A) \[\log (\sec x+\tan x)+c\]
B) \[\log {{(\sec x+\tan x)}^{1/2}}+c\]
C) \[\log \sec x(\sec x+\tan x)+c\]
D) None of these
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{{{(1+2{{\tan }^{2}}x+2\tan x\sec x)}^{1/2}}dx}\] \[=\int_{{}}^{{}}{{{({{\sec }^{2}}x+{{\tan }^{2}}x+2\tan x\sec x)}^{1/2}}dx}\] \[=\int_{{}}^{{}}{(\sec x+\tan x)\,dx}=\log (\sec x+\tan x)+\log \sec x+c\] \[=\log \sec x(\sec x+\tan x)+c\].You need to login to perform this action.
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