Integrand size = 34, antiderivative size = 26 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=4 \left (\frac {e^3}{x}-x\right ) \left (x+\frac {(4+2 x)^2}{x^3}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.50, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {14} \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=\frac {64 e^3}{x^4}+\frac {64 e^3}{x^3}-4 x^2-\frac {16 \left (4-e^3\right )}{x^2}-\frac {64}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {256 e^3}{x^5}-\frac {192 e^3}{x^4}-\frac {32 \left (-4+e^3\right )}{x^3}+\frac {64}{x^2}-8 x\right ) \, dx \\ & = \frac {64 e^3}{x^4}+\frac {64 e^3}{x^3}-\frac {16 \left (4-e^3\right )}{x^2}-\frac {64}{x}-4 x^2 \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=-\frac {4 \left (-4 e^3 (2+x)^2+x^2 \left (16+16 x+x^4\right )\right )}{x^4} \]
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Time = 0.14 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35
method | result | size |
norman | \(\frac {\left (16 \,{\mathrm e}^{3}-64\right ) x^{2}-64 x^{3}-4 x^{6}+64 x \,{\mathrm e}^{3}+64 \,{\mathrm e}^{3}}{x^{4}}\) | \(35\) |
risch | \(-4 x^{2}+\frac {-64 x^{3}+\left (16 \,{\mathrm e}^{3}-64\right ) x^{2}+64 x \,{\mathrm e}^{3}+64 \,{\mathrm e}^{3}}{x^{4}}\) | \(36\) |
default | \(-4 x^{2}+\frac {64 \,{\mathrm e}^{3}}{x^{4}}-\frac {64}{x}-\frac {4 \left (-4 \,{\mathrm e}^{3}+16\right )}{x^{2}}+\frac {64 \,{\mathrm e}^{3}}{x^{3}}\) | \(37\) |
parallelrisch | \(\frac {-4 x^{6}+16 x^{2} {\mathrm e}^{3}-64 x^{3}+64 x \,{\mathrm e}^{3}-64 x^{2}+64 \,{\mathrm e}^{3}}{x^{4}}\) | \(37\) |
gosper | \(\frac {-4 x^{6}+16 x^{2} {\mathrm e}^{3}-64 x^{3}+64 x \,{\mathrm e}^{3}-64 x^{2}+64 \,{\mathrm e}^{3}}{x^{4}}\) | \(38\) |
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Time = 0.23 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=-\frac {4 \, {\left (x^{6} + 16 \, x^{3} + 16 \, x^{2} - 4 \, {\left (x^{2} + 4 \, x + 4\right )} e^{3}\right )}}{x^{4}} \]
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Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.38 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=- 4 x^{2} - \frac {64 x^{3} + x^{2} \cdot \left (64 - 16 e^{3}\right ) - 64 x e^{3} - 64 e^{3}}{x^{4}} \]
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Time = 0.20 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=-4 \, x^{2} - \frac {16 \, {\left (4 \, x^{3} - x^{2} {\left (e^{3} - 4\right )} - 4 \, x e^{3} - 4 \, e^{3}\right )}}{x^{4}} \]
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Time = 0.25 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.46 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=-4 \, x^{2} - \frac {16 \, {\left (4 \, x^{3} - x^{2} e^{3} + 4 \, x^{2} - 4 \, x e^{3} - 4 \, e^{3}\right )}}{x^{4}} \]
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Time = 9.39 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {128 x^2+64 x^3-8 x^6+e^3 \left (-256-192 x-32 x^2\right )}{x^5} \, dx=\frac {-64\,x^3+\left (16\,{\mathrm {e}}^3-64\right )\,x^2+64\,{\mathrm {e}}^3\,x+64\,{\mathrm {e}}^3}{x^4}-4\,x^2 \]
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