Question

`int dx/(1 + e^-x)` = ______

Options

• log |1 + e^x| + c

• log|1 - e^x| + c

• 2log|1 + e^x| + c

• 2log|1 - e^x| + c

Answer 1

`int dx/(1 + e^-x)` = log |1 + e^x| + c

Explanation:

Let I = `int dx/(1 + e^-x)` 

= `int e^x/(1 + e^x)dx`

Put 1 + e^x = t ⇒ e^x dx = dt

∴ I = `int 1/t dt`

= log| t | + c

∴ I = log|1 + e^x| + c