Question

Use integration by parts to find the integral.

Answer 1

This is actually very simple if you follow the equation for by parts integration :)

Let \[u=t^n, du=nt^{n-1}\] and
\[dv=e^{-t}, v=-e^{-t}\]
Then following the equation\[uv-\int\limits vdu\]
We get\[-t^{n}e^{-t}+\int\limits nt^{n-1}e^{-t} dt\]

Factor out the n from the integral in the second term and you get your final answer :)