Integrand size = 18, antiderivative size = 12 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=(-3+e) \left (-5-\frac {5}{x^2}+x\right ) \]
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Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.58, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=\frac {5 (3-e)}{x^2}-(3-e) x \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (-3 \left (1-\frac {e}{3}\right )+\frac {10 (-3+e)}{x^3}\right ) \, dx \\ & = \frac {5 (3-e)}{x^2}-(3-e) x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=(-3+e) \left (-\frac {5}{x^2}+x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08
method | result | size |
default | \(\left ({\mathrm e}-3\right ) \left (x -\frac {5}{x^{2}}\right )\) | \(13\) |
gosper | \(\frac {\left ({\mathrm e}-3\right ) \left (x^{3}-5\right )}{x^{2}}\) | \(14\) |
norman | \(\frac {\left ({\mathrm e}-3\right ) x^{3}-5 \,{\mathrm e}+15}{x^{2}}\) | \(19\) |
risch | \(x \,{\mathrm e}-3 x -\frac {5 \,{\mathrm e}}{x^{2}}+\frac {15}{x^{2}}\) | \(21\) |
parallelrisch | \(\frac {x^{3} {\mathrm e}-3 x^{3}-5 \,{\mathrm e}+15}{x^{2}}\) | \(22\) |
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Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.75 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=-\frac {3 \, x^{3} - {\left (x^{3} - 5\right )} e - 15}{x^{2}} \]
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Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.42 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=- x \left (3 - e\right ) - \frac {-15 + 5 e}{x^{2}} \]
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Time = 0.17 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.33 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=x {\left (e - 3\right )} - \frac {5 \, {\left (e - 3\right )}}{x^{2}} \]
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Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.42 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=x e - 3 \, x - \frac {5 \, {\left (e - 3\right )}}{x^{2}} \]
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Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {-30-3 x^3+e \left (10+x^3\right )}{x^3} \, dx=\frac {\left (x^3-5\right )\,\left (\mathrm {e}-3\right )}{x^2} \]
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