Question

Integration by parts help please

Answer 1

\[\large
\frac{1}{x^3+x} = \frac{1}{x(x^2+1)} = \frac{A}{x} + \frac{Bx+C}{x^2+1} = \\ \large
x^2(A + B) + Cx + A = 1; ~~~A = 1; ~~~B = -1; ~~~C = 0 \\ \large
\frac{1}{x^3+x} = \frac{1}{x} - \frac{x}{x^2+1}
\]