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Let f(x)=integration of( (2x+1)÷(x²-2x+2))du from(o,x) then find the least value of f(x) in (-1,1)

Let f(x)=integration of( (2x+1)÷(x²-2x+2))du from(o,x) then find the least value of f(x) in (-1,1)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
put 2x+1=A.d/dx(x^2-2x+2)+B
2x+1=A(2x-2)+B
comapring coeff of x and constant terms
2=2A amd 1=-2A+B
=>A=1 and 1=-2+B=>B=3
hence integral of (2x+1)/(x^2-2x+2)dx
=integral(2x-2)/(x^2-2x+2) .dx+3integral dx/(x^-2x+3)
=logmod(x^2-2x+2)+3integraldx/(x-1)^2+1
=logmod(x^2-2x+2)+3 arctan(x-1) +C

Thanks & Regards
Rinkoo Gupta
AskIItians Faculty

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