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.

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- Apr 26th 2009, 07:09 AMgammamanIntegration 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. - Apr 26th 2009, 07:19 AMJester
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.