Question:

∫dt/(cos^2tsqarrt(1+tant)

Mywork:sqrt(1+tan(t)) = (1+tan(t))^(1/2)

let u = (1+tan(t))^(1/2)

du = (1/2) (1+tan(t))^(-1/2) sec^2(t) dt

du = 1/2 (1+tan^2(t))^(1/2) cos^2(t) dt

du = 1/2 sqrt(1+tan^2(t)) cos^2(t) dt

The given integral becomes

2∫ du

=2u + C

= 2sqrt(1+tan^2(t)) + C