Expert answers to "Find the indefinite integral. ∫exdx1+ex" - Plainmath

Kye

Answered question

2021-11-05

Find the indefinite integral.

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

Answer & Explanation

Nathaniel Kramer

Skilled2021-11-06Added 78 answers

Step 1
Given integral,

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

Step 2
Now solving the given integral,
Let

1 + e^{x} = u

\Rightarrow e^{x} d x = d u

Now integral

\int \frac{1}{u} d u = \ln (u) + C

= \ln (1 + e^{x}) + C

Step 3
Final answer:

\int \frac{e^{x} d x}{1 + e^{x}} = \ln (1 + e^{x}) + C

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