" 16."(e^(2x))/(e^(x)+1)

If y = (e^(x)-e^(-x))/(e^(x)+e^(-x)) then prove that y = (e^(2x)-1)/(e^(2x)+1) .

f(x) = ((e^(2x)-1)/(e^(2x)+1)) is

tan^(-1)((e^(2x)+1)/(e^(2x)-1))

Compute the following integrals: int(e^x+e^(-x))/(e^x-e^(-x)) dx or int(e^(2x) +1)/(e^(2x)-1)dx

f(x)=(e^(2x)-1)/(e^(2x)+1) is

f(x)=((e^(2x)-1)/(e^(2x)+1)) is

int2/((e^x+e^(-x))^2)\ dx (a) ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x))+C (c) (-1)/((e^x+1)^2)+C (d) 1/(e^x-e^(-x))+C

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

Integrate the following with respect to x. (i) (e^(2x) - 1)/(e^x) " " (ii) e^(3x)(e^(2x - 1)) .