What is the integration of $\int {\frac{{\left( {{x^2} + 2} \right)d}}{{x + 1}}} x$ ~~~~~[NCERT Exemp. Q. 3,Page 163 ]


Let $I = \int {\frac{{{x^2} + 2}}{{x + 1}}} dx$
$ = \int {\left( {x – 1 + \frac{3}{{x + 1}}} \right)} dx$


$ = \int {(x – 1)} dx + 3\int {\frac{1}{{x + 1}}} dx$


$ = \frac{{{x^2}}}{2} – x + 3\log |(x + 1)| + C$

 

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