Mathematics

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

$x + c$

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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