Optimal. Leaf size=49 \[ \frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \]
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Rubi [A] time = 0.02, antiderivative size = 49, 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} \[ \frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (108+432 x-261 x^2-3181 x^3-3083 x^4+4685 x^5+9600 x^6+4500 x^7\right ) \, dx\\ &=108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 49, normalized size = 1.00 \[ \frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 39, normalized size = 0.80 \[ \frac {1125}{2} x^{8} + \frac {9600}{7} x^{7} + \frac {4685}{6} x^{6} - \frac {3083}{5} x^{5} - \frac {3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.80, size = 39, normalized size = 0.80 \[ \frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.82 \[ \frac {1125}{2} x^{8}+\frac {9600}{7} x^{7}+\frac {4685}{6} x^{6}-\frac {3083}{5} x^{5}-\frac {3181}{4} x^{4}-87 x^{3}+216 x^{2}+108 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 39, normalized size = 0.80 \[ \frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 39, normalized size = 0.80 \[ \frac {1125\,x^8}{2}+\frac {9600\,x^7}{7}+\frac {4685\,x^6}{6}-\frac {3083\,x^5}{5}-\frac {3181\,x^4}{4}-87\,x^3+216\,x^2+108\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 46, normalized size = 0.94 \[ \frac {1125 x^{8}}{2} + \frac {9600 x^{7}}{7} + \frac {4685 x^{6}}{6} - \frac {3083 x^{5}}{5} - \frac {3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \]
Verification of antiderivative is not currently implemented for this CAS.
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