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britesoulusjhq

britesoulusjhq

Answered question

2022-05-17

Evaluate x tan x cos 2 x d x

Answer & Explanation

Maeve Holloway

Maeve Holloway

Beginner2022-05-18Added 25 answers

x tan ( x ) cos 2 ( x ) d x
x tan ( x ) sec 2 ( x ) d x
Do integration by parts with u=x and d v = sec 2 ( x ) tan ( x ) d x
Then du=dx and v = 1 2 sec 2 ( x ) or 1 2 tan 2 ( x ) depending on how you choose to take the antiderivative. It seems a little easier to choose the former.
Apply the formula for integration by parts to get
1 2 x sec 2 ( x ) 1 2 sec 2 ( x ) d x
1 2 x sec 2 ( x ) 1 2 tan ( x ) + C

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