Integration
Formulae
____
2_ 2
a |+C
=log| x+x
1.
 x dx

x
+C
n +1
19.
 dx
 x2 –a2
2.
 cos x dx = sin x + C
20.
 tan x dx = log | sec x | + C
3.
 sin x dx = – cos x + C
21.
 cot x dx = log | sin x | + C
4.
 sec2 x dx = tan x + C
22.
 sec x dx =log| sec x + tan x|+C
5.
 cosec2 x = – cot x + C
23.
 cosec x dx=log |cosec x–cot x |+C
6.
 sec x tan x dx = sec x + C
24.
 ex dx = ex + C
7.
 cosecx cot x dx = – cosecx +C
25.
8.

dx
=
2
 1 – x
sin-1 x + C
26.
 ax dx = ax/ log a + C
____
 x2_ a2 dx =

dx
=
2
 1 – x
– cos x + C
27.
tan-1 x + C
28.
9.
n
=
n+1
(x/2)x2_ a2 – (a2/2)log | x + x2_ a2 |+ C
-1
_____
 x2 + a2 dx =
(x/2) x2+ a2 +(a2/2)log |x+ x2+ a2 |+C
____
 a2_ x2 dx =
10.

dx
 1 + x2
=
11.

dx
 1 + x2
= – cot -1 x + C
12.

dx
 xx2 –1
13.
 dx
= – cosec-1 x +C
 xx2 –1

 dx
= 1 log x – a +C
2
2
x –a
2a
x+a

14.
sec-1 x + C
=
15.
 dx
= 1 log a+ x +C
2
2
a –x
2a
a–x
16.
 dx
 x2 + a2
17.
 dx
a2 – x2
18.
____
2
 dx
log|
x+x
+a2|+C
=
 x2+a2
(x/2)a2_ x2 +(a2/2) sin-1(x/a) + C



=
1 tan-1(x/a) + C
a

=
-1
sin (x/a) + C
Cone
Volume
= 1/3 r2h
CSA
= rl
TSA
= rl + r2
Cylinder
Volume
= r2h
CSA
= 2rh
TSA
=2rh+2r2
Sphere
Volume
= 4/3r3
TSA
= 4r2
Cuboid
Volume
= lbh
CSA
= 2(l +b)h
TSA
=2(lb+bh+hl)
Circle
Circumference = 2r
Area
= r2
Cube
Volume
= a3
CSA
= 4a2
TSA
= 6a2