Question

hola mate answer this ❤ find the factor of x²+1/x²+2(x-1/x) -5​

Answer 1

Step-by-step explanation:

Let

x/[(x²+1)(x-1)] = (ax+b)/(x²+1) + c/(x-1)

Multiply the above equality throughout by

(x²+1)(x-1)

x=(ax+b)(x-1)+c(x²+1)

x=ax²-ax+bx-b+cx²+c

x=(a+c)x²+(b-a)x+(c-b)

Comparing the co-efficients

a+c=0; b-a=1 ; c-b=0

b=c and c=-a

So, b=c=-a

Since b-a=1

And b=-a so, -a-a=1

-2a=1

a=-1/2

b=1/2

c=1/2

x/[(x²+1)(x-1)]=(-x/2 + 1/2)/(x²+1) +(1/2)/(x-1)

Integrating on both sides

I= ∫[x/[(x²+1)(x-1)]]dx = (-1/2)∫[x/(x²+1)]dx +(1/2) ∫ (1/(x²+1))dx +(1/2) ∫(1/(x-1))dx

I=(-1/4)ln|x²+1| +(1/2)tan-¹(x)+(1/2)ln|x-1|+c

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