Plot[Log[Cos[t]], {t, 0, 0.5*Pi}]

y[x_] = Log[Cos[x]]
Plot[y[x], {x, 0, 0.5*Pi}]

D[Log[Cos[x]], x]

∫Sec[x] \[DifferentialD]x

s[t_] = Log[Sec[t] + Tan[t]]
Plot[s[t], {t, 0, 0.5*Pi}]