using substitution how do i integrate :sec^2(x) / tan^3 (x) .dx??i'm pretty confused?

Answer 1

I = ∫ ( sec ² x / tan ³ x ) dx
Let u = tan x
du = sec ² x dx
I = ∫(1/u³) du
I = ∫ u^(-3) du
I = u ^( - 2) / ( - 2 ) + C
I = ( -1/2 ) / tan ² x + C
I = ( - 1/2 ) cot ² x + C