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Question

Question: \[\int_{}^{}{\frac{d\theta}{\sin\theta\cos^{3}\theta} =}\]...

∫dθsin⁡θcos⁡3θ=\int_{}^{}{\frac{d\theta}{\sin\theta\cos^{3}\theta} =}

A

logtanθ+tan⁡2θ+c{logtan}\theta + \tan^{2}\theta + c

B

logtanθ−12tan⁡2θ+c{logtan}\theta - \frac{1}{2}\tan^{2}\theta + c

C

logtanθ+12tan⁡2θ+c{logtan}\theta + \frac{1}{2}\tan^{2}\theta + c

D

∫1cos⁡−1x.1−x2dx=\int_{}^{}{\frac{1}{\cos^{- 1}x.\sqrt{1 - x^{2}}}dx =}

Answer

logtanθ+12tan⁡2θ+c{logtan}\theta + \frac{1}{2}\tan^{2}\theta + c

Explanation

Solution

∫x−2x(2log⁡x−x)dx=\int_{}^{}{\frac{x - 2}{x(2\log x - x)}dx} =

log⁡(2log⁡x−x)+c\log(2\log x - x) + c