Kye

2021-11-05

Find the indefinite integral.

$\int \frac{{e}^{x}dx}{1+{e}^{x}}$

Nathaniel Kramer

Skilled2021-11-06Added 78 answers

Step 1

Given integral,

$\int \frac{{e}^{x}dx}{1+{e}^{x}}$

Step 2

Now solving the given integral,

Let$1+{e}^{x}=u$

$\Rightarrow {e}^{x}dx=du$

Now integral

$\int \frac{1}{u}du=\mathrm{ln}\left(u\right)+C$

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

Step 3

Final answer:

$\int \frac{{e}^{x}dx}{1+{e}^{x}}=\mathrm{ln}(1+{e}^{x})+C$

Given integral,

Step 2

Now solving the given integral,

Let

Now integral

Step 3

Final answer: