A) \[y={{e}^{x}}+\sin x+\frac{{{x}^{2}}}{2}+\log \cos x+c\]
B) \[y={{e}^{x}}+\sin x+\frac{{{x}^{2}}}{2}+\log \sec x+c\]
C) \[y={{e}^{x}}-\sin x+\frac{{{x}^{2}}}{2}+\log \cos x+c\]
D) \[y={{e}^{x}}-\sin x+\frac{{{x}^{2}}}{2}+\log \sec x+c\]
Correct Answer: B
Solution :
\[\frac{dy}{dx}={{e}^{x}}+\cos x+x+\tan x\] On integrating both sides, we get \[y={{e}^{x}}+\sin x+\frac{{{x}^{2}}}{2}+\log \sec x+c\].
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