thanks for this. But I found that when I substituted in this value for u it doesn't work. I tried
x^2 = t
2xdx = dt
xdx = dt/2
then
\int \frac{x}{a^2+x^2}dx = \frac{1}{2} \int \frac{dt}{(a^2+t)} = \frac{1}{2}\ln|a^2+x^2|+c
can I do the last step, is this...