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Question: \[\int_{}^{}{\frac{\text{cose}\text{c}^{2}x}{1 + \cot x}dx =}\]...

∫cosec2x1+cot⁡xdx=\int_{}^{}{\frac{\text{cose}\text{c}^{2}x}{1 + \cot x}dx =}

A

log⁡(1+cot⁡x)+c\log(1 + \cot x) + c

B

−log⁡(1+cot⁡x)+c- \log(1 + \cot x) + c

C

12(1+cot⁡x)2+c\frac{1}{2(1 + \cot x)^{2}} + c

D

None of these

Answer

12(1+cot⁡x)2+c\frac{1}{2(1 + \cot x)^{2}} + c

Explanation

Solution

1+2x21+x2+c\frac{1 + 2x^{2}}{\sqrt{1 + x^{2}}} + c

1+x2+c\sqrt{1 + x^{2}} + c.