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

coexpennan 2021-10-11 Answered
Find the integrals
sect(sect+tant)dt
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Expert Answer

Alannej
Answered 2021-10-12 Author has 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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