Integrand size = 15, antiderivative size = 26 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5 \]
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Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45} \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20 x^5+5 x^4-\frac {59 x^3}{3}-3 x^2+9 x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (9-6 x-59 x^2+20 x^3+100 x^4\right ) \, dx \\ & = 9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5 \]
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Time = 1.84 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(\frac {x \left (60 x^{4}+15 x^{3}-59 x^{2}-9 x +27\right )}{3}\) | \(24\) |
default | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
norman | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
risch | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
parallelrisch | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
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Time = 0.22 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \]
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Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20 x^{5} + 5 x^{4} - \frac {59 x^{3}}{3} - 3 x^{2} + 9 x \]
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none
Time = 0.20 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \]
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Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \]
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Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^2 (3+5 x)^2 \, dx=20\,x^5+5\,x^4-\frac {59\,x^3}{3}-3\,x^2+9\,x \]
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