A) \[x\log 2x-\frac{{{x}^{2}}}{2}+c\]
B) \[x\log 2x-\frac{x}{2}+c\]
C) \[{{x}^{2}}\log 2x-\frac{x}{2}+c\]
D) \[x\log 2x-x+c\]
Correct Answer: D
Solution :
Let \[I=\int{\log 2x}\,\,dx\] or \[I=\int{1\cdot \log 2x\,\,dx}\] \[\Rightarrow \] \[I=\log 2x\int{1\cdot dx}-\int{\left\{ \left( \frac{d}{dx}\log 2x \right)\int{1\,\,dx)} \right\}}dx\] \[\Rightarrow \] \[I=x\log 2x-\int{\frac{1}{2x}\cdot 2\cdot x\,\,\,\,dx}\] \[\Rightarrow \] \[I=x\log 2x-x+c\]
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