Tricky partial fraction question

Question

Partial fraction$$\frac{1}{x(x^{50}+1)}$$

Here's what I did,

$$\frac{1}{x(x^{50}+1)}\equiv\frac{(x^{50}+1)-x^{50}}{x(x^{50}+1)}$$

$$\frac{1}{x(x^{50}+1)}\equiv\frac{1}{x}-\frac{x^{49}}{(x^{50}+1)}$$

Am I correct ?

Answer 1

Yes, the anwer is correct and ready to be integrated. $$\frac{1}{x(x^{50}+1)}\equiv\frac{1}{x}-\frac{x^{49}}{(x^{50}+1)}$$