A) \[{{e}^{x}}\cot x+c\]
B) \[{{e}^{x}}\text{cosec }x+c\]
C) \[-{{e}^{x}}\cot x+c\]
D) \[-{{e}^{x}}\text{cosec}\,x+c\]
Correct Answer: C
Solution :
\[I=\int{{{e}^{x}}(1-\cot x+{{\cot }^{2}}x)\,dx}=\int{{{e}^{x}}(-\cot x+\text{cose}{{\text{c}}^{2}}x)\,dx}\] \[={{e}^{x}}(-\cot x)+c\]\[=-{{e}^{x}}\,\cot x+c\].
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