Evaluate the integral ∫1/x[x+1/x]dx?

Answer 1

The integral = ∫1/x[x+1/x]dx = ∫ [1 + x^-2 ] dx
= x -x^-1 + c
= x - 1/x + c
If U mean :
∫ 1/[x(x+1/x)]dx
= ∫1/(x^2+1)dx
= tan^-1(x) + c

Answer 2

=Int(1+1/x^2)dx = x-1/x +C