Question

Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]

Answer 1

\[\int \left( \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \right)dx\]
\[ \Rightarrow \int \frac{\left( \sin x + \cos x \right)dx}{\sqrt{\sin^2 x + \cos^2 x + 2 \sin x \cos x}}\]
\[ \Rightarrow \int \frac{\left( \sin x + \cos x \right)dx}{\sqrt{\left( \sin x + \cos x \right)^2}}\]
\[ \Rightarrow \int dx\]
\[ \Rightarrow x + C\]