Optimal. Leaf size=45 \[ -\frac {5}{81} (3 x+2)^{10}+\frac {65}{243} (3 x+2)^9-\frac {1}{9} (3 x+2)^8+\frac {1}{81} (3 x+2)^7 \]
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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} \begin {gather*} -\frac {5}{81} (3 x+2)^{10}+\frac {65}{243} (3 x+2)^9-\frac {1}{9} (3 x+2)^8+\frac {1}{81} (3 x+2)^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^6 (3+5 x)^2 \, dx &=\int \left (\frac {7}{27} (2+3 x)^6-\frac {8}{3} (2+3 x)^7+\frac {65}{9} (2+3 x)^8-\frac {50}{27} (2+3 x)^9\right ) \, dx\\ &=\frac {1}{81} (2+3 x)^7-\frac {1}{9} (2+3 x)^8+\frac {65}{243} (2+3 x)^9-\frac {5}{81} (2+3 x)^{10}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 51, normalized size = 1.13 \begin {gather*} -3645 x^{10}-19035 x^9-42039 x^8-49221 x^7-29106 x^6-1764 x^5+10360 x^4+\frac {24112 x^3}{3}+2976 x^2+576 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)^6 (3+5 x)^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.12, size = 49, normalized size = 1.09 \begin {gather*} -3645 x^{10} - 19035 x^{9} - 42039 x^{8} - 49221 x^{7} - 29106 x^{6} - 1764 x^{5} + 10360 x^{4} + \frac {24112}{3} x^{3} + 2976 x^{2} + 576 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 49, normalized size = 1.09 \begin {gather*} -3645 \, x^{10} - 19035 \, x^{9} - 42039 \, x^{8} - 49221 \, x^{7} - 29106 \, x^{6} - 1764 \, x^{5} + 10360 \, x^{4} + \frac {24112}{3} \, x^{3} + 2976 \, x^{2} + 576 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 50, normalized size = 1.11 \begin {gather*} -3645 x^{10}-19035 x^{9}-42039 x^{8}-49221 x^{7}-29106 x^{6}-1764 x^{5}+10360 x^{4}+\frac {24112}{3} x^{3}+2976 x^{2}+576 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 49, normalized size = 1.09 \begin {gather*} -3645 \, x^{10} - 19035 \, x^{9} - 42039 \, x^{8} - 49221 \, x^{7} - 29106 \, x^{6} - 1764 \, x^{5} + 10360 \, x^{4} + \frac {24112}{3} \, x^{3} + 2976 \, x^{2} + 576 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 1.09 \begin {gather*} -3645\,x^{10}-19035\,x^9-42039\,x^8-49221\,x^7-29106\,x^6-1764\,x^5+10360\,x^4+\frac {24112\,x^3}{3}+2976\,x^2+576\,x \end {gather*}
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 \begin {gather*} - 3645 x^{10} - 19035 x^{9} - 42039 x^{8} - 49221 x^{7} - 29106 x^{6} - 1764 x^{5} + 10360 x^{4} + \frac {24112 x^{3}}{3} + 2976 x^{2} + 576 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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