Integrate [tex] \sqrt{1+sin( \frac{x}{2} } [/tex]. The answer should be of the form : [tex]tan \frac{x}{2} +4(sin \frac{x}{4} - cos \frac{x}{4} )[/tex]
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Integrate [tex] \sqrt{1+sin( \frac{x}{2} } [/tex]. The answer should be of the form : [tex]tan \frac{x}{2} +4(sin \frac{x}{4} - cos \frac{x}{4} )[/tex]
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using sin²x+cos²x=1
sin²x/4 +cos²x/4 =1
sinx/2=2sinx/4cosx/4
using these data i can solve this
I= ∫√sin²x/4+cos²x/4 + 2sinx/4cosx/4dx
it is in the form of (a+b)²= a²+b²+2ab
so using identity
I= ∫√(sinx/4+cosx/4)²dx
I= ∫sinx/4dx + ∫cosx/4dx
I = -4cosx/4+4sinx/4
I= 4 (sinx/4-cosx/4)+c answer is not in ur form dude