Optimal. Leaf size=35 \[ 12 x+4 x^2-\frac {89 x^3}{3}-\frac {79 x^4}{4}+\frac {168 x^5}{5}+30 x^6 \]
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Rubi [A]
time = 0.01, antiderivative size = 35, 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 = {78}
\begin {gather*} 30 x^6+\frac {168 x^5}{5}-\frac {79 x^4}{4}-\frac {89 x^3}{3}+4 x^2+12 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x) \, dx &=\int \left (12+8 x-89 x^2-79 x^3+168 x^4+180 x^5\right ) \, dx\\ &=12 x+4 x^2-\frac {89 x^3}{3}-\frac {79 x^4}{4}+\frac {168 x^5}{5}+30 x^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 35, normalized size = 1.00 \begin {gather*} 12 x+4 x^2-\frac {89 x^3}{3}-\frac {79 x^4}{4}+\frac {168 x^5}{5}+30 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 30, normalized size = 0.86
method | result | size |
gosper | \(\frac {x \left (1800 x^{5}+2016 x^{4}-1185 x^{3}-1780 x^{2}+240 x +720\right )}{60}\) | \(29\) |
default | \(12 x +4 x^{2}-\frac {89}{3} x^{3}-\frac {79}{4} x^{4}+\frac {168}{5} x^{5}+30 x^{6}\) | \(30\) |
norman | \(12 x +4 x^{2}-\frac {89}{3} x^{3}-\frac {79}{4} x^{4}+\frac {168}{5} x^{5}+30 x^{6}\) | \(30\) |
risch | \(12 x +4 x^{2}-\frac {89}{3} x^{3}-\frac {79}{4} x^{4}+\frac {168}{5} x^{5}+30 x^{6}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 29, normalized size = 0.83 \begin {gather*} 30 \, x^{6} + \frac {168}{5} \, x^{5} - \frac {79}{4} \, x^{4} - \frac {89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.68, size = 29, normalized size = 0.83 \begin {gather*} 30 \, x^{6} + \frac {168}{5} \, x^{5} - \frac {79}{4} \, x^{4} - \frac {89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 32, normalized size = 0.91 \begin {gather*} 30 x^{6} + \frac {168 x^{5}}{5} - \frac {79 x^{4}}{4} - \frac {89 x^{3}}{3} + 4 x^{2} + 12 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.77, size = 29, normalized size = 0.83 \begin {gather*} 30 \, x^{6} + \frac {168}{5} \, x^{5} - \frac {79}{4} \, x^{4} - \frac {89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 29, normalized size = 0.83 \begin {gather*} 30\,x^6+\frac {168\,x^5}{5}-\frac {79\,x^4}{4}-\frac {89\,x^3}{3}+4\,x^2+12\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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