How we can solve like this integral $\int \frac{dx}{x^n+1}$ (Hypergeometric function) In the wolfram given equation $\displaystyle\int \dfrac{dx}{x^n+1}=x\ {}_2F_1\left(1,\dfrac{1}{n};1+\dfrac{1}{n};-x^n\right)$,
But what it's mean? How we can solve without this.

Hint: First determine the complex roots of $x^n+1=0$, assuming $n \in \mathbb{N}$. Then apply $(x^n+1)=(x-x_1)\cdot \cdots \cdot(x-x_n)$. Then use partial fractions. The Integral is a sum of $\alpha_i\log(x-x_i)$ terms.
Can you do it from here?
