Question Detail

This integral can be solved using u-substitution.Let u = e2x - e-2x.Now, find the derivative of u with respect to x:du/dx = d/dx (e2x) - d/dx (e-2x)du/dx = (2e2x) - (-2e-2x)du/dx = 2e2x + 2e-2xdu/dx = 2(e2x + e-2x)From this, we can see that (e2x + e-2x) dx = (1/2) du.Substitute u and (1/2) du into the integral:∫ (1/u) * (1/2) du= (1/2) ∫ (1/u) du= (1/2) ln|u| + CNow, substitute back u = e2x - e-2x:= (1/2) ln|e2x - e-2x| + CTherefore, the correct option is C.