Question

Evaluate the indefinite integral. (dt) / (cost)^2 (9+tant)^1/5

Answer 1

int 1/{(cost)^2 (9+tant)^1/5} dt =

int sec^2(t)/(9+tan(t))^(1/5) dt.

Note that sec^2(t) is the differential coefft of (9+ tan(t)), so

int sec^2(t)/(9+tan(t))^(1/5) dt = (5/4)(9+tan(t))^(4/5) + const

Answer: (5/4)(9+tan(t))^(4/5) + const