1.

If `int ((x^2-x+1)/(x^2+1) ) e^(cot^(-1)x dx)=A(x) e^(cot^(-1)x)+c, A=`A. `-x`B. xC. `sqrt(1-x)`D. `sqrt(1+x)`

Answer» Correct Answer - B
`LHS=int[(x^(2)+1)/(x^(2)+1)-(x)/(x^(2)+1)]e^(cot^(-1)x)dx`
`=int1.e^(cot^(-1)x)dx-int(1)/(x^(2)+1)e^(cot^(-1)x)dx`
On integration by parts, we get
`xe^(cot(-1)x)-int x.e^(cot^(-1)x)(-(1)/(1+x^(2)))dx-int(x)/(1+x^(2))e^(cot^(-1)x)dx+C`
`=xe^(cot^(-1)x)+C`


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