# Integration using reduction formula.

• April 26th 2009, 07:09 AM
gammaman
Integration using reduction formula.
I do not understand the concept of reduction formula's at all.

How would I use a reduction formula to solve the following

$\int{x^4e^x}$

Is there something general to solve any kind of integral of this form.
• April 26th 2009, 07:19 AM
Jester
Quote:

Originally Posted by gammaman
I do not understand the concept of reduction formula's at all.

How would I use a reduction formula to solve the following

$\int{x^4e^x}$

Is there something general to solve any kind of integral of this form.

The reduction formula for this one is

$
\int x^n e^x\,dx = x^n e^x - n\int x^{n-1} e^x\,dx
$

so putting $n = 4$ gives

$
\int x^4 e^x\,dx = x^4 e^x - 4\int x^{3} e^x\,dx
$

now use the formula for $n=3$

$
\int x^4 e^x\,dx = x^4 e^x - 4\left(x^3 e^x - 3\int x^{2} e^x\,dx\right)
$

and keep going until you reach an integral like $\int e^x\,dx$ which you can do.