Optimal. Leaf size=36 \[ x-3 x^2+2 x^3+4 x^4-\frac {12 x^5}{5}-4 x^6-\frac {8 x^7}{7} \]
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Rubi [A]
time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {625}
\begin {gather*} -\frac {8 x^7}{7}-4 x^6-\frac {12 x^5}{5}+4 x^4+2 x^3-3 x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rule 625
Rubi steps
\begin {align*} \int \left (1-2 x-2 x^2\right )^3 \, dx &=\int \left (1-6 x+6 x^2+16 x^3-12 x^4-24 x^5-8 x^6\right ) \, dx\\ &=x-3 x^2+2 x^3+4 x^4-\frac {12 x^5}{5}-4 x^6-\frac {8 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 36, normalized size = 1.00 \begin {gather*} x-3 x^2+2 x^3+4 x^4-\frac {12 x^5}{5}-4 x^6-\frac {8 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 33, normalized size = 0.92
method | result | size |
default | \(x -3 x^{2}+2 x^{3}+4 x^{4}-\frac {12}{5} x^{5}-4 x^{6}-\frac {8}{7} x^{7}\) | \(33\) |
norman | \(x -3 x^{2}+2 x^{3}+4 x^{4}-\frac {12}{5} x^{5}-4 x^{6}-\frac {8}{7} x^{7}\) | \(33\) |
risch | \(x -3 x^{2}+2 x^{3}+4 x^{4}-\frac {12}{5} x^{5}-4 x^{6}-\frac {8}{7} x^{7}\) | \(33\) |
gosper | \(-\frac {x \left (40 x^{6}+140 x^{5}+84 x^{4}-140 x^{3}-70 x^{2}+105 x -35\right )}{35}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.11, size = 32, normalized size = 0.89 \begin {gather*} -\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.15, size = 32, normalized size = 0.89 \begin {gather*} -\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 34, normalized size = 0.94 \begin {gather*} - \frac {8 x^{7}}{7} - 4 x^{6} - \frac {12 x^{5}}{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.79, size = 32, normalized size = 0.89 \begin {gather*} -\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 32, normalized size = 0.89 \begin {gather*} -\frac {8\,x^7}{7}-4\,x^6-\frac {12\,x^5}{5}+4\,x^4+2\,x^3-3\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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