If J=∫sec3⁡xdx then J is equal to

Let J=∫sec3⁡xdxJ=∫secxsec2xdxUsing by partsJ=sec⁡x∫sec2⁡dx−∫ddx(sec⁡x)∫sec2⁡xdxdxJ=sec⁡xtan⁡x−∫sec⁡xtan⁡xtan⁡xdxJ=sec⁡xtan⁡x−∫sec⁡xsec2⁡x−1dx2J=sec⁡xtan⁡x+log⁡|sec⁡x+tan⁡x|J=12[sec⁡xtan⁡x+log⁡|sec⁡x+tan⁡x|]