Indefinite IntegrationHard
Question
If 
dx = p f(x) + q g(x) + C, where ′C′ is a constant of integration, then
dx = p f(x) + q g(x) + C, where ′C′ is a constant of integration, thenOptions
A.p = 1; q = 
; f(x) = x; g(x) = ln 
; f(x) = x; g(x) = ln B.p = 1; q = - ; f(x) = x; g(x) = ln
; f(x) = x; g(x) = ln C.p = 1; q = - 
; f(x) = x; g(x) = ln 
; f(x) = x; g(x) = ln D.p = 1; q = - ; f(x) = x; g(x) = ln
; f(x) = x; g(x) = ln Solution
I = 
dx = pf(x) + g(x) + C .......(i)
using tan 3x =
and cot 3x =
I =
dx
I = ∫1.dx - 2
dx = x - 2 
dx + C
= x -
= 1.x +
comparing with R.H.S. of equation (i), we get result.
dx = pf(x) + g(x) + C .......(i)using tan 3x =
and cot 3x =I =
dxI = ∫1.dx - 2
dx = x - 2 dx + C = x -
= 1.x +
comparing with R.H.S. of equation (i), we get result.
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