Integrand size = 32, antiderivative size = 14 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {1}{9 e^6 (-4+2 x)^4} \]
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Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {12, 2083, 32} \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {1}{144 e^6 (2-x)^4} \]
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Rule 12
Rule 32
Rule 2083
Rubi steps \begin{align*} \text {integral}& = -\frac {\int \frac {1}{-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5} \, dx}{e^6} \\ & = -\frac {\int \frac {1}{36 (-2+x)^5} \, dx}{e^6} \\ & = -\frac {\int \frac {1}{(-2+x)^5} \, dx}{36 e^6} \\ & = \frac {1}{144 e^6 (2-x)^4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {1}{144 e^6 (-2+x)^4} \]
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Time = 0.10 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
method | result | size |
default | \(\frac {{\mathrm e}^{-6}}{144 \left (-2+x \right )^{4}}\) | \(12\) |
norman | \(\frac {{\mathrm e}^{-6}}{144 \left (-2+x \right )^{4}}\) | \(12\) |
risch | \(\frac {{\mathrm e}^{-6}}{144 x^{4}-1152 x^{3}+3456 x^{2}-4608 x +2304}\) | \(25\) |
gosper | \(\frac {{\mathrm e}^{-6}}{144 x^{4}-1152 x^{3}+3456 x^{2}-4608 x +2304}\) | \(27\) |
parallelrisch | \(\frac {{\mathrm e}^{-6}}{144 x^{4}-1152 x^{3}+3456 x^{2}-4608 x +2304}\) | \(27\) |
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Leaf count of result is larger than twice the leaf count of optimal. 24 vs. \(2 (9) = 18\).
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.71 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {e^{\left (-6\right )}}{144 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 37 vs. \(2 (12) = 24\).
Time = 0.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 2.64 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {1}{144 x^{4} e^{6} - 1152 x^{3} e^{6} + 3456 x^{2} e^{6} - 4608 x e^{6} + 2304 e^{6}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 24 vs. \(2 (9) = 18\).
Time = 0.17 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.71 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {e^{\left (-6\right )}}{144 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}} \]
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none
Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {e^{\left (-6\right )}}{144 \, {\left (x - 2\right )}^{4}} \]
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Time = 0.08 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int -\frac {1}{e^6 \left (-1152+2880 x-2880 x^2+1440 x^3-360 x^4+36 x^5\right )} \, dx=\frac {{\mathrm {e}}^{-6}}{144\,{\left (x-2\right )}^4} \]
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