A) \[\log \,\sec \,x(\sec x-\tan x)+C\]
B) \[\log \,cosec\,x(\sec x+\tan x)+C\]
C) \[\log \,sec\,x(\sec x+\tan x)+C\]
D) \[\log \,(\sec x+\tan x)+C\]
Correct Answer: C
Solution :
\[{{\int{\left\{ 1+2{{\tan }^{2}}x+2\tan x\sec x \right\}}}^{\frac{1}{2}}}dx\] \[=\int{{{({{\sec }^{2}}x+{{\tan }^{2}}x+2\tan x\sec x)}^{\frac{1}{2}}}dx}\] \[=\int{(\sec x+\tan x)dx=\log \sec x(\sec x+\tan x)+C}\]You need to login to perform this action.
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