# Thread: When should one use integration by parts?

1. ## When should one use integration by parts?

I understand that u-sub is like the anti chain rule.

What what is integration by parts and when should I use it (such as visual cues)

small examples of what integration by parts should look like are nice.

2. Originally Posted by RET80
I understand that u-sub is like the anti chain rule.

What what is integration by parts and when should I use it (such as visual cues)

small examples of what integration by parts should look like are nice.
$\displaystyle \int xe^x \, dx$

$\displaystyle \int xe^{x^2} dx$

one you would use substitution ... one you would use parts.

try and determine which method for each integral, then think about why you chose as you didi.

3. Originally Posted by RET80
I understand that u-sub is like the anti chain rule.

What what is integration by parts and when should I use it (such as visual cues)

small examples of what integration by parts should look like are nice.
Use integration by parts when you have:

$\displaystyle \int x^n*e^{ax}dx$, $\displaystyle \int x^n*sin(ax)dx$, $\displaystyle \int x^n*cos(ax)dx$, $\displaystyle \int x^n*ln(x)dx$, $\displaystyle \int x^n*arcsin(ax)dx$, $\displaystyle \int x^n*arctan(ax)dx$, $\displaystyle \int e^{ax}*sin(bx)dx$, and $\displaystyle \int e^{ax}*cos(bx)dx$