$\int_0^\infty e^{-t}t^{312}\,dt$

Question

∫∞0e−t.t¯312.dt

Answer 1

Asagidaki esitligi kullanabilirsin: $$n!=\Gamma(n+1) =\int\limits_0^\infty t^{n}e^{-t}dt.$$ Eger Gamma fonksiyonu bilmem $\int\limits_0^\infty t^{n}e^{-t}dt$ icin parcali integral yontemini kullan. (integration by parts) $\int\limits_0^\infty t\cdot t^{n-1}e^{-t}dt.$