Find the integrals \int\sec t(\sec t+\tan t)dt

coexpennan

coexpennan

Answered question

2021-10-11

Find the integrals
sect(sect+tant)dt

Answer & Explanation

Alannej

Alannej

Skilled2021-10-12Added 104 answers

Given,
sec(t)(sec(t)+tan(t))dt
Now,
sec(t)+tan(t))dt
Let,
A=sec(t)tan(t)dt
Applying substitutuion method u=sec(t)
dy=tan(t)dt
A=1du
A=u+C
substituting back: u=sec(t)
A=sec(t)+C
The integral becomes,
=sec2(t)dt+Asec(t)
=tan(t)+sec(t)+C
sec(t)(sec(t)+tan(t)dt=tan(t)+sec(t)+C

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