Question

How to do integration of
$\sqrt{ \cot(x) }$
​

Answer 1

Answer:

I=∫(

√

tanx

+

√

cotx

)dx

=∫

sinx+cosx

√

sinxcosx

dx

Putting sinx−cosx=u, du=(cosx+sinx)dx,u2=1−2sinxcosx,sinxcosx=

u2−1

2

I=∫

√

2

du

√

1−u2

=

√

2

arcsinu+C=

√

2

arcsin(sinx−cosx)+C

where C is an arbitrary constant for indefinite integral.