1. ## Integration

Is it possible to integrate (t^2e^-t)/(t + 1)??

2. yes,,you can use quotient rule...

3. Isn't quotient rule for differentiation??

4. Originally Posted by CookieC
Isn't quotient rule for differentiation??
$\int t^2 e^{-t} (t+1)^{-1}$

$\int t^2 e^{-(t+1) + 1} (t+1)^{-1}$

$e \int t^2 e^{-(t+1) } (t+1)^{-1}$

Let $u = t + 1$

$e \int (u-1)^2 e^{-u } (u)^{-1}$

$e \int \frac{ u^2 - 2u + 1 }{ ue^u }$

$e \int \frac{ u}{ e^u } - 2e \int e^{-u} + e \int (ue^u)^{-1}$

All of the above can be evaluated fairly easily. Use By Parts for most of them.

5. (ue^u)-1

uumm how do you integrate that one??

6. Originally Posted by CookieC
(ue^u)-1

uumm how do you integrate that one??
I lied, we cannot use by parts on that particular integral. It cannot be evaluated in elementary functions: Wolfram Mathematica Online Integrator

It's defined as $Ei(-x)$

So it would appear as if I have taken you down a path where you can integrate the integrand but not in terms of elementary functions. I'm sure an alternative approach will yield a result that can be fully explained in terms of elementary functions (i'll think of another way to start it off).

Calling...Simplependulum!!

7. Originally Posted by CookieC
Is it possible to integrate (t^2e^-t)/(t + 1)??
Where has this integral come from? Is it meant to be indefinite or defininte?

8. Its an indefinite integral..got it from my tutorial sheet...

9. Originally Posted by CookieC
Its an indefinite integral..got it from my tutorial sheet...
Are you expected to solve it using elementary functions?

10. That's where the problem lies we're suppose to solve it using elementary functions but I've searched it and apparently it cant be done using elementary >.< Might go back and ask the tutor whether the question is right...