Question

How can I use integration by parts to find `int_{0}^{5}te^{-t}dt`?

Answer 1

You can do this:

Using this approach you should get:
`int_0^5(te^(-t))dt=-e^-t*t-int(-e^-t)*1dt=`
`=-e^-t*t-e^-t=`
`=-e^(-t)(t+1)`
Now you must use your extrema: `0 and 5`
You get:
`-e^-5*(5+1)-[-e^0*(0+1)]=`
`=1-6e^-5`