Integrand size = 22, antiderivative size = 42 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=36 x+42 x^2-\frac {227 x^3}{3}-\frac {341 x^4}{2}+\frac {109 x^5}{5}+230 x^6+\frac {900 x^7}{7} \]
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Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900 x^7}{7}+230 x^6+\frac {109 x^5}{5}-\frac {341 x^4}{2}-\frac {227 x^3}{3}+42 x^2+36 x \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (36+84 x-227 x^2-682 x^3+109 x^4+1380 x^5+900 x^6\right ) \, dx \\ & = 36 x+42 x^2-\frac {227 x^3}{3}-\frac {341 x^4}{2}+\frac {109 x^5}{5}+230 x^6+\frac {900 x^7}{7} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=36 x+42 x^2-\frac {227 x^3}{3}-\frac {341 x^4}{2}+\frac {109 x^5}{5}+230 x^6+\frac {900 x^7}{7} \]
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Time = 2.28 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81
method | result | size |
gosper | \(\frac {x \left (27000 x^{6}+48300 x^{5}+4578 x^{4}-35805 x^{3}-15890 x^{2}+8820 x +7560\right )}{210}\) | \(34\) |
default | \(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\) | \(35\) |
norman | \(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\) | \(35\) |
risch | \(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\) | \(35\) |
parallelrisch | \(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\) | \(35\) |
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Time = 0.22 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900}{7} \, x^{7} + 230 \, x^{6} + \frac {109}{5} \, x^{5} - \frac {341}{2} \, x^{4} - \frac {227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \]
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Time = 0.02 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.93 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900 x^{7}}{7} + 230 x^{6} + \frac {109 x^{5}}{5} - \frac {341 x^{4}}{2} - \frac {227 x^{3}}{3} + 42 x^{2} + 36 x \]
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Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900}{7} \, x^{7} + 230 \, x^{6} + \frac {109}{5} \, x^{5} - \frac {341}{2} \, x^{4} - \frac {227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \]
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Time = 0.26 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900}{7} \, x^{7} + 230 \, x^{6} + \frac {109}{5} \, x^{5} - \frac {341}{2} \, x^{4} - \frac {227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \]
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Time = 0.04 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx=\frac {900\,x^7}{7}+230\,x^6+\frac {109\,x^5}{5}-\frac {341\,x^4}{2}-\frac {227\,x^3}{3}+42\,x^2+36\,x \]
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