Optimal. Leaf size=54 \[ -1000 x^9-\frac {3675 x^8}{2}+\frac {230 x^7}{7}+\frac {3617 x^6}{2}+\frac {3279 x^5}{5}-\frac {2659 x^4}{4}-375 x^3+108 x^2+108 x \]
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Rubi [A] time = 0.02, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} -1000 x^9-\frac {3675 x^8}{2}+\frac {230 x^7}{7}+\frac {3617 x^6}{2}+\frac {3279 x^5}{5}-\frac {2659 x^4}{4}-375 x^3+108 x^2+108 x \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (108+216 x-1125 x^2-2659 x^3+3279 x^4+10851 x^5+230 x^6-14700 x^7-9000 x^8\right ) \, dx\\ &=108 x+108 x^2-375 x^3-\frac {2659 x^4}{4}+\frac {3279 x^5}{5}+\frac {3617 x^6}{2}+\frac {230 x^7}{7}-\frac {3675 x^8}{2}-1000 x^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 54, normalized size = 1.00 \begin {gather*} -1000 x^9-\frac {3675 x^8}{2}+\frac {230 x^7}{7}+\frac {3617 x^6}{2}+\frac {3279 x^5}{5}-\frac {2659 x^4}{4}-375 x^3+108 x^2+108 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)^3 (2+3 x)^2 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.12, size = 44, normalized size = 0.81 \begin {gather*} -1000 x^{9} - \frac {3675}{2} x^{8} + \frac {230}{7} x^{7} + \frac {3617}{2} x^{6} + \frac {3279}{5} x^{5} - \frac {2659}{4} x^{4} - 375 x^{3} + 108 x^{2} + 108 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 44, normalized size = 0.81 \begin {gather*} -1000 \, x^{9} - \frac {3675}{2} \, x^{8} + \frac {230}{7} \, x^{7} + \frac {3617}{2} \, x^{6} + \frac {3279}{5} \, x^{5} - \frac {2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, 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 = 0.83 \begin {gather*} -1000 x^{9}-\frac {3675}{2} x^{8}+\frac {230}{7} x^{7}+\frac {3617}{2} x^{6}+\frac {3279}{5} x^{5}-\frac {2659}{4} x^{4}-375 x^{3}+108 x^{2}+108 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 44, normalized size = 0.81 \begin {gather*} -1000 \, x^{9} - \frac {3675}{2} \, x^{8} + \frac {230}{7} \, x^{7} + \frac {3617}{2} \, x^{6} + \frac {3279}{5} \, x^{5} - \frac {2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, 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 = 0.81 \begin {gather*} -1000\,x^9-\frac {3675\,x^8}{2}+\frac {230\,x^7}{7}+\frac {3617\,x^6}{2}+\frac {3279\,x^5}{5}-\frac {2659\,x^4}{4}-375\,x^3+108\,x^2+108\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 51, normalized size = 0.94 \begin {gather*} - 1000 x^{9} - \frac {3675 x^{8}}{2} + \frac {230 x^{7}}{7} + \frac {3617 x^{6}}{2} + \frac {3279 x^{5}}{5} - \frac {2659 x^{4}}{4} - 375 x^{3} + 108 x^{2} + 108 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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