Integrand size = 13, antiderivative size = 23 \[ \int (1-2 x)^2 (3+5 x) \, dx=3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4 \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45} \[ \int (1-2 x)^2 (3+5 x) \, dx=5 x^4-\frac {8 x^3}{3}-\frac {7 x^2}{2}+3 x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (3-7 x-8 x^2+20 x^3\right ) \, dx \\ & = 3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (3+5 x) \, dx=3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4 \]
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Time = 1.84 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(\frac {x \left (30 x^{3}-16 x^{2}-21 x +18\right )}{6}\) | \(19\) |
default | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
norman | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
risch | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
parallelrisch | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
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Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^2 (3+5 x) \, dx=5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \]
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Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (3+5 x) \, dx=5 x^{4} - \frac {8 x^{3}}{3} - \frac {7 x^{2}}{2} + 3 x \]
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Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^2 (3+5 x) \, dx=5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \]
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^2 (3+5 x) \, dx=5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \]
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Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^2 (3+5 x) \, dx=5\,x^4-\frac {8\,x^3}{3}-\frac {7\,x^2}{2}+3\,x \]
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