Optimal. Leaf size=34 \[ -\frac {1}{27} (3 x+2)^{10}+\frac {37}{243} (3 x+2)^9-\frac {7}{216} (3 x+2)^8 \]
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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} \[ -\frac {1}{27} (3 x+2)^{10}+\frac {37}{243} (3 x+2)^9-\frac {7}{216} (3 x+2)^8 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^7+\frac {37}{9} (2+3 x)^8-\frac {10}{9} (2+3 x)^9\right ) \, dx\\ &=-\frac {7}{216} (2+3 x)^8+\frac {37}{243} (2+3 x)^9-\frac {1}{27} (2+3 x)^{10}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 53, normalized size = 1.56 \[ -2187 x^{10}-11583 x^9-\frac {207765 x^8}{8}-30942 x^7-18774 x^6-1512 x^5+6468 x^4+\frac {15520 x^3}{3}+1952 x^2+384 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 49, normalized size = 1.44 \[ -2187 x^{10} - 11583 x^{9} - \frac {207765}{8} x^{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac {15520}{3} x^{3} + 1952 x^{2} + 384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 49, normalized size = 1.44 \[ -2187 \, x^{10} - 11583 \, x^{9} - \frac {207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac {15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 50, normalized size = 1.47 \[ -2187 x^{10}-11583 x^{9}-\frac {207765}{8} x^{8}-30942 x^{7}-18774 x^{6}-1512 x^{5}+6468 x^{4}+\frac {15520}{3} x^{3}+1952 x^{2}+384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 49, normalized size = 1.44 \[ -2187 \, x^{10} - 11583 \, x^{9} - \frac {207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac {15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 1.44 \[ -2187\,x^{10}-11583\,x^9-\frac {207765\,x^8}{8}-30942\,x^7-18774\,x^6-1512\,x^5+6468\,x^4+\frac {15520\,x^3}{3}+1952\,x^2+384\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 51, normalized size = 1.50 \[ - 2187 x^{10} - 11583 x^{9} - \frac {207765 x^{8}}{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac {15520 x^{3}}{3} + 1952 x^{2} + 384 x \]
Verification of antiderivative is not currently implemented for this CAS.
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