Optimal. Leaf size=49 \[ 108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2} \]
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Rubi [A]
time = 0.01, 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 = {90}
\begin {gather*} \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 \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 \begin {gather*} 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 {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 40, normalized size = 0.82
method | result | size |
gosper | \(\frac {x \left (236250 x^{7}+576000 x^{6}+327950 x^{5}-258972 x^{4}-334005 x^{3}-36540 x^{2}+90720 x +45360\right )}{420}\) | \(39\) |
default | \(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\) | \(40\) |
norman | \(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\) | \(40\) |
risch | \(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 39, normalized size = 0.80 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 39, normalized size = 0.80 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 46, normalized size = 0.94 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.48, size = 39, normalized size = 0.80 \begin {gather*} \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 \end {gather*}
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 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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