Indefinite IntegrationHard
Question
If 
dx = - 2
+ C, then
dx = - 2+ C, then Options
A.A = 
, B = 
, B = B.A = , B = 
, B = C.A = - , B =
, B = D.none of these
Solution
I =
= ∫(tan x)-11/2 sec4 x dx
= ∫(tan x)-11/2 (1 + tan2 x)sec2x dx put tan x = t ⇒ sec2 xdx = dt
∴ I = ∫(t-11/2 + t-7/2)dt
=
t-5/2 + C
=
(tan x)-9/2 + 
(tan x)-5/2 + C ⇒ A = 
, B = 
= ∫(tan x)-11/2 sec4 x dx
= ∫(tan x)-11/2 (1 + tan2 x)sec2x dx put tan x = t ⇒ sec2 xdx = dt
∴ I = ∫(t-11/2 + t-7/2)dt
=
t-5/2 + C=
(tan x)-9/2 + (tan x)-5/2 + C ⇒ A = , B = Create a free account to view solution
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