Question Detail

This integral can be solved using substitution.Let u = e2x - e-2x.Then, find the differential du:du = d/dx(e2x - e-2x) dxdu = (2e2x - (-2e-2x)) dxdu = (2e2x + 2e-2x) dxdu = 2(e2x + e-2x) dxFrom this, we can see that (e2x + e-2x) dx = (1/2) du.Substitute u and du into the integral:∫ (1/u) * (1/2) du= (1/2) ∫ (1/u) du= (1/2) ln|u| + CFinally, substitute back u = e2x - e-2x:= (1/2) ln|e2x - e-2x| + CThis matches option C.