# Thread: Which rule of integration applies here?

1. ## Which rule of integration applies here?

I need to integrate (x^4)(e^-x) but am not sure what rule it is.

Thanks.

2. ## Re: Which rule of integration applies here?

Have you tried integration by parts?

3. ## Re: Which rule of integration applies here?

Originally Posted by Siron
Have you tried integration by parts?
See I thought it was obviously this but then it didn't work out, unless I made a momentous miscalculation somewhere.

EDIT: Oh no wait by parts does work, it just takes a lot of workings.

4. ## Re: Which rule of integration applies here?

Can you show some work? Proably you'll need integration by parts 4 times.
We have:
$\displaystyle \int x^4e^{-x}dx=\int x^4d(-e^{-x})=-x^4e^{-x}+\int e^{-x}4x^3dx=-x^4e^{-x}+4\int e^{-x}x^3dx$

Now you have to apply integration by parts again to calculate:
$\displaystyle \int e^{-x}x^3dx$

etc ...

5. ## Re: Which rule of integration applies here?

Originally Posted by Siron
Can you show some work? Proably you'll need integration by parts 4 times.
We have:
$\displaystyle \int x^4e^{-x}dx=\int x^4d(-e^{-x})=-x^4e^{-x}+\int e^{-x}4x^3dx$

Now you have to apply integration by parts again to calculate:
$\displaystyle \int e^{-x}x^3dx$

etc ...
Thanks for your time, I just reworked it and got the correct answer, I must have gone wrong somewhere.

6. ## Re: Which rule of integration applies here?

You're welcome
In fact it's not difficult, you just have to pay attention with the signs etc ...

7. ## Re: Which rule of integration applies here?

Originally Posted by Siron
You're welcome
In fact it's not difficult, you just have to pay attention with the signs etc ...
Yeah it's easy, I have a habit of working too fast when patience is required. :P