F.5 DEFINITE INTEGRATION 1條

Using change of variable, d ( sec x) = tan x sec x dx.
The integral becomes (tan^3 x/sec x)(d(sec x)/sec x tan x) = tan^2 x d(sec x)/sec^2 x
= (sec^2 x - 1)d(sec x)/sec^2 x
= (1 - 1/sec^2 x) d(sec x)
= sec x + 1/sec x + C
Substitute in the limit will be the answer of the definite integral.