Integrate (x^2 + 1)/x?

Question

how do you integrate (x^2 +1)/x

Answer 1

Substitute x as t:

therfore, dx = dt

integral (t^2 + 1)/t = t + t^(-1) = t + log(t) + c

                              = 1/2x^2 + log(x) +c

Answer 2

Integral (  (x^2 + 1)/x  dx )

One way is to split into two fractions.

Integral (  [ (x^2)/x  +  (1/x) ] dx )

Which reduces to

Integral (  [x + (1/x)] dx )

And now we can integrate term by term.

(1/2)x^2 + ln|x| + C