微積分:部分積分

5.5

Integration by Parts

For instance, integration by part works well with integrals such as R

 ln  R  and R sin     

Integration by parts is based on the formula for the dervative of product

 [] =    +    = 0+ 0 We have  = Z 0 + Z 0

Theorem 67 If  and  are function of  and have continuous derivative,

then _Z

 = ₋ Z



Technique:

1  2Trigonometric 3 Polynomial 4 Otherwise (ex. ln  sin−1 tan−1)

Example 141 R54ln  R (2+ 7)923 R ln R 2 R 2sin  R

sec3_