Integration of a and b integral I'm trying to solve this integral $$\int \frac{x^a}{1+x^b}dx $$ I'm not sure how I should approach this.I've looked up for similar integrals but nothing seems to apply to this.Any help?I'm thinking of Leibniz rule but not sure how to apply

Welcome to the world of hypergeometric functions
$$\int \frac{x^a}{1+x^b}dx=\frac{x^{a+1} }{a+1}\, _2F_1\left(1,\frac{a+1}{b};\frac{a+b+1}{b};-x^b\right)$$
Edit
It is possible that, without noticing it, you already used them. Being simplistic, use the well known series
$$\frac 1{1+t}=\sum_{n=0}^\infty (-1)^n t^n$$ Make $t=x^b$ to get
$$\frac{x^a}{1+x^b}=\sum_{n=0}^\infty  (-1)^n x^{a+b n}$$
$$\int \frac{x^a}{1+x^b}dx=\sum_{n=0}^\infty \frac{(-1)^n x^{a+b n+1}}{a+b n+1}$$
