Is the following inequality true for all $t_1, t_2, P, \alpha$? How I can show/prove that?
$$\alpha\int_{n\times t_1}^\frac{n\times t_1}{1+P} t^{n-1}e^{-t}dt+ (1-\alpha)\int_{n\times t_2}^\frac{n\times t_2}{1+P}t^{n-1}e^{-t}dt > \int_{n(\alpha t_1 + (1 - \alpha)t_2)}^\frac{n(\alpha t_1 + (1 - \alpha)t_2)}{1+P}t^{n-1}e^{-t}dt$$ where $t_2>t_1 > 0$, $P>0$, $0<\alpha<1$ and $n$ is a large positive integer.
Thanks.