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sir please help in finding the integral of ∫ (3sinx+2cosx)dx/(3cosx+2sinx).

sir please help in finding the integral of 
     ∫ (3sinx+2cosx)dx/(3cosx+2sinx).
 

Grade:12

1 Answers

Aditya Gupta
2081 Points
3 years ago
write the numerator as 12/13*(2sinx+3cosx) – 5/13*(2cosx – 3sinx)
also note that if you substitute 3cosx+2sinx=y then dy=(2cosx – 3sinx)dx
final answer:
=12x/13 – 5/13*ln|2sinx+3cosx|+C

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