Integration formulas

ntegration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives.

1. del ‘5
ti) LE de MEUT EL
a

w

cos x) in x

(vip A in 9) = c08 à
(vi) Ln) ze y
as
(ii Log nee y
4
00 Le ae x an x

ma) tomes 1) =coseox cot ¥

D E log sin x)= cot x

(ity L log cos x) tan x
rs

(i) Loge tan max

oss) inter me

> fat de=

> | sinxdr

pre
X
+C,ne-1
+1

> J Lareloge|x]+c
5

area

+0
log, a

cos x4C

= | cor dre sin x+C
> [ee rdre tan x+C
> | cose? x dx =—cotr+C

= [sec x tan x dr msee x 4 C

= | cose x cot x dr = =ensee x +C
> | cotr dr = logl sin z]+¢
> | tan xde=log| cos x[+€
= [see x die log sec x tan x|+€

> | cose x dr = log | cosee x ~cot x] +C

J parle

2. (xx) feosech x-coth x dx =-cosechx + c

(xxix) [ht +a?
(xxx) pe -a?

(xxxi) fe" «sin bx dr =

= (asin bx - beos bx) + €

(xxxii) [e“ «cos by dx =—* m (acosta + bein bx) + €
a+b