CHAPTER 30
30.32
30.33
Let
252
Then
[from Problem
2 In
So
Now, z
3 + 1 = (z + l)(z
2 - z + 1). So,
Let
Then
Then z = A(z
2 - z + 1) + (z + l)(Bz + C). Let z = -l.
Equate coefficients of z
2 : 0 = ,4 + B, B=->1=^
Equate constant coefficients:
Hence,
In
Hence, our complete answer is
In
In
Then
Now,
In
In
In
In
30.29] = 2z + ln
1 + e' = z
2
,
e* d* = 2z dz,
(z
2 - 1) dx = 2z dz,
+ C = 2z + ln
+ C = 2z + lne*-21n|z + l| + C =
dz = 2z + In
+ C
Let
A: = z
3
,
dx = 3z
2 dz.
0=A+C,
C=-A=\.
In
In