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∫ cosec x / log(tan x/2) dx , please ans asap, thank you.

∫ cosec x / log(tan x/2) dx , please ans asap, thank you.

Grade:12

2 Answers

Arun
25757 Points
5 years ago
This can be written as
1/sin x* log tan(x/2)
= 1/ 2sin(x/2) cos(x/2) * log tan(x/2)
Multiply by cos (x/2) in both numerator or denominator
= 1/ 2tan(x/2) cos²(x/2) * log tan(x/2)
 
Now assume 
Log tan(x/2) = t
Sec²(x/2)/ 2*tan(x/2) dx = dt
dx/ 2 cos²(x/2) tan(x/2) = dt
Hope now you can do it further
ASHISH yadav
13 Points
2 years ago
Using substitution ,  denote the denominator by t
t=log tanx/2 , differentiating on both sides 
dt/dx = 1/tanx/2×sec^2 x/2×1/2
Hence we get dt =1/sinx dx 
Substitute  the value of dx as dt×sinx in cosec x/ t  dt
From this we get log log tan x/2 + c

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