If-f-x-x-0-e-f-t-dt-Determine-f-x-

Question Number 196394 by Erico last updated on 24/Aug/23

If f (x) = {\int_{0}}^{x} e^{- f (t)} d t

Determine f (x)

Answered by mr W last updated on 24/Aug/23

\frac{d f (x)}{d x} = e^{- f (x)}

e^{f (x)} d f (x) = d x

\int e^{f (x)} d f (x) = \int d x

e^{f (x)} = x + C

\Rightarrow f (x) = \ln (x + C)

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