Integrand size = 12, antiderivative size = 36 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=x-3 x^2+2 x^3+4 x^4-\frac {12 x^5}{5}-4 x^6-\frac {8 x^7}{7} \]
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Time = 0.01 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {625} \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=-\frac {8 x^7}{7}-4 x^6-\frac {12 x^5}{5}+4 x^4+2 x^3-3 x^2+x \]
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Rule 625
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.00 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.00 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=x-3 x^2+2 x^3+4 x^4-\frac {12 x^5}{5}-4 x^6-\frac {8 x^7}{7} \]
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Time = 0.38 (sec) , antiderivative size = 33, normalized size of antiderivative = 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 | \(x -3 x^{2}+2 x^{3}+4 x^{4}-\frac {12}{5} x^{5}-4 x^{6}-\frac {8}{7} x^{7}\) | \(33\) |
parallelrisch | \(x -3 x^{2}+2 x^{3}+4 x^{4}-\frac {12}{5} x^{5}-4 x^{6}-\frac {8}{7} x^{7}\) | \(33\) |
gosper | \(-\frac {x \left (40 x^{6}+140 x^{5}+84 x^{4}-140 x^{3}-70 x^{2}+105 x -35\right )}{35}\) | \(34\) |
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none
Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.89 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=-\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \]
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Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.94 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=- \frac {8 x^{7}}{7} - 4 x^{6} - \frac {12 x^{5}}{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} + x \]
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none
Time = 0.18 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.89 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=-\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \]
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none
Time = 0.31 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.89 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=-\frac {8}{7} \, x^{7} - 4 \, x^{6} - \frac {12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x \]
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Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.89 \[ \int \left (1-2 x-2 x^2\right )^3 \, dx=-\frac {8\,x^7}{7}-4\,x^6-\frac {12\,x^5}{5}+4\,x^4+2\,x^3-3\,x^2+x \]
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