(ii)
We look for a function whose derivative is 3x2 + 4x3 Note that
(
)
3
4
d
x
x
dx
+
= 3x2 + 4x3 Therefore, an anti derivative of 3x2 + 4x3  is  x3 + x4 (iii)
We know that
1
1
1
(log )
0 and
[log (
)]
(
1)
0
d
d
x
,x
– x
–
,x
dx
x
dx
– x
x
=
>
=
=
<
Combining above, we get 
(
)
1
log
0
d
x
, x
dx
=x
≠
Therefore, 
1
log
dx
x
x
=
∫
 is one of the anti derivatives of 1
x