Integrand size = 15, antiderivative size = 27 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-2+\frac {\sqrt [4]{2}}{e^3}-e^x+e^{4+e^5+x}-x \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2225} \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x-e^x+e^{x+e^5+4} \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = -x-\int e^x \, dx+\int e^{4+e^5+x} \, dx \\ & = -e^x+e^{4+e^5+x}-x \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-e^x+e^{4+e^5+x}-x \]
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Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56
method | result | size |
default | \(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\) | \(15\) |
risch | \(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\) | \(15\) |
parallelrisch | \(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\) | \(15\) |
parts | \(-{\mathrm e}^{x}-x +{\mathrm e}^{{\mathrm e}^{5}+4+x}\) | \(15\) |
norman | \(\left ({\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{5}}-1\right ) {\mathrm e}^{x}-x\) | \(16\) |
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none
Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx={\left ({\left (e^{\left (e^{5} + 4\right )} - 1\right )} e^{\left (x + e^{5} + 4\right )} - x e^{\left (e^{5} + 4\right )}\right )} e^{\left (-e^{5} - 4\right )} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=- x + \left (-1 + e^{4} e^{e^{5}}\right ) e^{x} \]
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none
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x + e^{\left (x + e^{5} + 4\right )} - e^{x} \]
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none
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx=-x + e^{\left (x + e^{5} + 4\right )} - e^{x} \]
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Time = 0.07 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \left (-1-e^x+e^{4+e^5+x}\right ) \, dx={\mathrm {e}}^x\,\left ({\mathrm {e}}^{{\mathrm {e}}^5+4}-1\right )-x \]
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