Added angle formula to solve this indefinite integral &#x222B;<!-- ∫ --> 2 co

hanglutuupx6

hanglutuupx6

Answered question

2022-06-02

Added angle formula to solve this indefinite integral 2 cos x sin x 3 sin x + 5 cos x d x

Answer & Explanation

Kuehne2rcun

Kuehne2rcun

Beginner2022-06-03Added 2 answers

I = 2 cos x sin x 3 sin x + 5 cos x d x
2 cos x sin x = 5 cos ( x + a ) ,where tan a = 1 / 2 and 3 sin x + 5 cos x = 34 cos ( x b ) where tan b = 3 / 5
I = 5 cos ( x + a ) 34 cos ( x b ) d xSubstitute t=x-b so that
I = 5 / 34 cos ( t + a + b ) cos t d t
The integrand is now: cos ( a + b ) tan t sin ( a + b )

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