If ∫dxsin⁡$$2x$$−$$2sin$$⁡$$x=C$$−$$14log$$⁡|$$f(x)$$|$$+18sin2$$⁡$$x2thenf(x)$$ is equal to

Question

If ∫dxsin⁡$$2x$$−$$2sin$$⁡$$x=C$$−$$14log$$⁡|$$f(x)$$|$$+18sin2$$⁡$$x2thenf(x)$$ is equal to

Infinity Learn · Accepted Answer

∫dxsin⁡$$2x$$−$$2sin$$⁡$$x=12$$∫dxsin⁡$$x($$$$cos$$⁡x−$$1)=12$$∫$$sin$$⁡$$xdx1$$−$$cos2$$⁡$$x($$$$cos$$⁡x−$$1)=12$$∫−$$sin$$⁡$$xdx(1$$−$$cos$$⁡$$x)2(1+$$$$cos$$⁡$$x)=12$$∫$$dt(1$$−$$t)2(1+t)$$                       $$(t$$ $$=$$$$cos$$ $$x)=14$$∫$$1211+t+1211$$−$$t+1(1$$−$$t)2dt=1412log$$⁡|$$1+t$$|−$$12log$$⁡|$$1$$−t|$$+11$$−$$t+C=1411$$−$$cos$$⁡$$x+12log$$⁡$$1+$$$$cos$$⁡$$x1$$−$$cos$$⁡$$x+C=181sin2$$⁡$$x2$$−$$18log$$⁡$$2sin2$$⁡$$x/22cos2$$⁡$$x/2+C=181sin2$$⁡$$x/2$$−$$14log$$⁡|$$tan$$⁡$$x/2$$|$$+C$$

If $\begin{array}{l} \int \frac{d x}{\sin 2 x - 2 \sin x} = C - \frac{1}{4} \log | f (x) | + \frac{1}{8 \sin^{2} \frac{x}{2}} \end{array}$ then
$f (x)$ is equal to

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If ∫dxsin⁡2x−2sin⁡x=C−14log⁡|f(x)|+18sin2⁡x2thenf(x) is equal to

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If $\begin{array}{l} \int \frac{d x}{\sin 2 x - 2 \sin x} = C - \frac{1}{4} \log | f (x) | + \frac{1}{8 \sin^{2} \frac{x}{2}} \end{array}$ then
$f (x)$ is equal to