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 :
\[\int{f(x)\cos xdx+\int{g(x){{e}^{x}}dx}}\] \[=\int{{{e}^{x}}\cos xdx+\int{(-\sin x){{e}^{x}}dx}}\] \[=\frac{{{e}^{x}}}{2}(\cos x+\sin x)-\frac{{{e}^{x}}}{2}(\sin x-\cos x)+c\] \[=\frac{{{e}^{x}}}{2}(2\cos x)+c\]\[={{e}^{x}}\cos x+c\].You need to login to perform this action.
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