\( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This rule is called subst....
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\( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This
P
rule is called substitution rule. Answer the following questions:
If
\( \int \sec x \tan x \sqrt{\sec ^{2} x+1} d x=\frac{1}{2} \sinh ^{-1}(\sec x)+\frac{1}{2} f(x)+c \) then \( f(x) \) is
(1) \( \tan x \sqrt{\sec ^{2} x+1} \)
(2) \( \quad \sec x \sqrt{\sec ^{2} x+1} \)
(3) \( \sec x \sqrt{\tan x} \)
(4) \( \sec ^{2} x \sqrt{\tan x} \)
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