∫$$tan$$⁡$$xsin4$$⁡$$x+cos4$$⁡xdx is equal to

Correct option is 212loge⁡tan2⁡x+1+tan4⁡x+C

Questions

$\int \frac{\tan x}{\sqrt{\sin^{4} x + \cos^{4} x}} d x$ is equal to

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loge⁡tan2⁡x+1+tan4⁡x+C

12loge⁡tan2⁡x+1+tan4⁡x+C

14log⁡tan2⁡x+1+tan4⁡x+C

none of these

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detailed solution

Correct option is B

LetI=∫tan⁡xsin4⁡x+cos4⁡xdx= l=∫tan⁡xsec2⁡xtan4⁡x+1dx=12∫1tan2⁡x2+1dtan2⁡x⇒ I=12loge⁡tan2⁡x+1+tan4⁡x+C

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∫tan⁡xsin4⁡x+cos4⁡xdx is equal to

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$\int \frac{\tan x}{\sqrt{\sin^{4} x + \cos^{4} x}} d x$ is equal to