A) \[g(x)f(x)-g(x)f'(x)+C\]
B) \[g(x)f'(x)+C\]
C) \[g(x)f(x)+C\]
D) \[g(x){{f}^{2}}(x)+C\]
Correct Answer: C
Solution :
[c] \[\int{g(x)\{f(x)+f'(x)\}dx}\] \[=\int{g(x)f(x)dx+\int{g(x)f'(x)dx}}\] \[=f(x)\int{g(x)dx-\int{\{f'(x)g(x)dx\}dx+\int{g(x)f'(x)dx}}}\] \[=f(x)g(x)-\int{f'(x)g(x)dx+\int{g(x)f'(x)dx}}\] [Given \[\int{g(x)dx=g(x)}\]] \[=f(x)g(x)+c\]You need to login to perform this action.
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