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$\int \frac{\sin 2 t}{\sin^{4} t + \cos^{4} t} d t is equal to$

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detailed solution

Correct option is A

Let I=∫sin⁡2tsin4⁡t+cos4⁡tdt=∫2sin⁡tcos⁡tcos4⁡ttan4⁡t+1dtI=∫2sintcostsec2tdt(tant)4+1 Put tan2⁡t=x⇒2tan⁡tsec2⁡tdt=dxI=∫dxx2+1=tan−1⁡(x)+C=tan−1⁡tan2⁡t+C

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∫sin⁡2tsin4⁡t+cos4⁡tdt is equal to

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$\int \frac{\sin 2 t}{\sin^{4} t + \cos^{4} t} d t is equal to$