integrate-sec-3-xdx-

Question Number 21970 by j.masanja06@gmail.com last updated on 07/Oct/17

i n t e g r a t e

\int {s e c}^{3} x d x

Answered by Tikufly last updated on 07/Oct/17

\int \sec^{3} x d x = \int (\sec x) (\sec^{2} x) d x

\int \sec^{3} x d x = \sec x \tan x - \int \sec x \tan^{2} x d x

\int \sec^{3} x d x = \sec x \tan x - \int \sec x (\sec^{2} x - 1) d x

\int \sec^{3} x d x = \sec x \tan x - \int \sec^{3} x d x + \int \sec x d x

2 \int \sec^{3} x d x = \sec x \tan x + \log ∣ \sec x + \tan x ∣

\int {s e c}^{3} x d x = \frac{1}{2} s e c x t a n x + \frac{1}{2} l o g ∣ s e c x + t a n x ∣ + C

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