Question

integral of cosec square x /1 +cot x

Answer 1

$\int\frac{cosec^2x}{1+cotx}dx$
Let cotx = z
now, differentiate
- cosec²x.dx = dz
cosec²x.dx = -dz put it in integration ,

$\int\frac{cosec^2x}{1+cotx}dx \\ \\ = \int \frac{ - dz}{1 + z} \\ \\ = - ln(1 + z) + C$
now, put z = cotx
then,
I =-ln(1 + cotx) + C