Tabular integration instead of reccurance (1 Viewer)

[Dumbledore]

do any of you know if you can use tabular integration instead of obtaining recurrance formulas?
like integral(x^n * e^x) (S = integral)

f(x) : x^n, g(x) : e^x
f'(x): nx^(n-1) Sg(x) : e^x
f''(x): n(n-1)x^(n-2) SSg(x): e^x
f[k'](x): n!/(n-k)!*x^(n-k) [kS]g(x):e^x
... ....
0 e^x

and S[x^n * e^x] = x^n * e^x - nx^(x-1) * e^x +...+ (-1)^n*n!/(n-k)!*x^(n-k) * e^x

and represent this as:
n
Sigma (-1)^n* n!/(n-k)! * x^(n-k) * e^x
k=0

to me this is alot easier than recurrance cause its just differentiating one side a few times and integrating the other a few times
and if they ask you "hence evaluate when n=?" you can just sub n in once instead of repeatedly subbing I(sub n) in.

 

[jet]

Nah, you can't. The whole point is developing the skills of using integration by parts. They are pretty much the same thing anyway. Sorry.

 

[jack_smith]

yes. you can

my teacher confirmed this last term

 

[Trebla]

I wouldn't bother using it. Most HSC questions ask you to prove a reduction formula involving a recurrence of the integral first. Very rarely are you asked to obtain the factorial form of the integral.