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

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

Text Solution

Verified by Experts

We have given
`int(5cosx+6)/(sinx+2cosx+3)\ dx`
`I=int(5cosx+6)/(sinx+2cosx+3)\ dx`
`(5cosx+6)=A(sinx+2cosx+3)+B[d/(dx)(sinx+2cosx+3)]+C`
`(5cosx+6)=A(sinx+2cosx+3)+B(cosx-2sinx)+C`
On comparing both sides and solving them we get
`A=1,B=2`and `C=0`
`I=int((-2sinx+cosx)+2(2cosx+sinx+3))/(2cosx+sinx+3) dx`
...
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