I want to solve an inequality of the type: $$\int_{x}^{+\infty} f(t) \cdot dt + \int_{0}^{x} g(t) \cdot dt > 0$$ Is there a general-case solution for this with $f$ and $g$ known?
If not, is there a solution for the specific case $$a \cdot \int_{x}^{+\infty} t^{\alpha-1}\cdot e^{-t\cdot\beta} \cdot dt - p\cdot \int_{0}^{x} t^{\alpha}\cdot e^{-t\cdot\beta} \cdot dt > 0$$ where $a$, $p$, $\alpha$, and $\beta$ are known constants?