Integration using reduction formula.

**gammaman** · April 26th 2009, 07:09 AM

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.

**Danny** · April 26th 2009, 07:19 AM

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.

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