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.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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