Integrand size = 27, antiderivative size = 19 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=-\frac {16}{x^4}-\frac {4}{x^2}+(5-e+x)^2 \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {6, 14} \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=-\frac {16}{x^4}+x^2-\frac {4}{x^2}+2 (5-e) x \]
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Rule 6
Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \frac {64+8 x^2+(10-2 e) x^5+2 x^6}{x^5} \, dx \\ & = \int \left (-2 (-5+e)+\frac {64}{x^5}+\frac {8}{x^3}+2 x\right ) \, dx \\ & = -\frac {16}{x^4}-\frac {4}{x^2}+2 (5-e) x+x^2 \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.42 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=2 \left (-\frac {8}{x^4}-\frac {2}{x^2}+5 x-e x+\frac {x^2}{2}\right ) \]
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Time = 0.16 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.21
method | result | size |
default | \(x^{2}-2 x \,{\mathrm e}+10 x -\frac {4}{x^{2}}-\frac {16}{x^{4}}\) | \(23\) |
risch | \(-2 x \,{\mathrm e}+x^{2}+10 x +\frac {-4 x^{2}-16}{x^{4}}\) | \(24\) |
norman | \(\frac {-16+x^{6}+\left (-2 \,{\mathrm e}+10\right ) x^{5}-4 x^{2}}{x^{4}}\) | \(25\) |
gosper | \(-\frac {2 x^{5} {\mathrm e}-x^{6}-10 x^{5}+4 x^{2}+16}{x^{4}}\) | \(30\) |
parallelrisch | \(-\frac {2 x^{5} {\mathrm e}-x^{6}-10 x^{5}+4 x^{2}+16}{x^{4}}\) | \(30\) |
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.37 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=\frac {x^{6} - 2 \, x^{5} e + 10 \, x^{5} - 4 \, x^{2} - 16}{x^{4}} \]
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Time = 0.06 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=x^{2} + x \left (10 - 2 e\right ) + \frac {- 4 x^{2} - 16}{x^{4}} \]
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Time = 0.19 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=x^{2} - 2 \, x {\left (e - 5\right )} - \frac {4 \, {\left (x^{2} + 4\right )}}{x^{4}} \]
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Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=x^{2} - 2 \, x e + 10 \, x - \frac {4 \, {\left (x^{2} + 4\right )}}{x^{4}} \]
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Time = 13.91 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32 \[ \int \frac {64+8 x^2+10 x^5-2 e x^5+2 x^6}{x^5} \, dx=x^2-\frac {4\,x^2+16}{x^4}-x\,\left (2\,\mathrm {e}-10\right ) \]
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