Evaluate `int(3cosx+2)/(sinx+2cosx+3)`dx

Explanation

We have



`int frac{3 cos x+2}{sin x+2 cos x+3} d x`


`text { Here, }`


`(3 cos x+2)=lambda(sin x+2 cos x+3)+mu(cos x-2 sin x)+u`


`(3 cos x+2)=(2 lambda+u) cos x+(lambda-2 u) sin x+(3 lambda+u) `


`therefore 2 lambda+u=3, quad lambda-2 mu=0, quad 3 lambda+u=2 `


`text { so, } `


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