Irodov – Problems in General Physics

xn+1

xn dx= — (n —1) n+1

dx = x

x

S

sin x dx= — cos x

cos x dx= sin x

tan x dx= — in cos x

S

cot x dx = In sin x

.c

dx cos x — tan x

C dx — cot x

j sin' x

ex dx= ex

dx

J 1+0 =arctanx

arcsin x

In (x+ 17 Z^2 -

V x 2 -1

Integration by parts: u du = uv— v du

9. Derivatives and Integrals

Function Derivative Function Derivative Function Derivative

xn

1

x

1

xn

1 7x

ex

enx

ax

In x

nxn-1

1

--x T

_ n

sin x

cos x

tan x

cot x

cos x

—sin x arcsin x

arccos x

aretan x

1

V 1— x 2

1

cos

1

2 x

1

1 / 1— x 2

xn+i 1

1 sing x 1-{-x'

2 v x -. f

ex

nenx

ax Ina

—^1

x

Vu

In u

_ u

v

u'

arccot x

sinh x

cosh x

tank x

cosh x

2 Va +

u'

— a

vu'v'u

1 x2

cosh x

sinh x

1

cosha x

1

v 2

sinh 2 x

Some Definite Integrals

1

1, (^) n=0
et e-x dx= tili ll ii-, n=1/2
o 1, n=1
2, n= 2
00 I 1 /2.1iTT, u=^0
5 x n tr* xa dx = i "2' -: n = 1
o^1 /^4 17 a., n=2
1/2, n=3
(^0) c ° zn dx
—
2.31, n=1/2
n 2 /6, n=1
2.405, n-= 2
n 4 /15, n= 3
24.9, n=4

r c& x 3 dx

0.225, a= 1

1.18, a= 2

2.56, cc= 3

4.91, a= 5

6.43, cc= 10

j ex— 1

o

ex 1

o