A) \[{{e}^{x}}+\sin x+2x\]
B) \[{{e}^{x}}+\sin x\]
C) \[{{e}^{x}}-\sin x\]
D) \[{{e}^{x}}+\sin x+x\]
Correct Answer: B
Solution :
\[I\int_{{}}^{{}}{\frac{\left( {{e}^{x}}+\cos x+1 \right)-\left( {{e}^{x}}+\sin x+x \right)}{{{e}^{x}}+\sin x+x}dx}\] \[\Rightarrow \,\,I=In\left( {{e}^{x}}+\sin x+x \right)-x+c\] \[\therefore \,f(x)={{e}^{x}}+\sin x+x\] and \[g(x)=-x\] \[\therefore \,\,f(x)+g(x)={{e}^{x}}+\sin x\].You need to login to perform this action.
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