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Evaluate ∫ (sinx+2cosx)/(2sinx+cosx)dx

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Evaluate ∫ (sinx+2cosx)/(2sinx+cosx)dx

\(\int\frac{sinx+2cosx}{2sinx+cosx}\)dx

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1 Answer

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Best answer

Given,

∫ (sinx+2cosx)/(2sinx+cosx)dx

Equating ‘sin x’ coeff: - 

1 = 2A - B 

B = 2A - 1

Equating ’cos x’ coeff:- 

2 = A+2B 

2 = A+2(2A-1) 

2 = A + 4A - 2 

4 = 5A

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