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 December 30th, 2017, 03:05 AM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 integrate root(cos2x)/sinx integrate root(cos2x)/sinx December 30th, 2017, 08:19 AM   #2
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 Originally Posted by mared integrate root(cos2x)/sinx
Wolfram|Alpha: Computational Knowledge Engine) December 30th, 2017, 07:04 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra Two approaches:Weierstrauss substitution; $\displaystyle \frac{\sqrt{\cos{(2x)}}}{\sin x} = \sin x \frac{\sqrt{2\cos^2 x - 1}}{1-\cos^2 x}$ December 30th, 2017, 09:47 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,113 Thanks: 2327 Assuming $|x| \leqslant \pi/4$, $\displaystyle \frac12\ln\left(\frac{2\cos(x) + 1 - \sqrt{\cos(2x)}}{2\cos(x) - 1 + \sqrt{\cos(2x)}}\right) + \sqrt2\ln\left(\sqrt{2\cos(2x)} + 2\cos(x)\right) + \ln\!|\!\tan(x/2)| + \text{C}$, where $\text{C}$ is a constant. Tags integrate, rootcos2x or sinx Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mared Calculus 9 September 2nd, 2014 07:38 PM mared Calculus 3 May 18th, 2014 05:39 PM obakgd Trigonometry 1 April 16th, 2014 01:07 PM mared Calculus 3 April 4th, 2014 05:53 AM szpaq234 Calculus 1 March 23rd, 2014 03:06 AM

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