3.1 Basic Integration


3.1 Integration as the Inverse of Differentiation, Integration of axn and integration of the Functions of the Sum/Difference of Algebraic Terms

Type 1:

a d x = a x + C Example 2 d x = 2 x + C


Type 2:

a x n d x = a x n + 1 n + 1 + C E x a m p l e 1 2 x 3 d x = 2 x 4 4 + C = x 4 2 + C E x a m p l e 2 2 3 x 5 d x = 2 3 x 5 d x = 2 3 ( x 4 4 ) + C = 2 3 ( x 4 4 ) + C = x 4 6 + C



Type 3:

( u+v )dx= udx± vdx u and v are functions in x Example 1 3 x 2 +2xdx= 3 x 2 dx+ 2xdx = 3 x 3 3 + 2 x 2 2 +C = 3 x 3 3 + 2 x 2 2 +C = x 3 + x 2 +C


E x a m p l e 2 ( x + 2 ) ( 3 x + 1 ) d x = 3 x 2 + 7 x + 2 d x = 3 x 2 d x + 7 x d x + 2 d x = 3 x 3 3 + 7 x 2 2 + 2 x + C = x 3 + 7 x 2 2 + 2 x + C


E x a m p l e 3 3 x 3 + x 2 x x d x = 3 x 2 + x 1 d x = 3 x 2 d x + x d x 1 d x = 3 x 3 3 + x 2 2 x + C = x 3 + x 2 2 x + C
 

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