Integrand size = 15, antiderivative size = 9 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{9 e^{10 x}} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2320, 2225} \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{9 e^{10 x}} \]
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Rule 12
Rule 2225
Rule 2320
Rubi steps \begin{align*} \text {integral}& = 90 \int e^{9 e^{10 x}+10 x} \, dx \\ & = 9 \text {Subst}\left (\int e^{9 x} \, dx,x,e^{10 x}\right ) \\ & = e^{9 e^{10 x}} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{9 e^{10 x}} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89
method | result | size |
derivativedivides | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
default | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
norman | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
risch | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
parallelrisch | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
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Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \]
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Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{9 e^{10 x}} \]
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Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \]
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Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx=e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \]
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Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 90 e^{9 e^{10 x}+10 x} \, dx={\mathrm {e}}^{9\,{\mathrm {e}}^{10\,x}} \]
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