Sometimes if you use integration by parts twice, you get back to where you started from — which, unlike getting lost, is not a waste of time.
![image0.png](https://www.dummies.com/wp-content/uploads/219775.image0.png)
First, use the LIATE mnemonic device to pick your u:
![image1.png](https://www.dummies.com/wp-content/uploads/219776.image1.png)
To pick your u, go down this list in order; the first type of function on this list that appears in the integrand is the u.
![image2.png](https://www.dummies.com/wp-content/uploads/219777.image2.png)
Now fast forward to the formula step:
![image3.png](https://www.dummies.com/wp-content/uploads/219778.image3.png)
Now, substitute the right side of the above equation for the
![image4.png](https://www.dummies.com/wp-content/uploads/219779.image4.png)
from the original solution:
![image5.png](https://www.dummies.com/wp-content/uploads/219780.image5.png)
You can now solve this equation for the integral
![image6.png](https://www.dummies.com/wp-content/uploads/219781.image6.png)
Use I in place of that integral to make this messy equation easier on the eyes:
![image7.png](https://www.dummies.com/wp-content/uploads/219782.image7.png)
Add I to both sides:
![image8.png](https://www.dummies.com/wp-content/uploads/219783.image8.png)
Multiply both sides by 1/2:
![image9.png](https://www.dummies.com/wp-content/uploads/219784.image9.png)