Question

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Answer 1

$Hey Guys here is your answer$

$x^2+X+1÷X+2)(x^2+1)=A/(X+2)$

$+ Bx+c/(x^2+1)$

$x^2+X+1=Ax^2+A+Bx^2+2Bx+$

$Cx+2c$

$x^2+X+1=x^2(A+B)+X(B+C)+$

$+(A+c)$

$A+B=1------------------(1) equation$

$B+c=1-----------------(2) equation$

$A+C=1-----------------(3) equation$

equation 2- equation 3

B+C=1

A+C=1

_________

B-A=0-----------------------(4) equation

Keeping the value of option 4 to the value of 1--

A+B=1

A+A=1

A=1/2

B=1/2

C=1/2

$x^2+X+1÷(X+2)(x^2+X+1)=1/$

$2(X+2)+X/2+1/2÷(x^2+1)$

$-1/(X+1)-1/2log^(X+1)+$

$1/2[X/(x^2+1)dx+1/(1+x^2)$

$-1/(X+1)-1/2log^(X+1)+$

$1/4log^(x^2+1)+1/2*tan^-1x+c$ ✏️✏️✏️✏️✏️

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Answer 2

Step-by-step explanation:

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