y = ln(cosx), 0 ≤ x ≤ Pi/4
f`(x)=(1/cosx)*(cosx)`=(1/cosx)*(-sinx)=-tgx
1+(f`(x))^2=1+(-tgx)^2=1+tg^2x=1/cos^2x
sqrt(1+tg^2x)=1/cosx
L= ∫ ^(π/4)_(0)sqrt(1+(-tgx)^2) dx= ∫ ^(π/4)_(0)(1/cosx) dx=ln|tg((x/2)+(π/4))|(π/4)_(0)=ln|tg (3π/8)|-ln|tg(π/4)|=ln|tg(3π/8)|-0