Begin2.DVI

Table 12.1 Short Table of Integrals

1.

∫

zndz =z

n+1

n+ 1

+c, n
=− 1 11.

∫

sinh z dz = cosh z+c

2.

∫ dz

z = log z+c 12.

∫

cosh z dz = sinh z+c

3.

∫

ezdz =ez+c 13.

∫

tanh z dz = log ( cosh z) + c

4.

∫

kzdz =

kz

log k+c, k is a constant 14.

∫

sech^2 z dz = tanh z+c

5.

∫

sin z dz =−cos z+c 15.

∫ dz

√z (^2) +α 2 = log (z+
√
z^2 +α^2 ) + c

6.

∫

cos z dz = sin z+c 16.

∫ dz

z^2 +α^2 =

1

αtan

− 1 z

α+c

7.

∫

tan z dz = log sec z+c=−log cos z+c 17.

∫ dz

z^2 −α^2 =

1

2 αlog

(z−α

z+α

)

+c

8.

∫

sec^2 z dz = tan z+c 18.

∫ dz

√α (^2) −z 2 = sin −^1 zα+c

9.

∫

sec ztan z dz = sec z+c 19.

∫

eαz sin βz dz =eαz αsin βzα 2 −+ββ 2 cos βz +c

10.

∫

csc zcot z dz =−csc z+c 20.

∫

eαz cos βz dz =eαz αcos βzα 2 ++ββ 2 sin βz +c

c denotes an arbitrary constant of integration

Definite integrals

The definite integral of a complex function f(t) = u(t) + iv (t)which is continuous

for ta≤t≤tbhas the form

∫tb

ta

f(t)dt =

∫tb

ta

u(t)dt +i

∫tb

ta

v(t)dt (12.189)

and has the following properties.

1. The integral of a linear combination of functions is a linear combination of the

integrals of the functions or

∫tb

ta

[c 1 f(t) + c 2 g(t)] dt =c 1

∫tb

ta

f(t)dt +c 2

∫tb

ta

g(t)dt

where c 1 and c 2 are complex constants.