Integrand size = 55, antiderivative size = 23 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=3+\frac {e^{3 \left (x+3 e^{4+x} x\right )} x}{2+x} \]
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Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(23)=46\).
Time = 0.18 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.83, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {27, 2326} \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {e^{9 e^{x+4} x+3 x} \left (x^2+3 e^{x+4} \left (x^3+3 x^2+2 x\right )+2 x\right )}{(x+2)^2 \left (3 e^{x+4} x+3 e^{x+4}+1\right )} \]
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Rule 27
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{(2+x)^2} \, dx \\ & = \frac {e^{3 x+9 e^{4+x} x} \left (2 x+x^2+3 e^{4+x} \left (2 x+3 x^2+x^3\right )\right )}{(2+x)^2 \left (1+3 e^{4+x}+3 e^{4+x} x\right )} \\ \end{align*}
Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {e^{3 x+9 e^{4+x} x} x}{2+x} \]
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Time = 3.62 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87
method | result | size |
norman | \(\frac {{\mathrm e}^{9 x \,{\mathrm e}^{4} {\mathrm e}^{x}+3 x} x}{2+x}\) | \(20\) |
risch | \(\frac {{\mathrm e}^{3 x \left (3 \,{\mathrm e}^{4+x}+1\right )} x}{2+x}\) | \(20\) |
parallelrisch | \(\frac {{\mathrm e}^{9 x \,{\mathrm e}^{4} {\mathrm e}^{x}+3 x} x}{2+x}\) | \(20\) |
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Time = 0.25 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {x e^{\left (9 \, x e^{\left (x + 4\right )} + 3 \, x\right )}}{x + 2} \]
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Time = 0.12 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {x e^{9 x e^{4} e^{x} + 3 x}}{x + 2} \]
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Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {x e^{\left (9 \, x e^{\left (x + 4\right )} + 3 \, x\right )}}{x + 2} \]
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Timed out. \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\text {Timed out} \]
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Time = 10.85 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{4+4 x+x^2} \, dx=\frac {x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{9\,x\,{\mathrm {e}}^4\,{\mathrm {e}}^x}}{x+2} \]
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