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Evaluate: int(5cosx+6)/(2cosx+sinx+3)dx...

Evaluate: `int(5cosx+6)/(2cosx+sinx+3)dx`

Text Solution

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Let `5cos x+6=A(2cosx+sinx+3)+B(-2sinx+cosx)+C ----(1)`
`=>(A-2B)sinx+(2A+B)cosx+3A+C`
`A-2B=0 ----(2)`
`2A+B=4 ----(3)`
`3A+C=6 ----(4)`
Solving these equations we get, `A=2, B=1` and `C=0`
Substituting these values to eq.(1), we get
`=int(frac{2(2cosx+sinx+3)+(-2sinx+cosx)}{2cosx+sinx+3})dx` ...
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