Evaluate the integral ∫10 e−x−exe−x+ex dx.

Question

Evaluate the integral

∫1

0

e^-x - e^x / e^-x + e^x dx

a)ln (2/ | e^-1 + e | )

b)ln ( | e^-1 + e | / 2)

c)ln (| e^-1 - e | / 2 )

d)ln (2/ | e^-1 - e | )

Answer 1

let u = e^-x+e^x ---> du = (-e^-x+e^x)dx

when x = 0, u = 2. when x=1, u = e^-1+e¹

-∫du/u = -ln(u) for u= 2 to e^-1+e¹

-ln(e^-1+e¹) - (-ln(2) = ln(2/(e^-1+e¹)) which is a)