Integrand size = 28, antiderivative size = 27 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx=x+\frac {x}{e^4}+e^5 (4-2 x)^2 \left (-5+\frac {3 x}{2}\right )^2 \]
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Time = 0.01 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.41, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12} \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx=9 e^5 x^4-96 e^5 x^3+376 e^5 x^2-640 e^5 x+\left (1+\frac {1}{e^4}\right ) x \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )\right ) \, dx}{e^4} \\ & = \left (1+\frac {1}{e^4}\right ) x+e^5 \int \left (-640+752 x-288 x^2+36 x^3\right ) \, dx \\ & = \left (1+\frac {1}{e^4}\right ) x-640 e^5 x+376 e^5 x^2-96 e^5 x^3+9 e^5 x^4 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx=x+\frac {x}{e^4}-640 e^5 x+376 e^5 x^2-96 e^5 x^3+9 e^5 x^4 \]
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Time = 0.36 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.22
method | result | size |
risch | \(9 x^{4} {\mathrm e}^{5}-96 x^{3} {\mathrm e}^{5}+376 x^{2} {\mathrm e}^{5}-640 x \,{\mathrm e}^{5}+x +{\mathrm e}^{-4} x\) | \(33\) |
parallelrisch | \({\mathrm e}^{-4} \left ({\mathrm e}^{4} {\mathrm e}^{5} \left (9 x^{4}-96 x^{3}+376 x^{2}-640 x \right )+\left ({\mathrm e}^{4}+1\right ) x \right )\) | \(37\) |
gosper | \(x \left (9 x^{3} {\mathrm e}^{4} {\mathrm e}^{5}-96 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}+376 x \,{\mathrm e}^{4} {\mathrm e}^{5}-640 \,{\mathrm e}^{4} {\mathrm e}^{5}+{\mathrm e}^{4}+1\right ) {\mathrm e}^{-4}\) | \(42\) |
norman | \(376 x^{2} {\mathrm e}^{5}-96 x^{3} {\mathrm e}^{5}+9 x^{4} {\mathrm e}^{5}-{\mathrm e}^{-4} \left (640 \,{\mathrm e}^{4} {\mathrm e}^{5}-{\mathrm e}^{4}-1\right ) x\) | \(42\) |
default | \({\mathrm e}^{-4} \left (9 \,{\mathrm e}^{4} {\mathrm e}^{5} x^{4}-96 x^{3} {\mathrm e}^{4} {\mathrm e}^{5}+376 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}-640 x \,{\mathrm e}^{4} {\mathrm e}^{5}+x \,{\mathrm e}^{4}+x \right )\) | \(46\) |
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Time = 0.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx={\left ({\left (9 \, x^{4} - 96 \, x^{3} + 376 \, x^{2} - 640 \, x\right )} e^{9} + x e^{4} + x\right )} e^{\left (-4\right )} \]
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Time = 0.04 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx=9 x^{4} e^{5} - 96 x^{3} e^{5} + 376 x^{2} e^{5} + \frac {x \left (- 640 e^{9} + 1 + e^{4}\right )}{e^{4}} \]
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Time = 0.21 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx={\left ({\left (9 \, x^{4} - 96 \, x^{3} + 376 \, x^{2} - 640 \, x\right )} e^{9} + x e^{4} + x\right )} e^{\left (-4\right )} \]
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Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx={\left ({\left (9 \, x^{4} - 96 \, x^{3} + 376 \, x^{2} - 640 \, x\right )} e^{9} + x e^{4} + x\right )} e^{\left (-4\right )} \]
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Time = 9.15 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26 \[ \int \frac {1+e^4+e^9 \left (-640+752 x-288 x^2+36 x^3\right )}{e^4} \, dx=9\,{\mathrm {e}}^5\,x^4-96\,{\mathrm {e}}^5\,x^3+376\,{\mathrm {e}}^5\,x^2+{\mathrm {e}}^{-4}\,\left ({\mathrm {e}}^4-640\,{\mathrm {e}}^9+1\right )\,x \]
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