Find the definite integral of the (- SX) power of e multiplied by the nth power of X from 0 to positive infinity. (n is a real number)

Find the definite integral of the (- SX) power of e multiplied by the nth power of X from 0 to positive infinity. (n is a real number)

a=∫[0,+∞]e^(-sx)x^ndx=-1/s*∫[0,+∞]x^nde^(-sx)
=-1/s*[0,+∞]x^ne^(-sx)+n/s∫[0,+∞]e^(-sx)x^(n-1)dx
=n/s∫[0,+∞]e^(-sx)x^(n-1)dx
So a = Na / s
a=1/s
therefore
a/a=n/s
a/a=(n-1)/s
……
a/a=1/s
Multiply
a/a=n!/s^n
So a = n! / S ^ (n + 1)

Elden Ring Premiere

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