Indefinite IntegrationHard

Question

If dx = Ax + B ln |9e2x - 4| + C, then

Options

A.A = - , B = , C = 0
B.A = , B = , C ∈ R
C.A = - , B = , C ∈ R
D.A = , B = , C ∈ R

Solution

. dx = Ax + Bln |9e2x - 4|  + C
put  4ex + 6e-x = P(9ex - 4e-x) + Q (9ex + 4e-x)
⇒ 4 = 9P + 9Q and  6 = 4Q - 4P
comparing,  P = -
I = -
= - ln |(9ex - 4e-x)| + C
= - ln |(9e2x - 4)| - x + C
= ln |(9e2x - 4)| - x + C
= ln |(9ex2 - 4)| - x + C
So  A = - , B = , C ∈ R

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