# Integrate: x+2 / (x+1)^2

Answers (1)

Solution:

$I=\int \frac{x+2}{(x+1)^{2}}dx\\ \\ \Rightarrow \hspace{1cm}I=\int \frac{x+1+1}{(x+1)^{2}}dx\\ \\ \Rightarrow \hspace{1cm}I=\int (\frac{x+1}{(x+1)^{2}}+\frac{1}{(x+1)^{2}})dx \\ \\ \Rightarrow \hspace{1cm}I=\ln \left | x+1 \right |-\frac{1}{x+1}+c$

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