Can someone help me out with the proof of the Laplace transform of the function t(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}?

I did have a go at this one.

[tex]L[t^n] = \int_0^{\infty} t^n e^{-st}dt[/tex]

[tex]= t^n\frac{-e^{-st}}{s}\vert_0^{\infty} + {1\over s}\int_0^{\infty} nt^{n-1}e^{-st}dt[/tex]

[tex]={n\over s}\int_0^{\infty} t^{n-1}e^{-st}dt[/tex]

[tex]={n\over s}L[t^{n-1}][/tex]

I am supposed to arrive at the result:

[tex]L[t^n] = \frac{(n+1)!}{s^{n+1}}[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof for this Laplace transform

**Physics Forums | Science Articles, Homework Help, Discussion**