$\int_0^t x^a e^{-x/2}\,dx\le t^{a+1}/(a+1)$ for $a>-1$, $t\ge0$ · Prove2Me

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$\int_0^t x^a e^{-x/2}\,dx\le t^{a+1}/(a+1)$ for $a>-1$, $t\ge0$ · Prove2Me