Integrand size = 33, antiderivative size = 19 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=3+e^{\frac {15 \left (\frac {e}{25}+x\right )}{x}}-x \]
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Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 14, 2240} \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=e^{\frac {3 e}{5 x}+15}-x \]
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Rule 12
Rule 14
Rule 2240
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{x^2} \, dx \\ & = \frac {1}{5} \int \left (-5-\frac {3 e^{16+\frac {3 e}{5 x}}}{x^2}\right ) \, dx \\ & = -x-\frac {3}{5} \int \frac {e^{16+\frac {3 e}{5 x}}}{x^2} \, dx \\ & = e^{15+\frac {3 e}{5 x}}-x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=e^{15+\frac {3 e}{5 x}}-x \]
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Time = 0.16 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79
method | result | size |
derivativedivides | \(-x +{\mathrm e}^{15+\frac {3 \,{\mathrm e}}{5 x}}\) | \(15\) |
default | \(-x +{\mathrm e}^{15+\frac {3 \,{\mathrm e}}{5 x}}\) | \(15\) |
risch | \(-x +{\mathrm e}^{\frac {\frac {3 \,{\mathrm e}}{5}+15 x}{x}}\) | \(17\) |
parallelrisch | \(-x +{\mathrm e}^{\frac {\frac {3 \,{\mathrm e}}{5}+15 x}{x}}\) | \(17\) |
parts | \(-x +{\mathrm e}^{\frac {3 \,{\mathrm e}+75 x}{5 x}}\) | \(19\) |
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Time = 0.26 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=-{\left (x e - e^{\left (\frac {80 \, x + 3 \, e}{5 \, x}\right )}\right )} e^{\left (-1\right )} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=- x + e^{\frac {15 x + \frac {3 e}{5}}{x}} \]
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Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=-x + e^{\left (\frac {3 \, e}{5 \, x} + 15\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (17) = 34\).
Time = 0.32 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.47 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx=\frac {{\left (\frac {{\left (80 \, x + 3 \, e\right )} e^{\left (\frac {80 \, x + 3 \, e}{5 \, x}\right )}}{x} - 3 \, e^{2} - 80 \, e^{\left (\frac {80 \, x + 3 \, e}{5 \, x}\right )}\right )} e^{\left (-1\right )}}{\frac {80 \, x + 3 \, e}{x} - 80} \]
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Time = 14.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-3 e^{1+\frac {3 e+75 x}{5 x}}-5 x^2}{5 x^2} \, dx={\mathrm {e}}^{\frac {3\,\mathrm {e}}{5\,x}+15}-x \]
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