Integrand size = 26, antiderivative size = 19 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=1+e^{e^x}+\frac {6}{x^6}-\frac {25 x^2}{4} \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 7, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 14, 2320, 2225} \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=\frac {6}{x^6}-\frac {25 x^2}{4}+e^{e^x} \]
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Rule 12
Rule 14
Rule 2225
Rule 2320
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{x^7} \, dx \\ & = \frac {1}{2} \int \left (2 e^{e^x+x}+\frac {-72-25 x^8}{x^7}\right ) \, dx \\ & = \frac {1}{2} \int \frac {-72-25 x^8}{x^7} \, dx+\int e^{e^x+x} \, dx \\ & = \frac {1}{2} \int \left (-\frac {72}{x^7}-25 x\right ) \, dx+\text {Subst}\left (\int e^x \, dx,x,e^x\right ) \\ & = e^{e^x}+\frac {6}{x^6}-\frac {25 x^2}{4} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=e^{e^x}+\frac {6}{x^6}-\frac {25 x^2}{4} \]
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Time = 0.11 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79
method | result | size |
default | \(-\frac {25 x^{2}}{4}+\frac {6}{x^{6}}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(15\) |
risch | \(-\frac {25 x^{2}}{4}+\frac {6}{x^{6}}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(15\) |
parts | \(-\frac {25 x^{2}}{4}+\frac {6}{x^{6}}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(15\) |
parallelrisch | \(-\frac {25 x^{8}-4 \,{\mathrm e}^{{\mathrm e}^{x}} x^{6}-24}{4 x^{6}}\) | \(21\) |
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Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (15) = 30\).
Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.63 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=\frac {{\left (4 \, x^{6} e^{\left (x + e^{x}\right )} - {\left (25 \, x^{8} - 24\right )} e^{x}\right )} e^{\left (-x\right )}}{4 \, x^{6}} \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=- \frac {25 x^{2}}{4} + e^{e^{x}} + \frac {6}{x^{6}} \]
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none
Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=-\frac {25}{4} \, x^{2} + \frac {6}{x^{6}} + e^{\left (e^{x}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (15) = 30\).
Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.63 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx=-\frac {{\left (25 \, x^{8} e^{x} - 4 \, x^{6} e^{\left (x + e^{x}\right )} - 24 \, e^{x}\right )} e^{\left (-x\right )}}{4 \, x^{6}} \]
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Time = 12.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-72+2 e^{e^x+x} x^7-25 x^8}{2 x^7} \, dx={\mathrm {e}}^{{\mathrm {e}}^x}-\frac {25\,x^2}{4}+\frac {6}{x^6} \]
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