Let


Put


A(x2+x+1)+(Bx+C)(x-1)=1


Now putting x-1=0


X=1


A(1+1+1)+0=1



By equating the coefficient of x2 and constant term, A+B=0




A-C=1





From the equation(1), we get,






Put t=x2+x+1


dt=(2x+1)dx






1