INTEGRATION SHORT NOTE

NO TYPES / RULES EXAMPLE

1.  dx  x  C  3dx  3x  C

 xn dx  xn1  C i. x5 dx  x6  C
63
n 1
ii. x dx  2x2  C
2. where n  1 3

 Kuasa bertambah satu... iii. 1 dx  x2dx   1  C
x2
 dengan kuasa itu... x

    3.  1 xdx  12 1
2
x 2 dx

k f x dx  k f x dx 3

 x2 C 1
3

ax  bn For linear
function ONLY

NO TYPES / RULES EXAMPLE

4. (ax  b)n dx , n  1  (3x  2)3dx

 (ax  b)n1  C  (3x  2)4  C
a(n  1)
34
Kuasa bertambah satu...
 dengan kuasa itu...  (3x  2)4  C
12

2

11 For linear
x ax  b function ONLY

NO TYPES / RULES EXAMPLE

5. i.  3 dx  3 1 dx
x x

(a)  1 dx  ln x  C  3ln x  C
x

ii.  1 dx  1  1 dx
3x 3 x

 1 ln x  C
3

3

NO TYPES / RULES EXAMPLE

5. i.  5 dx
2x  3

(b)  1 dx  ln ax  b  C  5 2 1 3 dx
ax  a x
b
 5ln 2x  3  C
2
For linear 3
function ONLY ii.  1 3x dx

 3 1 1 dx
 3x

 3ln1  3x  C
3

  ln1  3x  C 4

e x & eaxb For linear function
ONLY

NO TYPES / RULES EXAMPLE

6. i. 3ex dx  3 ex dx

(a) exdx  ex  C  3ex  C

Salin semula soalan... ii.  8ex dx   8 ex dx
 dengan differentiate power...
 8ex  C

5

NO TYPES / RULES EXAMPLE

For linear function i. e2x dx  e2x  C
2
6. ONLY
ii. 25e15x dx
(b) eaxbdx  eaxb  C
 25 e15x dx
a
 25e15x  C
Salin semula soalan... 5
 dengan differentiate power...
 5e15x  C
6