# Evaluating $\int_0^{D}\frac{1}{x^{a}+1}dx$ for Different Values of $a$?

I am trying to simplify an integration expression

$$\int_0^{D}\frac{1}{x^{a}+1}dx$$

I know that for $a=2$, I can have it as $\arctan(x)$. But what about the general case?

• If you want the most general answer for any real $a$, it is given in terms of Hyper Geometric function $I = \int {{1 \over {{x^a} + 1}} = } x\,\,{}_2^{}F_1^{}\left( {1,{1 \over a};1 + {1 \over a}; - {x^a}} \right)$ – H. R. Dec 4 '15 at 16:08
• For positive integer values of $a,$ see Solving this integral?. – Dave L. Renfro Dec 4 '15 at 16:30
• @Cardinal Your suggestion of partial fractions is not useful. Prove me wrong with a full answer for general $a$ or even just arbitrary positive integer $a$ if you think otherwise. – Simon S Dec 4 '15 at 18:13