Multiple choice question of indefinite integral, $\int \frac{x + 9}{x^3 + 9x} dx$. If $\int \frac{x + 9}{x^3 + 9x} dx = k\arctan(mx) + n\ln (x) + p \ln (x^2 + 9) + c$, then $(m+n)/(k+p) = $
(A) 6
(B) -8
(C) -3
(D) 4  
I tried solving it by differentiating the R.H.S. but couldn't arrive at the answer.

The derivative of the right hand side is
$$
\frac{km}{1+m^2x^2}+\frac{n}{x}+\frac{2px}{x^2+9}
$$
which should equal
$$
\frac{x + 9}{x^3 + 9x}
$$
Thus you need $m=1/3$ and then you can go on.
