Question

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

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

Answer 1

The correct option is B $x+c$

$\int \frac{sinx+cosx}{\sqrt{1+sin\left(2x\right)}}dx$

$\to \int \frac{sinx+cosx}{\sqrt{si{n}^{2}x+co{s}^{2}x+2sinxcosx}}dx$

$\to \int \frac{sinx+cosx}{{\sqrt{sinx+cosx}}^2}dx$

$\to \int \frac{sinx+cosx}{sinx+cosx}dx$

$\to \int dx$

$\to x+c$