Integrand size = 13, antiderivative size = 9 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 e^{e^{2 x}} \]
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Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {12, 2320, 2225} \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 e^{e^{2 x}} \]
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Rule 12
Rule 2225
Rule 2320
Rubi steps \begin{align*} \text {integral}& = 10 \int e^{e^{2 x}+2 x} \, dx \\ & = 5 \text {Subst}\left (\int e^x \, dx,x,e^{2 x}\right ) \\ & = 5 e^{e^{2 x}} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 e^{e^{2 x}} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89
method | result | size |
derivativedivides | \(5 \,{\mathrm e}^{{\mathrm e}^{2 x}}\) | \(8\) |
default | \(5 \,{\mathrm e}^{{\mathrm e}^{2 x}}\) | \(8\) |
norman | \(5 \,{\mathrm e}^{{\mathrm e}^{2 x}}\) | \(8\) |
risch | \(5 \,{\mathrm e}^{{\mathrm e}^{2 x}}\) | \(8\) |
parallelrisch | \(5 \,{\mathrm e}^{{\mathrm e}^{2 x}}\) | \(8\) |
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Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 \, e^{\left (e^{\left (2 \, x\right )}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 e^{e^{2 x}} \]
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Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 \, e^{\left (e^{\left (2 \, x\right )}\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5 \, e^{\left (e^{\left (2 \, x\right )}\right )} \]
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Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 10 e^{e^{2 x}+2 x} \, dx=5\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}} \]
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