Integration by Parts

Choosing u and dv (LIATE Rule)

Choose in order of preference:

1. Logarithmic functions
2. Inverse trigonometric functions
3. Algebraic functions ()
4. Trigonometric functions
5. Exponential functions

Example: Basic Integration by Parts

Evaluate .

Example: Integration by Parts Twice

Evaluate .

Special Cases: Cyclic Integration

Sometimes integration by parts leads back to the original integral. In such cases, solve algebraically.

Example: Cyclic Case

Evaluate .