Optimal. Leaf size=45 \[ \frac {20}{729} (3 x+2)^9-\frac {2}{9} (3 x+2)^8+\frac {13}{27} (3 x+2)^7-\frac {49}{486} (3 x+2)^6 \]
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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 {20}{729} (3 x+2)^9-\frac {2}{9} (3 x+2)^8+\frac {13}{27} (3 x+2)^7-\frac {49}{486} (3 x+2)^6 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^5+\frac {91}{9} (2+3 x)^6-\frac {16}{3} (2+3 x)^7+\frac {20}{27} (2+3 x)^8\right ) \, dx\\ &=-\frac {49}{486} (2+3 x)^6+\frac {13}{27} (2+3 x)^7-\frac {2}{9} (2+3 x)^8+\frac {20}{729} (2+3 x)^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 48, normalized size = 1.07 \begin {gather*} 540 x^9+1782 x^8+1917 x^7+\frac {273 x^6}{2}-1218 x^5-770 x^4+\frac {224 x^3}{3}+248 x^2+96 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)^5 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.06, size = 44, normalized size = 0.98 \begin {gather*} 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac {273}{2} x^{6} - 1218 x^{5} - 770 x^{4} + \frac {224}{3} x^{3} + 248 x^{2} + 96 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 44, normalized size = 0.98 \begin {gather*} 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac {273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac {224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 1.00 \begin {gather*} 540 x^{9}+1782 x^{8}+1917 x^{7}+\frac {273}{2} x^{6}-1218 x^{5}-770 x^{4}+\frac {224}{3} x^{3}+248 x^{2}+96 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 44, normalized size = 0.98 \begin {gather*} 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac {273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac {224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 44, normalized size = 0.98 \begin {gather*} 540\,x^9+1782\,x^8+1917\,x^7+\frac {273\,x^6}{2}-1218\,x^5-770\,x^4+\frac {224\,x^3}{3}+248\,x^2+96\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 46, normalized size = 1.02 \begin {gather*} 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac {273 x^{6}}{2} - 1218 x^{5} - 770 x^{4} + \frac {224 x^{3}}{3} + 248 x^{2} + 96 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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