Solveeit Logo
Login

Question

Question: \[\int_{}^{}{\frac{1}{\sqrt{1 + \cos x}}\mspace{6mu} dx =}\]...

∫11+cos⁡x 6mudx=\int_{}^{}{\frac{1}{\sqrt{1 + \cos x}}\mspace{6mu} dx =}

A

2log⁡(sec⁡x2+tan⁡x2)+K\sqrt{2}\log\left( \sec\frac{x}{2} + \tan\frac{x}{2} \right) + K

B

12log⁡(sec⁡x2+tan⁡x2)+K\frac{1}{\sqrt{2}}\log\left( \sec\frac{x}{2} + \tan\frac{x}{2} \right) + K

C

log⁡(sec⁡x2+tan⁡x2)+K\log\left( \sec\frac{x}{2} + \tan\frac{x}{2} \right) + K

D

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

Answer

log⁡(sec⁡x2+tan⁡x2)+K\log\left( \sec\frac{x}{2} + \tan\frac{x}{2} \right) + K

Explanation

Solution

13(1−tan⁡2x)3/2+c\frac{1}{3}(1 - \tan^{2}x)^{3/2} + c