If ∫$$sin$$⁡$$2xcos4$$⁡$$x+sin4$$⁡$$xdx=$$$$tan$$−$$1$$⁡$$(f(x))+C$$ then

Correct option is 4f(x)=tan2⁡x

Questions

If $\int \frac{\sin 2 x}{\cos^{4} x + \sin^{4} x} d x = \tan^{- 1} (f (x)) + C$ then

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f(x)=x2

f(x)=cos⁡x

f(x)=sin⁡x

f(x)=tan2⁡x

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detailed solution

Correct option is D

sin⁡2xcos4⁡x+sin4⁡x=2sin⁡xcos⁡xcos4⁡x+sin4⁡x=2tan⁡xsec2⁡x1+tan4⁡xNow put tan2⁡x=t.

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If ∫sin⁡2xcos4⁡x+sin4⁡xdx=tan−1⁡(f(x))+C then

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If $\int \frac{\sin 2 x}{\cos^{4} x + \sin^{4} x} d x = \tan^{- 1} (f (x)) + C$ then