promotion image of download ymail app
Promoted

Find the ∫sec^3 xdx?

Find the integral of ∫sec^3 xdx

I need the steps used and answer please. I'll give 10 points to the best answer!

1 Answer

Relevance
  • J D
    Lv 5
    1 decade ago
    Favorite Answer

    ∫sec^3 x dx

    ∫sec x sec^2 x dx

    let u = sec x; dv = sec^2 x dx

    du = sec x tan x; v = tan x

    sec x tan x - ∫tan x sec x tan x dx

    sec x tan x - ∫sec x tan^2 x dx

    sec x tan x - ∫sec x (sec^2 x - 1) dx

    so at this point we have...

    ∫sec^3 x dx = sec x tan x - ∫sec^3 x dx - ∫sec x dx

    2∫sec^3 x dx = sec x tan x - ∫sec x dx

    2∫sec^3 x dx = sec x tan x - ln|sec x + tan x| + c

    ∫sec^3 x dx = 1/2 sec x tan x - 1/2 ln|sec x + tan x| + c

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.