Question

find the anti- derivative of e^2x-1/e^2x+1​

Answer 1

Answer:

e^2 x = e^x * e^x .

so divide the equation by e^x above and below .

(e^2x +1 )/(e^2x - 1 ) = {(e^2x+1)/e^x}{(e^2x -1)/e^x}= (e^x+e^-x)/(e^x - e^-x)

d(e^x-e^-x) = (e^x + e^-x)

let (e^x + e^-x) =t

so , int [(e^2x+1)/(e^2x-1)] = int (dt/t) = log t = log (e^x+e^-x)

Answer 2

check the attachment______♡