What is the integral of (1-e^{-x})/(x+e^{-x)-pi} ?

The integral of (1-e^{-x})/(x+e^{-x)-pi} is ln|x+e^{-x}-pi|+C

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integral of (1-e^{-x})/(x+e^{-x)-pi}

\int \frac{1 - e ^{- x}}{x + e ^{- x} - π} d x

ln x + e^{- x} - π + C

Solution steps

\int \frac{1 - e ^{- x}}{x + e ^{- x} - π} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + e^{- x} - π

= ln x + e^{- x} - π

Add a constant to the solution

= ln x + e^{- x} - π + C

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What is the integral of (1-e^{-x})/(x+e^{-x)-pi} ?
The integral of (1-e^{-x})/(x+e^{-x)-pi} is ln|x+e^{-x}-pi|+C