Optimal. Leaf size=32 \[ 3 x^3-6 x^4+\frac {22 x^5}{5}-\frac {4 x^6}{3}+\frac {x^7}{7} \]
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Rubi [A]
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712}
\begin {gather*} \frac {x^7}{7}-\frac {4 x^6}{3}+\frac {22 x^5}{5}-6 x^4+3 x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {align*} \int x^2 \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x^2-24 x^3+22 x^4-8 x^5+x^6\right ) \, dx\\ &=3 x^3-6 x^4+\frac {22 x^5}{5}-\frac {4 x^6}{3}+\frac {x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 32, normalized size = 1.00 \begin {gather*} 3 x^3-6 x^4+\frac {22 x^5}{5}-\frac {4 x^6}{3}+\frac {x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.66, size = 27, normalized size = 0.84
method | result | size |
gosper | \(\frac {x^{3} \left (15 x^{4}-140 x^{3}+462 x^{2}-630 x +315\right )}{105}\) | \(26\) |
default | \(3 x^{3}-6 x^{4}+\frac {22}{5} x^{5}-\frac {4}{3} x^{6}+\frac {1}{7} x^{7}\) | \(27\) |
norman | \(3 x^{3}-6 x^{4}+\frac {22}{5} x^{5}-\frac {4}{3} x^{6}+\frac {1}{7} x^{7}\) | \(27\) |
risch | \(3 x^{3}-6 x^{4}+\frac {22}{5} x^{5}-\frac {4}{3} x^{6}+\frac {1}{7} x^{7}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.76, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 27, normalized size = 0.84 \begin {gather*} \frac {x^{7}}{7} - \frac {4 x^{6}}{3} + \frac {22 x^{5}}{5} - 6 x^{4} + 3 x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.38, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^7}{7}-\frac {4\,x^6}{3}+\frac {22\,x^5}{5}-6\,x^4+3\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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