Optimal. Leaf size=36 \[ -\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x \]
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Rubi [A] time = 0.0116741, antiderivative size = 36, normalized size of antiderivative = 1., 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 = {611} \[ -\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x \]
Antiderivative was successfully verified.
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Rule 611
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*}
Mathematica [A] time = 0.0012721, size = 36, normalized size = 1. \[ -\frac{8 x^7}{7}-4 x^6-\frac{12 x^5}{5}+4 x^4+2 x^3-3 x^2+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 33, normalized size = 0.9 \begin{align*} 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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.945616, size = 43, normalized size = 1.19 \begin{align*} -\frac{8}{7} \, x^{7} - 4 \, x^{6} - \frac{12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.82526, size = 77, normalized size = 2.14 \begin{align*} -\frac{8}{7} x^{7} - 4 x^{6} - \frac{12}{5} x^{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.055361, size = 34, normalized size = 0.94 \begin{align*} - \frac{8 x^{7}}{7} - 4 x^{6} - \frac{12 x^{5}}{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06285, size = 43, normalized size = 1.19 \begin{align*} -\frac{8}{7} \, x^{7} - 4 \, x^{6} - \frac{12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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