Find the integral of \sec(x)

William Burnett

William Burnett

Answered question

2021-12-12

Find the integral of sec(x)

Answer & Explanation

Daniel Cormack

Daniel Cormack

Beginner2021-12-13Added 34 answers

(sec(x)(sec(x)+tan(x))sec(x)+tan(x))dx
(sec2(x)+sec(x)tan(x)sec(x)+tan(x))dx
Make the substitution:
u=sec(x)+tan(x)
du=(sec(x)tan(x)+sec2(x))dx=(sec2(x)+sec(x)tan(x))dx
Apply the substitution:
duu=ln|u|+C
Rewrite in terms of x to get:
sec(x)dx=ln|sec(x)+tan(x)|+C
accimaroyalde

accimaroyalde

Beginner2021-12-14Added 29 answers

Use the common integral
sec(x)dx=ln|tan(x)+sec(x)|
Add a constant to a solution
sec(x)dx=ln|tan(x)+sec(x)|+C

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