I am trying to solve $\int \limits _u^v x^{m-1}e^{-x} dx$. I checked table of integrals too but there is no direct solution for this, any help?
2026-03-25 06:00:09.1774418409
integrating gamma pdf over fixed limits
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In terms of the lower incomplete gamma function, defined by $$\gamma(a,x) = \int_0^x t^{a - 1} e^{-t} \, dt, \quad a > 0,$$ your integral can be rewritten as
$$\int_u^v x^{m - 1} e^{-x} \, dx = \int_0^v x^{m - 1} e^{-x} \, dx - \int_0^u x^{m - 1} e^{-x} \, dx = \gamma (m,v) - \gamma (m,u), \quad m > 0.$$