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∫√tan x
Let tanx=t2,..................(1)
then differentiating both sides,we get,
sec2x dx=2t dt
(1+tan2x) dx=2t dt
(1+t4) dx=2t dt.................from(1)
dx=[2t/(1+t4)] dt
now,
∫√tanx
=∫√(t2).[2t/(1+t4)] dt
=∫[2t2/(1+t4)] dt
and solve further.
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