7.1 Integration Techniques
Integration by Parts
Question #1 (Easy): Solving Indefinite Integral
Integration by parts is useful when the integral contains two seemingly different function that cannot
further be simplified, so t∫at: ) ( ) ( ) ( ) ∫ ( ) ( ) .
This is after the form of the Product Rule. Assign simpler variables likeand let ( ) ,
then by taking derivative of , ( )and by taking the anti-derivative o, ( ).
Evaluate the integral using integration by parts.
∫( ) ( )
More complex function that simplifies when its derivative is taken should be assigned to . So here,
. Then ( ) . Taking derivative ogives , and taking the anti-
derivative of gives ( ) ( ).
Given the form of integration by parts:
∫ ( ) ( )