Optimal. Leaf size=45 \[ \frac {5}{243} (3 x+2)^{12}-\frac {16}{99} (3 x+2)^{11}+\frac {91}{270} (3 x+2)^{10}-\frac {49}{729} (3 x+2)^9 \]
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Rubi [A] time = 0.03, 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} \begin {gather*} \frac {5}{243} (3 x+2)^{12}-\frac {16}{99} (3 x+2)^{11}+\frac {91}{270} (3 x+2)^{10}-\frac {49}{729} (3 x+2)^9 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^8+\frac {91}{9} (2+3 x)^9-\frac {16}{3} (2+3 x)^{10}+\frac {20}{27} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {49}{729} (2+3 x)^9+\frac {91}{270} (2+3 x)^{10}-\frac {16}{99} (2+3 x)^{11}+\frac {5}{243} (2+3 x)^{12}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 67, normalized size = 1.49 \begin {gather*} 10935 x^{12}+\frac {647352 x^{11}}{11}+\frac {1307097 x^{10}}{10}+144315 x^9+59616 x^8-39312 x^7-62160 x^6-\frac {134112 x^5}{5}+3200 x^4+\frac {24832 x^3}{3}+3712 x^2+768 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.78, size = 59, normalized size = 1.31 \begin {gather*} 10935 x^{12} + \frac {647352}{11} x^{11} + \frac {1307097}{10} x^{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac {134112}{5} x^{5} + 3200 x^{4} + \frac {24832}{3} x^{3} + 3712 x^{2} + 768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 59, normalized size = 1.31 \begin {gather*} 10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 60, normalized size = 1.33 \begin {gather*} 10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 59, normalized size = 1.31 \begin {gather*} 10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 59, normalized size = 1.31 \begin {gather*} 10935\,x^{12}+\frac {647352\,x^{11}}{11}+\frac {1307097\,x^{10}}{10}+144315\,x^9+59616\,x^8-39312\,x^7-62160\,x^6-\frac {134112\,x^5}{5}+3200\,x^4+\frac {24832\,x^3}{3}+3712\,x^2+768\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 1.44 \begin {gather*} 10935 x^{12} + \frac {647352 x^{11}}{11} + \frac {1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac {134112 x^{5}}{5} + 3200 x^{4} + \frac {24832 x^{3}}{3} + 3712 x^{2} + 768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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