Integrand size = 18, antiderivative size = 17 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=21-\frac {9 e^{17}}{2 x}-\frac {2 x}{3} \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14} \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {2 x}{3}-\frac {9 e^{17}}{2 x} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{6} \int \frac {27 e^{17}-4 x^2}{x^2} \, dx \\ & = \frac {1}{6} \int \left (-4+\frac {27 e^{17}}{x^2}\right ) \, dx \\ & = -\frac {9 e^{17}}{2 x}-\frac {2 x}{3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {9 e^{17}}{2 x}-\frac {2 x}{3} \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71
method | result | size |
default | \(-\frac {2 x}{3}-\frac {9 \,{\mathrm e}^{17}}{2 x}\) | \(12\) |
risch | \(-\frac {2 x}{3}-\frac {9 \,{\mathrm e}^{17}}{2 x}\) | \(12\) |
norman | \(\frac {-\frac {2 x^{2}}{3}-\frac {9 \,{\mathrm e}^{17}}{2}}{x}\) | \(15\) |
gosper | \(-\frac {4 x^{2}+27 \,{\mathrm e}^{17}}{6 x}\) | \(16\) |
parallelrisch | \(-\frac {4 x^{2}+27 \,{\mathrm e}^{17}}{6 x}\) | \(16\) |
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Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {4 \, x^{2} + 27 \, e^{17}}{6 \, x} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=- \frac {2 x}{3} - \frac {9 e^{17}}{2 x} \]
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Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {2}{3} \, x - \frac {9 \, e^{17}}{2 \, x} \]
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Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {2}{3} \, x - \frac {9 \, e^{17}}{2 \, x} \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \frac {27 e^{17}-4 x^2}{6 x^2} \, dx=-\frac {2\,x}{3}-\frac {9\,{\mathrm {e}}^{17}}{2\,x} \]
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