A) \[\tan x+\log \cos x+c\]
B) \[\frac{{{x}^{2}}}{2}{{\sec }^{2}}x+\log \cos x+c\]
C) \[x\tan x+\log \sec x+c\]
D) \[x\tan x+\log \cos x+c\]
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{x{{\sec }^{2}}x\,dx=x\tan x}-\int_{{}}^{{}}{\tan x\,dx}\] \[=x\tan x+\log (\cos x)+c.\]
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