∫cosec^2x/(1- cot^2x)dx = ?

Question

\(\int\frac{cosec^2x}{(1-cot^2x)}dx\) = ?

∫cosec²x/(1- cot²x)dx

A.\(\frac{1}2log|\frac{1+cot\,x}{1-cot\,x}|\) + C

B. \(-\frac{1}2log|\frac{1+cot\,x}{1-cot\,x}|\) + C

C. \(\frac{1}2log|\frac{1-cot\,x}{1+cot\,x}|\) + C

D. none of these

Answer 1

\(\int\frac{cosec^2x}{1-cot^2x}dx\)

Let cot x = t 

-cosec² x dx = dt

put t = cot x

\(-\frac{1}2log|\frac{1+cot\,x}{1-cot\,x}|\) + C