Question

`int dx/(e^x + e^(-x))` is equal to ______.

विकल्प

• tan^-1(e^x) + C

• tan^-1(e^-x) + C

• log (e^x – e^-x) + C

• log (e^x + e^-x) + C

Answer 1

`int dx/(e^x + e^(-x))` is equal to tan^-1(e^x) + C.

Explanation:

Let I = `int dx/(e^x + e^(- x))`

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

`= int (e^x dx)/(e^(2x) + 1)`

Put e^x = t

e^x dx = dt

`therefore I = int dt/(t^2 + 1) = tan^-1 t + C`

`= tan^-1 (e^x) + C`