`int(dx)/((e^x-1)^2)`

int (1)/((e^(x)-1)^(2))dx=

(i) int (dx)/(e^x+e^(-x)) (ii) int e^x/(e^(2x)+1) dx

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

int(dx)/(sqrt(e^(2x)-1))=

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

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

int(dx)/(sqrt(e^(2x)-1)) =……+c

The value of int (dx)/(sqrt(e^(2x)-1)) is equal to -

STATEMENT-1 : int(dx)/(e^(x)+e^(-x)+2)=-(1)/(e^(x)+1)+c and STATEMENT-2 : int(d(f(x)))/((f(x))^(2))=-(1)/(f(x))+c