Evaluate π/4<Φ<0 (1+e^tanΦ)sec^2dΦ

Question

Under derivative in calculus

Answer 1

Let y=e^(tanø), y'=e^(tanø) * sec^2(ø), so dy=e^(tanø)sec^2(ø)dø.

The expression becomes sec^2(ø)dø+dy which integrates to tanø+e^(tanø).

Apply the limits: π/4>ø>0: (1+e)-(0+1))=e.