MathCastle
CalculusEasyNon-Elementary Integration

Non-Elementary Integration · Easy problem

Using the Gamma function Γ(s)=∫0∞xs−1e−x dx\Gamma(s)=\displaystyle\int_0^{\infty} x^{s-1}e^{-x}\,dx and the fact that Γ(n)=(n−1)!\Gamma(n)=(n-1)! for positive integers nn, evaluate ∫0∞x3e−x dx\displaystyle\int_0^{\infty} x^{3}e^{-x}\,dx.