Optimal. Leaf size=67 \[ \frac {125 (3 x+2)^{12}}{2187}-\frac {3800 (3 x+2)^{11}}{8019}+\frac {1657 (3 x+2)^{10}}{1458}-\frac {4099 (3 x+2)^9}{6561}+\frac {763 (3 x+2)^8}{5832}-\frac {7}{729} (3 x+2)^7 \]
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Rubi [A] time = 0.03, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {125 (3 x+2)^{12}}{2187}-\frac {3800 (3 x+2)^{11}}{8019}+\frac {1657 (3 x+2)^{10}}{1458}-\frac {4099 (3 x+2)^9}{6561}+\frac {763 (3 x+2)^8}{5832}-\frac {7}{729} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^6+\frac {763}{243} (2+3 x)^7-\frac {4099}{243} (2+3 x)^8+\frac {8285}{243} (2+3 x)^9-\frac {3800}{243} (2+3 x)^{10}+\frac {500}{243} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {7}{729} (2+3 x)^7+\frac {763 (2+3 x)^8}{5832}-\frac {4099 (2+3 x)^9}{6561}+\frac {1657 (2+3 x)^{10}}{1458}-\frac {3800 (2+3 x)^{11}}{8019}+\frac {125 (2+3 x)^{12}}{2187}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 67, normalized size = 1.00 \[ 30375 x^{12}+\frac {1749600 x^{11}}{11}+\frac {685017 x^{10}}{2}+363093 x^9+\frac {1081971 x^8}{8}-110115 x^7-\frac {464744 x^6}{3}-61804 x^5+10172 x^4+20208 x^3+8640 x^2+1728 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 59, normalized size = 0.88 \[ 30375 x^{12} + \frac {1749600}{11} x^{11} + \frac {685017}{2} x^{10} + 363093 x^{9} + \frac {1081971}{8} x^{8} - 110115 x^{7} - \frac {464744}{3} x^{6} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 59, normalized size = 0.88 \[ 30375 \, x^{12} + \frac {1749600}{11} \, x^{11} + \frac {685017}{2} \, x^{10} + 363093 \, x^{9} + \frac {1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac {464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 60, normalized size = 0.90 \[ 30375 x^{12}+\frac {1749600}{11} x^{11}+\frac {685017}{2} x^{10}+363093 x^{9}+\frac {1081971}{8} x^{8}-110115 x^{7}-\frac {464744}{3} x^{6}-61804 x^{5}+10172 x^{4}+20208 x^{3}+8640 x^{2}+1728 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 59, normalized size = 0.88 \[ 30375 \, x^{12} + \frac {1749600}{11} \, x^{11} + \frac {685017}{2} \, x^{10} + 363093 \, x^{9} + \frac {1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac {464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 59, normalized size = 0.88 \[ 30375\,x^{12}+\frac {1749600\,x^{11}}{11}+\frac {685017\,x^{10}}{2}+363093\,x^9+\frac {1081971\,x^8}{8}-110115\,x^7-\frac {464744\,x^6}{3}-61804\,x^5+10172\,x^4+20208\,x^3+8640\,x^2+1728\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 0.97 \[ 30375 x^{12} + \frac {1749600 x^{11}}{11} + \frac {685017 x^{10}}{2} + 363093 x^{9} + \frac {1081971 x^{8}}{8} - 110115 x^{7} - \frac {464744 x^{6}}{3} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \]
Verification of antiderivative is not currently implemented for this CAS.
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