Integrand size = 5, antiderivative size = 16 \[ \int -\frac {18 x}{25} \, dx=5+25 e^{-32+e}-\frac {9 x^2}{25} \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \[ \int -\frac {18 x}{25} \, dx=-\frac {9 x^2}{25} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = -\frac {18 \int x \, dx}{25} \\ & = -\frac {9 x^2}{25} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {18 x}{25} \, dx=-\frac {9 x^2}{25} \]
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Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.38
method | result | size |
gosper | \(-\frac {9 x^{2}}{25}\) | \(6\) |
default | \(-\frac {9 x^{2}}{25}\) | \(6\) |
norman | \(-\frac {9 x^{2}}{25}\) | \(6\) |
risch | \(-\frac {9 x^{2}}{25}\) | \(6\) |
parallelrisch | \(-\frac {9 x^{2}}{25}\) | \(6\) |
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none
Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {18 x}{25} \, dx=- \frac {9 x^{2}}{25} \]
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none
Time = 0.18 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]
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none
Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9\,x^2}{25} \]
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