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If int(2cosx-sinx+lambda)/(cosx+sinx-2)d...

If `int(2cosx-sinx+lambda)/(cosx+sinx-2)dx=Aln|cosx+sinx-2|+B x+C ,` then the value of `A+B+|lambda|` is______

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The correct Answer is:
3
`(d)/(dx)(A " In"|cosx+sinx-2|+Bx+C)`
`=A(cosx-sinx)/(cosx+sinx-2)+B`
`=(Acosx-Asinx+Bcosx+Bsinx-2B)/(cosx+sinx-2)`
` :. 2=A+B,-1=-A+B, lambda=-2B`
` :. A=3//2, B=1//2, lambda=-1`
` :. A+B+|lambda|=3`
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