sec-3-xdx-

Question Number 495 by 13/NaSaNa(N)056565 last updated on 25/Jan/15

\int \sec^{3} x d x

Answered by prakash jain last updated on 15/Jan/15

\tan x = t

\sec^{2} x d x = d t

\sec x = \sqrt{1 + t^{2}}

\int \sec^{3} x d x = \int \sqrt{1 + t^{2}} d t

= \frac{t}{2} \sqrt{1 + t^{2}} + \frac{1}{2} \ln ∣ t + \sqrt{1 + t^{2}} ∣ + C

= \frac{\tan x \sec x}{2} + \frac{1}{2} \ln ∣ \sec x + \tan x ∣ + C