Integrand size = 20, antiderivative size = 31 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6 \]
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Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=-75 x^6-183 x^5-128 x^4+\frac {85 x^3}{3}+78 x^2+36 x \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (36+156 x+85 x^2-512 x^3-915 x^4-450 x^5\right ) \, dx \\ & = 36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6 \]
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Time = 0.70 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94
method | result | size |
gosper | \(-\frac {x \left (225 x^{5}+549 x^{4}+384 x^{3}-85 x^{2}-234 x -108\right )}{3}\) | \(29\) |
default | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
norman | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
risch | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
parallelrisch | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
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Time = 0.22 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=-75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \]
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Time = 0.02 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=- 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac {85 x^{3}}{3} + 78 x^{2} + 36 x \]
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Time = 0.20 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=-75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \]
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none
Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=-75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \]
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Time = 0.03 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx=-75\,x^6-183\,x^5-128\,x^4+\frac {85\,x^3}{3}+78\,x^2+36\,x \]
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