Integral Calculus Question: Integration by partial fractions.?

Question

So the question is to evaluate the integral of (x+1)/(x(x^2+1)) dx

I broke up it into A/(x) + (Bx+C)/(x^2+1)

Did the whole shabang and got 1/2 ln(x^2+1) +arctanx + C but this was marked wrong on my test. Can someone tell me what the real answer is and if I broke up the partial fractions wrong. Oh and I got the values of A=0, B=1, C=1 when solving the linear equations.

THank you if you could help me find my mistake or tell me what the right answer would have been.

Answer 1

breaking it up:
Ax^2+A+Bx^2+Cx=x+1
A=-B
A=1
B=-1
C=1

Answer 2

I think you are on the right track, but the value for B should be -1,

the answer would be ln|x| - 1/2 ln|(X^2+1)| + Tan-1(x) + C

Answer 3

answer:
(1/2)*ln(x^2/(x^2+1))+arctan(x)+C