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Evaluate: ∫ (2sin x + cos x/ 3 sin x + 2cos x) dx

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Evaluate: ∫ (2sin x + cos x/ 3 sin x + 2cos x) dx

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Best answer

2sin x + cos x 

= l(3 sin x + 2 cos x) + m(3 cos x – 2sin x) 

= (3l – 2m) sin x + (2l + 3m) cos x 

Comparing the co-efficients of sin x and cos x, we get 

3l – 2m = 2 and 2l + 3m = 1 

On solving, we get, 

l = 4/5 and m = – 3/ 5

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