Integrand size = 24, antiderivative size = 18 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-5 e^{4/x}-x^3 (10+x) \]
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Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {14, 2240, 45} \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-x^4-10 x^3-5 e^{4/x} \]
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Rule 14
Rule 45
Rule 2240
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {20 e^{4/x}}{x^2}-2 x^2 (15+2 x)\right ) \, dx \\ & = -\left (2 \int x^2 (15+2 x) \, dx\right )+20 \int \frac {e^{4/x}}{x^2} \, dx \\ & = -5 e^{4/x}-2 \int \left (15 x^2+2 x^3\right ) \, dx \\ & = -5 e^{4/x}-10 x^3-x^4 \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-5 e^{4/x}-10 x^3-x^4 \]
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Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
method | result | size |
derivativedivides | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
default | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
risch | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
parallelrisch | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
parts | \(-x^{4}-10 x^{3}-5 \,{\mathrm e}^{\frac {4}{x}}\) | \(20\) |
norman | \(\frac {-10 x^{4}-x^{5}-5 x \,{\mathrm e}^{\frac {4}{x}}}{x}\) | \(25\) |
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Time = 0.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-x^{4} - 10 \, x^{3} - 5 \, e^{\frac {4}{x}} \]
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Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=- x^{4} - 10 x^{3} - 5 e^{\frac {4}{x}} \]
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Time = 0.21 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-x^{4} - 10 \, x^{3} - 5 \, e^{\frac {4}{x}} \]
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Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-x^{4} {\left (\frac {10}{x} + \frac {5 \, e^{\frac {4}{x}}}{x^{4}} + 1\right )} \]
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Time = 13.30 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {20 e^{4/x}-30 x^4-4 x^5}{x^2} \, dx=-5\,{\mathrm {e}}^{4/x}-10\,x^3-x^4 \]
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