Question

The value of integral $I=\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2x}}$ is

• A. $\sqrt{1+\cos 2x}$
• B. $\sqrt{x}$
• C. $x$
• D. $\sqrt{1+2x}$

Answer 1

The correct option is C $x$

Let $I=\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2x}}$

we know,

$1+\sin 2x=(\sin x+\cos x{)}^2$

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