evaluate -pie/4 to e-1 of f(x) dx if f(x)=sec^2x for x<=o and f(x)=(1)/(x+1) for x>0

Answer 1

∫_-π/4⁰sec²xdx + ∫₀^1/e1/(x + 1)dx = tanx_-π/4⁰ + lnIx + 1I₀^1/e = tan0 - tan(-π/4) + lnI1/e + 1I - ln1 = 1 + ln(e + 1) - 1 = ln(e + 1)