A) \[-\cot x-2x+c\]
B) \[-2\cot x-2x+c\]
C) \[-2\cot x-x+c\]
D) \[-2\cot x+x+c\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\frac{1+{{\cos }^{2}}x}{{{\sin }^{2}}x}}\,dx=\int_{{}}^{{}}{(\text{cose}{{\text{c}}^{2}}x+{{\cot }^{2}}x)\,dx}\] \[=\int_{{}}^{{}}{(2\text{cose}{{\text{c}}^{2}}x-1)\,dx=-2\cot x-x+c.}\]
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