INTEGRALS         295
Example 1 Write an anti derivative for each of the following functions using the
method of inspection:
(i)
cos 2x
(ii)
3x2 + 4x3
(iii)
1
x , x ≠ 0
Solution
(i)
We look for a function whose derivative is cos 2x Recall that
d
dx  sin 2x = 2 cos 2x
or
cos 2x = 1
2
d
dx  (sin 2x) =
21 sin 2
d
x
dx






Therefore, an anti derivative of cos 2x is 
1 sin 2
2
x (ii)
We look for a function whose derivative is 3x2 + 4x3 Note that
(
)
3
4
d
x
x
dx
+
= 3x2 + 4x3