Optimal. Leaf size=34 \[ -\frac {10}{297} (3 x+2)^{11}+\frac {37}{270} (3 x+2)^{10}-\frac {7}{243} (3 x+2)^9 \]
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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} \begin {gather*} -\frac {10}{297} (3 x+2)^{11}+\frac {37}{270} (3 x+2)^{10}-\frac {7}{243} (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+3 x)^8 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^8+\frac {37}{9} (2+3 x)^9-\frac {10}{9} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {7}{243} (2+3 x)^9+\frac {37}{270} (2+3 x)^{10}-\frac {10}{297} (2+3 x)^{11}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 62, normalized size = 1.82 \begin {gather*} -\frac {65610 x^{11}}{11}-\frac {356481 x^{10}}{10}-92421 x^9-133164 x^8-110160 x^7-41328 x^6+\frac {62496 x^5}{5}+24576 x^4+\frac {42752 x^3}{3}+4480 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+3 x)^8 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.96, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} x^{11} - \frac {356481}{10} x^{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac {62496}{5} x^{5} + 24576 x^{4} + \frac {42752}{3} x^{3} + 4480 x^{2} + 768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, 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 = 55, normalized size = 1.62 \begin {gather*} -\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 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 = 54, normalized size = 1.59 \begin {gather*} -\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 54, normalized size = 1.59 \begin {gather*} -\frac {65610\,x^{11}}{11}-\frac {356481\,x^{10}}{10}-92421\,x^9-133164\,x^8-110160\,x^7-41328\,x^6+\frac {62496\,x^5}{5}+24576\,x^4+\frac {42752\,x^3}{3}+4480\,x^2+768\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 60, normalized size = 1.76 \begin {gather*} - \frac {65610 x^{11}}{11} - \frac {356481 x^{10}}{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac {62496 x^{5}}{5} + 24576 x^{4} + \frac {42752 x^{3}}{3} + 4480 x^{2} + 768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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