Integrand size = 47, antiderivative size = 40 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=3+\frac {\frac {3}{x}-x}{x}-\left (e^4-x^2-\frac {(2+4 x)^2}{x}\right )^2 \]
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Time = 0.02 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.25, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {14} \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=-x^4-32 x^3-2 \left (144-e^4\right ) x^2-\frac {13}{x^2}-8 \left (65-4 e^4\right ) x-\frac {8 \left (16-e^4\right )}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (8 \left (-65+4 e^4\right )+\frac {26}{x^3}-\frac {8 \left (-16+e^4\right )}{x^2}+4 \left (-144+e^4\right ) x-96 x^2-4 x^3\right ) \, dx \\ & = -\frac {13}{x^2}-\frac {8 \left (16-e^4\right )}{x}-8 \left (65-4 e^4\right ) x-2 \left (144-e^4\right ) x^2-32 x^3-x^4 \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.28 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=-\frac {13}{x^2}-\frac {128}{x}+\frac {8 e^4}{x}-520 x+32 e^4 x-288 x^2+2 e^4 x^2-32 x^3-x^4 \]
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Time = 0.06 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.12
method | result | size |
norman | \(\frac {-13+\left (2 \,{\mathrm e}^{4}-288\right ) x^{4}+\left (8 \,{\mathrm e}^{4}-128\right ) x +\left (32 \,{\mathrm e}^{4}-520\right ) x^{3}-32 x^{5}-x^{6}}{x^{2}}\) | \(45\) |
risch | \(-x^{4}+2 x^{2} {\mathrm e}^{4}-32 x^{3}+32 x \,{\mathrm e}^{4}-288 x^{2}-520 x +\frac {\left (8 \,{\mathrm e}^{4}-128\right ) x -13}{x^{2}}\) | \(46\) |
default | \(-x^{4}+2 x^{2} {\mathrm e}^{4}-32 x^{3}+32 x \,{\mathrm e}^{4}-288 x^{2}-520 x -\frac {2 \left (-4 \,{\mathrm e}^{4}+64\right )}{x}-\frac {13}{x^{2}}\) | \(48\) |
gosper | \(\frac {-x^{6}+2 x^{4} {\mathrm e}^{4}-32 x^{5}+32 x^{3} {\mathrm e}^{4}-288 x^{4}-520 x^{3}+8 x \,{\mathrm e}^{4}-128 x -13}{x^{2}}\) | \(49\) |
parallelrisch | \(\frac {-x^{6}+2 x^{4} {\mathrm e}^{4}-32 x^{5}+32 x^{3} {\mathrm e}^{4}-288 x^{4}-520 x^{3}+8 x \,{\mathrm e}^{4}-128 x -13}{x^{2}}\) | \(49\) |
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Time = 0.23 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.10 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=-\frac {x^{6} + 32 \, x^{5} + 288 \, x^{4} + 520 \, x^{3} - 2 \, {\left (x^{4} + 16 \, x^{3} + 4 \, x\right )} e^{4} + 128 \, x + 13}{x^{2}} \]
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Time = 0.08 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.02 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=- x^{4} - 32 x^{3} - x^{2} \cdot \left (288 - 2 e^{4}\right ) - x \left (520 - 32 e^{4}\right ) - \frac {x \left (128 - 8 e^{4}\right ) + 13}{x^{2}} \]
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Time = 0.18 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.05 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=-x^{4} - 32 \, x^{3} + 2 \, x^{2} {\left (e^{4} - 144\right )} + 8 \, x {\left (4 \, e^{4} - 65\right )} + \frac {8 \, x {\left (e^{4} - 16\right )} - 13}{x^{2}} \]
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Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.12 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=-x^{4} - 32 \, x^{3} + 2 \, x^{2} e^{4} - 288 \, x^{2} + 32 \, x e^{4} - 520 \, x + \frac {8 \, x e^{4} - 128 \, x - 13}{x^{2}} \]
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Time = 0.07 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.08 \[ \int \frac {26+128 x-520 x^3-576 x^4-96 x^5-4 x^6+e^4 \left (-8 x+32 x^3+4 x^4\right )}{x^3} \, dx=x^2\,\left (2\,{\mathrm {e}}^4-288\right )+\frac {x\,\left (8\,{\mathrm {e}}^4-128\right )-13}{x^2}-32\,x^3-x^4+x\,\left (32\,{\mathrm {e}}^4-520\right ) \]
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