∫ln⁡$$($$$$tan$$⁡$$x)$$$$sin$$⁡x⋅$$cos$$⁡xdx, is equal to

Correct option is 312(ln⁡(tan⁡x))2+C

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$\int \frac{\ln (\tan x)}{\sin x \cdot \cos x} d x, is equal to$

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12ln⁡(tan⁡x)+C

12ln⁡tan2⁡x+C

12(ln⁡(tan⁡x))2+C

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detailed solution

Correct option is C

I=∫ln⁡(tan⁡x)sin⁡x⋅cos⁡xdx, let t=ln⁡(tan⁡x)⇒ dtdx=sec2⁡xtan⁡x⇒dt=dxsin⁡x⋅cos⁡x∴ I=∫tdt=12t2+C=12(ln⁡(tan⁡x))2+C

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∫ln⁡(tan⁡x)sin⁡x⋅cos⁡xdx, is equal to

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free study material

$\int \frac{\ln (\tan x)}{\sin x \cdot \cos x} d x, is equal to$