Question

If $\int_{}^{}{\sec x\mspace{6mu} dx =}$ then ${logtan}\left( \frac{\pi}{8} + \frac{x}{2} \right) + c$ is.

• A. $\int_{}^{}{\sqrt{1 + \sin x}\mspace{6mu} dx =}$
• B. $\frac{1}{2}\left( \sin\frac{x}{2} + \cos\frac{x}{2} \right) + c$
• C. $\frac{1}{2}\left( \sin\frac{x}{2} - \cos\frac{x}{2} \right) + c$
• D. $2\sqrt{1 + \sin x} + c$

Answer 1

Answer: (A)

$\int_{}^{}{\sqrt{1 + \sin x}\mspace{6mu} dx =}$

Answer 2

Sol. Trick : Let $\int_{}^{}{\tan^{4}x\mspace{6mu} dx =}$ then$\tan^{3}x - \tan x + x + c$

$\frac{1}{3}\tan^{3}x - \tan x + x + c$