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If int (3sinx+2cosx)/ (3cosx+2sinx) dx=a...

If `int (3sinx+2cosx)/ (3cosx+2sinx) dx=a x+b ln|2sinx+3cosx|+C`, then (a)`a=-(12)/(13),b=(15)/(39)` (b) `a=-7/(13),b=6/(13)` (c)`a=(12)/(13),b=(15)/(39)` (d) `a=-7/(13),b=-6/(13)`

A

`a= -(12)/(13)`

B

`b=(6)/(13)`

C

`a=(12)/(13)`

D

`b= -(15)/(39)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Differentiating both sides w.r.t. x, we get
`(3sin x+2 cosx)/(3cosx+2sinx)=a+(b(2cosx-3sinx))/((2sinx+3cosx))`
`=(sinx.(2a-3b)+cosx.(3a+2b))/((3cosx+2 sinx))`
Comparing like terms on both sides, we get
`3=2a-3b, 2=3a+2b`
`implies a=(12)/(13), b= -(15)/(39)`
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