Integrate the rational functions`1/(x(x^n+1)`[Hint: multiply numerator and denominator by `x^(n-1)`and put `x^n=t`]

Explanation

To solve the integral \( \int \frac{1}{x(x^n + 1)} \, dx \), we can follow these steps:

### Step 1: Simplify the Integral
Multiply the numerator and denominator by \( x^{n-1} \):
\[ \int \frac{1}{x(x^n + 1)} \, dx = \int \frac{x^{n-1}}{x^n(x^n + 1)} \, dx \]
This gives us:
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