Caculus Help : Integrating with trig identities?

eay444
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Homework Statement



integrate: sin (2x)/(1+sinx)



Homework Equations



(sin x)^2 + (cos x) ^2 = 1
sin (2x) = 2 sin x cos x
cos (2x) = (cos x)^2 - (sin x)^2



The Attempt at a Solution



I've been trying to integrate this thing for about an hour by rearranging various trig idenities with no luck. Am I missing something? I don't think this problem is supposed to be that hard. Someone please help!
 
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I would try first replacing sin (2x) with 2 sin x cos x then do u sub and let u = cos x. Try that and see if it helps
 
I got it now, Thanks for your help.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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