3 x+2)^7+\frac {7}{486} (3 x+2)^6 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^5 (3+5 x)^2 \, dx &=\int \left (\frac {7}{27} (2+3 x)^5-\frac {8}{3} (2+3 x)^6+\frac {65}{9} (2+3 x)^7-\frac {50}{27} (2+3 x)^8\right ) \, dx\\ &=\frac {7}{486} (2+3 x)^6-\frac {8}{63} (2+3 x)^7+\frac {65}{216} (2+3 x)^8-\frac {50}{729} (2+3 x)^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 52, normalized size = 1.16 \[ -1350 x^9-\frac {49005 x^8}{8}-\frac {79434 x^7}{7}-\frac {20631 x^6}{2}-3390 x^5+2090 x^4+\frac {8240 x^3}{3}+1272 x^2+288 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 44, normalized size = 0.98 \[ -1350 x^{9} - \frac {49005}{8} x^{8} - \frac {79434}{7} x^{7} - \frac {20631}{2} x^{6} - 3390 x^{5} + 2090 x^{4} + \frac {8240}{3} x^{3} + 1272 x^{2} + 288 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 44, normalized size = 0.98 \[ -1350 \, x^{9} - \frac {49005}{8} \, x^{8} - \frac {79434}{7} \, x^{7} - \frac {20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac {8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 1.00 \[ -1350 x^{9}-\frac {49005}{8} x^{8}-\frac {79434}{7} x^{7}-\frac {20631}{2} x^{6}-3390 x^{5}+2090 x^{4}+\frac {8240}{3} x^{3}+1272 x^{2}+288 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 44, normalized size = 0.98 \[ -1350 \, x^{9} - \frac {49005}{8} \, x^{8} - \frac {79434}{7} \, x^{7} - \frac {20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac {8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 44, normalized size = 0.98 \[ -1350\,x^9-\frac {49005\,x^8}{8}-\frac {79434\,x^7}{7}-\frac {20631\,x^6}{2}-3390\,x^5+2090\,x^4+\frac {8240\,x^3}{3}+1272\,x^2+288\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 49, normalized size = 1.09 \[ - 1350 x^{9} - \frac {49005 x^{8}}{8} - \frac {79434 x^{7}}{7} - \frac {20631 x^{6}}{2} - 3390 x^{5} + 2090 x^{4} + \frac {8240 x^{3}}{3} + 1272 x^{2} + 288 x \]
Verification of antiderivative is not currently implemented for this CAS.
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