Mathematics

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


ANSWER

$$x + c$$


SOLUTION
$$\displaystyle\int \dfrac{sin x +cos x }{\sqrt{1 + sin(2x)}}dx$$
$$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{\sqrt{sin^2x+ cos^2x + 2sinxcosx}}dx$$
$$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{\sqrt{sinx + cosx}^2}dx$$
$$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{sinx+ cosx}dx$$
$$\displaystyle\rightarrow\int dx$$
$$\displaystyle\rightarrow x + c$$
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Single Correct Medium Published on 17th 09, 2020
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