Integrand size = 18, antiderivative size = 28 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5 \]
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Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78} \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12 x^5+4 x^4-\frac {37 x^3}{3}-\frac {5 x^2}{2}+6 x \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (6-5 x-37 x^2+16 x^3+60 x^4\right ) \, dx \\ & = 6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=6 x-\frac {5 x^2}{2}-\frac {37 x^3}{3}+4 x^4+12 x^5 \]
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Time = 1.84 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86
method | result | size |
gosper | \(\frac {x \left (72 x^{4}+24 x^{3}-74 x^{2}-15 x +36\right )}{6}\) | \(24\) |
default | \(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\) | \(25\) |
norman | \(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\) | \(25\) |
risch | \(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\) | \(25\) |
parallelrisch | \(6 x -\frac {5}{2} x^{2}-\frac {37}{3} x^{3}+4 x^{4}+12 x^{5}\) | \(25\) |
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none
Time = 0.22 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \]
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Time = 0.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12 x^{5} + 4 x^{4} - \frac {37 x^{3}}{3} - \frac {5 x^{2}}{2} + 6 x \]
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none
Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \]
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none
Time = 0.30 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12 \, x^{5} + 4 \, x^{4} - \frac {37}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 6 \, x \]
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Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int (1-2 x)^2 (2+3 x) (3+5 x) \, dx=12\,x^5+4\,x^4-\frac {37\,x^3}{3}-\frac {5\,x^2}{2}+6\,x \]
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