I have to integrate the following :
$$\int_0^\infty x^{s-1}e^{(-ax^p-bx^{-q})}dx$$
Please help me I am not able to solve this .. However there is this identity available in a book
$$\int_0^\infty x^{s-1}e^{(-ax^p-bx^{-p})}dx = 2 p^{-1}(\frac{b}{a})^{(\frac{p}{2s})}K_{(\frac{s}{p})}(2a^{(\frac{1}{2})}b^{(\frac{1}{2})})$$
where K is first kind bessels function. I am not able to reprove the identity in the book, even if we can do that, it will eventually lead to the solution of the question.