What is the integration of  $\int {\frac{{(1 + \cos x)}}{{x + \sin x}}} dx$ ~~~~~[NCERT Exemp. Q. 5,Page 164 ]

Consider that, $I = \int {\frac{{(1 + \cos x)}}{{(x + \sin x)}}} dx$


Let $x + \sin x = t \Rightarrow (1 + \cos x)dx = dt$

therefore,$I = \int_t^1 d t = \log |t| + C$

$ = \log |(x + \sin x)| + C$

 

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