# Stupid Tabular Method for Integration by parts

1. Oct 28, 2007

Is this the correct way to use the Tabular Method for
$$\int x^2e^{-5x}dx$$

repeated diff:

$$x^2$$

$$2x$$

$$2$$

repeated Integration:

$$e^{-5x}$$

$$-\frac{1}{5}e^{-5x}$$

$$\frac{1}{25}e^{-5x}$$

$$-\frac{1}{125}e^{-5x}$$

=$$-\frac{x^2}{5}e^{-5x}+\frac{2x}{25}e^{-5x}+\frac{2}{125}e^{-5x}+C$$

I hate this.

Casey

2. Oct 28, 2007

### bob1182006

yes but the signs of the 2nd/3rd terms are wrong.

You should write out the table and include the alternating +/-

writing it out this way might be easier to do since all you do is read across to find the terms
Code (Text):

$$e^{-5x}$$
+   $$x^2$$   $$\frac{-e^{-5x}}{5}$$

-   $$2x$$   $$\frac{e^{-5x}}{25}$$

3. Oct 28, 2007

Then I clearly have no idea what I am doing. I am looking at the tabular method in my book, and from what i have read I take the diagonal product of x^2*(-1/5)e^{-5x} and then ADD it to the next product of 2x*(1/25)e^{-5x} and now subtract the product of 2*(-1/125)e^{-5x}

Am I off on all of them by a step?

4. Oct 28, 2007

$$-\frac{x^2}{5}e^{-5x}-\frac{2x}{25}e^{-5x}-\frac{2}{125}e^{-5x}+C$$