# Thread: Integration using reduction formula.

1. ## 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

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

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

2. 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

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

Is there something general to solve any kind of integral of this form.
The reduction formula for this one is

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

so putting $\displaystyle n = 4$ gives

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

now use the formula for $\displaystyle n=3$

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

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