December 31st, 2011, 11:24 PM  #1 
Newbie Joined: Dec 2011 Posts: 25 Thanks: 0  integral of sin2x/2sincos^2x
I'm studying integral calculus right now.. and my teacher gave as assignments.. I really don't have idea to answer this integral of sin2x/2sincos^2x but I try to answer this.. and I got I rewrite it to: 2sinxcosx/2sincos^2x then divide them and I got 1/cosx integral of sec x = ln sec x + tan x + c ln sec x + tan x + c this was my final answer.. is this correct? Happy new year and thank you in advance. 
December 31st, 2011, 11:38 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: integral of sin2x/2sincos^2x
I assume you mean: Let: and we have: You are correct. 
December 31st, 2011, 11:53 PM  #3 
Newbie Joined: Dec 2011 Posts: 25 Thanks: 0  Re: integral of sin2x/2sincos^2x
Ohh my, am I really correct? Wow... Thank you very much.... as in super thank you She also gave this homework... integral of dx / 1cosx I let u = sin x du =x dx=du integral of dx / u = dx/ sinx = 1/sinx = integral of csc x then my final answer was lncsc x + cot x  + c Am I also correct here? Thank you again... 
December 31st, 2011, 11:58 PM  #4  
Newbie Joined: Dec 2011 Posts: 25 Thanks: 0  Re: integral of sin2x/2sincos^2x Quote:
Sir the denominator is only 2sincos^2x... is it ok to divide with 2sinxcosx... and get 1 because there is x before cosx in numerator  
January 1st, 2012, 12:21 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: integral of sin2x/2sincos^2x
We are given: Observing that we may write: 
January 1st, 2012, 01:05 AM  #6 
Newbie Joined: Dec 2011 Posts: 25 Thanks: 0  Re: integral of sin2x/2sincos^2x
You're so good... thank you again.. 
January 1st, 2012, 06:34 PM  #7  
Global Moderator Joined: Dec 2006 Posts: 20,104 Thanks: 1907  Quote:
Using cos x = 1  2sin²(x/2), The substitution u = sin x (for which du = cos x dx) wouldn't have helped.  

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