A) \[f(x)g(x)+c\]
B) \[f(x)+g(x)+c\]
C) \[{{e}^{x}}\cos x+c\]
D) \[f(x)-g(x)+c\]
E) \[{{e}^{x}}\cos x+f(x)g(x)+c\]
Correct Answer: C
Solution :
\[\because \]\[\int{f(x)dx}={{e}^{x}}\]and\[\int{g(x)}\,dx=\cos x\] \[\Rightarrow \]\[f(x)={{e}^{x}}\]and\[g(x)=-\sin x\] \[\therefore \] \[\int{f(x)\cos x}dx+\int{g(x)}{{e}^{x}}dx\] \[=\int{{{e}^{x}}\cos xdx-\int{{{e}^{x}}\sin xdx}}\] \[={{e}^{x}}\cos x+\int{\sin x{{e}^{x}}dx-\int{{{e}^{x}}\sin x\,dx}}\] \[={{e}^{x}}\cos x+c\]
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