December 5th, 2016, 02:39 PM  #1 
Member Joined: Oct 2016 From: Slovenia, Europe Posts: 46 Thanks: 5  integral(dx/sqrt(tanx))
Does anyone have any useful ideas how to solve this integral: integral(dx/sqrt(tanx)) $\displaystyle \int \frac{dx}{\sqrt{tan{x}}}$ I really do not know how to start solving it. Please help me guys! 
December 5th, 2016, 03:20 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,388 Thanks: 2100 Math Focus: Mainly analysis and algebra 
Weierstrass substitution $t= \tan \frac{x}2$.

December 5th, 2016, 08:41 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,384 Thanks: 844 Math Focus: Elementary mathematics and beyond 
Make the sub $t^2=\tan x$. You'll end up with $$2\int\frac{1}{1+t^4}\text{ d}t$$ $1+t^4$ factors as $(t^2+\sqrt2t+1)(t^2\sqrt2t+1)$ Now use partial fractions with complex numbers ... etc. 
December 8th, 2016, 02:12 AM  #4  
Member Joined: Oct 2016 From: Melbourne Posts: 63 Thanks: 33  Quote:
which matches what Greg said. Now follow the rest of his advice  

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integraldx or sqrttanx 
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