Integrand size = 20, antiderivative size = 40 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=108 x+324 x^2+345 x^3-\frac {1111 x^4}{4}-1061 x^5-\frac {1975 x^6}{2}-\frac {2250 x^7}{7} \]
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Time = 0.01 (sec) , antiderivative size = 40, 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} \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=-\frac {2250 x^7}{7}-\frac {1975 x^6}{2}-1061 x^5-\frac {1111 x^4}{4}+345 x^3+324 x^2+108 x \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (108+648 x+1035 x^2-1111 x^3-5305 x^4-5925 x^5-2250 x^6\right ) \, dx \\ & = 108 x+324 x^2+345 x^3-\frac {1111 x^4}{4}-1061 x^5-\frac {1975 x^6}{2}-\frac {2250 x^7}{7} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.00 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=108 x+324 x^2+345 x^3-\frac {1111 x^4}{4}-1061 x^5-\frac {1975 x^6}{2}-\frac {2250 x^7}{7} \]
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Time = 2.13 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85
method | result | size |
gosper | \(-\frac {x \left (9000 x^{6}+27650 x^{5}+29708 x^{4}+7777 x^{3}-9660 x^{2}-9072 x -3024\right )}{28}\) | \(34\) |
default | \(108 x +324 x^{2}+345 x^{3}-\frac {1111}{4} x^{4}-1061 x^{5}-\frac {1975}{2} x^{6}-\frac {2250}{7} x^{7}\) | \(35\) |
norman | \(108 x +324 x^{2}+345 x^{3}-\frac {1111}{4} x^{4}-1061 x^{5}-\frac {1975}{2} x^{6}-\frac {2250}{7} x^{7}\) | \(35\) |
risch | \(108 x +324 x^{2}+345 x^{3}-\frac {1111}{4} x^{4}-1061 x^{5}-\frac {1975}{2} x^{6}-\frac {2250}{7} x^{7}\) | \(35\) |
parallelrisch | \(108 x +324 x^{2}+345 x^{3}-\frac {1111}{4} x^{4}-1061 x^{5}-\frac {1975}{2} x^{6}-\frac {2250}{7} x^{7}\) | \(35\) |
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none
Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=-\frac {2250}{7} \, x^{7} - \frac {1975}{2} \, x^{6} - 1061 \, x^{5} - \frac {1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \]
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Time = 0.02 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.92 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=- \frac {2250 x^{7}}{7} - \frac {1975 x^{6}}{2} - 1061 x^{5} - \frac {1111 x^{4}}{4} + 345 x^{3} + 324 x^{2} + 108 x \]
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none
Time = 0.19 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=-\frac {2250}{7} \, x^{7} - \frac {1975}{2} \, x^{6} - 1061 \, x^{5} - \frac {1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \]
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Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=-\frac {2250}{7} \, x^{7} - \frac {1975}{2} \, x^{6} - 1061 \, x^{5} - \frac {1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \]
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Time = 0.04 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx=-\frac {2250\,x^7}{7}-\frac {1975\,x^6}{2}-1061\,x^5-\frac {1111\,x^4}{4}+345\,x^3+324\,x^2+108\,x \]
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