Integrand size = 14, antiderivative size = 17 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=x+e^{8/3} \left (-5+e+e^x+x+\log (4)\right ) \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2225} \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=\left (1+e^{8/3}\right ) x+e^{x+\frac {8}{3}} \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = \left (1+e^{8/3}\right ) x+\int e^{\frac {8}{3}+x} \, dx \\ & = e^{\frac {8}{3}+x}+\left (1+e^{8/3}\right ) x \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=e^{\frac {8}{3}+x}+x+e^{8/3} x \]
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Time = 0.16 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65
method | result | size |
risch | \(x +{\mathrm e}^{\frac {8}{3}} x +{\mathrm e}^{x +\frac {8}{3}}\) | \(11\) |
derivativedivides | \({\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}+\left ({\mathrm e}^{\frac {8}{3}}+1\right ) \ln \left ({\mathrm e}^{x}\right )\) | \(15\) |
default | \(x +{\mathrm e}^{\frac {8}{3}} x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(16\) |
parts | \(x +{\mathrm e}^{\frac {8}{3}} x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(16\) |
norman | \(\left ({\mathrm e}^{\frac {8}{3}}+1\right ) x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(17\) |
parallelrisch | \(\left ({\mathrm e}^{\frac {8}{3}}+1\right ) x +{\mathrm e}^{\frac {8}{3}} {\mathrm e}^{x}\) | \(17\) |
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \]
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Time = 0.04 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=x \left (1 + e^{\frac {8}{3}}\right ) + e^{\frac {8}{3}} e^{x} \]
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none
Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx=x e^{\frac {8}{3}} + x + e^{\left (x + \frac {8}{3}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \left (1+e^{8/3}+e^{\frac {8}{3}+x}\right ) \, dx={\mathrm {e}}^{x+\frac {8}{3}}+x\,\left ({\mathrm {e}}^{8/3}+1\right ) \]
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