Question

The value of $\frac{\sin x+\cos x}{\sqrt{1+\sin 2x}}dx$ is

• A. $\sin x+c$
• B. $x+c$
• C. $\cos x+c$
• D. $\frac{1}{2}(\sin x+\cos x)$

Answer 1

Answer: (B)

$x+c$

$=\int \frac{\sin x+\cos x}{\sqrt{1+sin2x}}dx$

$=\int \frac{\sin x+\cos x}{\sqrt{{\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x}}dx$

$=\int \frac{\sin x+\cos x}{\sqrt{{(\sin x+\cos x)}^2}}dx$

$=\int \frac{\sin x+\cos x}{\sin x+\cos x}dx$

$=\int 1dx$

$=x+c$

Hence, this is the answer.

Option (B) is correct.