Integrand size = 14, antiderivative size = 16 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=2-\frac {1}{25} x (3+x)^2+4 \log (2) \]
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Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {12} \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {x^3}{25}-\frac {6 x^2}{25}-\frac {9 x}{25} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{25} \int \left (-9-12 x-3 x^2\right ) \, dx \\ & = -\frac {9 x}{25}-\frac {6 x^2}{25}-\frac {x^3}{25} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {3}{25} \left (3 x+2 x^2+\frac {x^3}{3}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75
method | result | size |
gosper | \(-\frac {x \left (x^{2}+6 x +9\right )}{25}\) | \(12\) |
default | \(-\frac {1}{25} x^{3}-\frac {6}{25} x^{2}-\frac {9}{25} x\) | \(15\) |
norman | \(-\frac {1}{25} x^{3}-\frac {6}{25} x^{2}-\frac {9}{25} x\) | \(15\) |
risch | \(-\frac {1}{25} x^{3}-\frac {6}{25} x^{2}-\frac {9}{25} x\) | \(15\) |
parallelrisch | \(-\frac {1}{25} x^{3}-\frac {6}{25} x^{2}-\frac {9}{25} x\) | \(15\) |
parts | \(-\frac {1}{25} x^{3}-\frac {6}{25} x^{2}-\frac {9}{25} x\) | \(15\) |
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {1}{25} \, x^{3} - \frac {6}{25} \, x^{2} - \frac {9}{25} \, x \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=- \frac {x^{3}}{25} - \frac {6 x^{2}}{25} - \frac {9 x}{25} \]
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Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {1}{25} \, x^{3} - \frac {6}{25} \, x^{2} - \frac {9}{25} \, x \]
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {1}{25} \, x^{3} - \frac {6}{25} \, x^{2} - \frac {9}{25} \, x \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50 \[ \int \frac {1}{25} \left (-9-12 x-3 x^2\right ) \, dx=-\frac {x\,{\left (x+3\right )}^2}{25} \]
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