Indefinite IntegrationHard
Question
+ C, then Options
A.A = 
, B = 1
, B = 1B.A = 1, B = -
C.A = - , B = 1
, B = 1D.none of these
Solution
I = 
Let
1 = a(x + 1)x2 + bx(x + 1) + c(x + 1)) + dx3 = a + b + c(x + 1) + dx3
0 = a + d
0 = a + b
0 = b + c
c = 1, b = -1, a = 1, d = -1
⇒
= ln|x| +
- ln|x + 1| + C
Comparing
B = 1, A = -
Let
1 = a(x + 1)x2 + bx(x + 1) + c(x + 1)) + dx3 = a + b + c(x + 1) + dx3
0 = a + d
0 = a + b
0 = b + c
c = 1, b = -1, a = 1, d = -1
⇒
= ln|x| +
- ln|x + 1| + C Comparing
B = 1, A = -
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