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:

adx =ax+C Example 2dx =2x+C


Type 2:

a x n dx = a x n+1 n+1 +C Example 1 2 x 3 dx = 2 x 4 4 +C= x 4 2 +C Example 2 2 3 x 5 dx = 2 3 x 5 dx= 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




Example 2 (x+2)(3x+1)dx = 3 x 2 +7x+2dx = 3 x 2 dx + 7xdx + 2dx = 3 x 3 3 + 7 x 2 2 +2x+C = x 3 + 7 x 2 2 +2x+C



Example 3 3 x 3 + x 2 x x dx = 3 x 2 +x1dx = 3 x 2 dx + xdx 1dx = 3 x 3 3 + x 2 2 x+C = x 3 + x 2 2 x+C