Question

how to integrate x/x+1

Answer 1

∫xx+1dx=x−ln|x+1|+C

Explanation:

∫xx+1dx

=∫x+1−1x+1dx

=∫(1−1x+1)dx

=x−ln|x+1|+C


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Answer 2

Hope u like my process
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$= > \frac{x}{x + 1} \\ \\ = \frac{1 + x - 1}{x + 1} = \frac{1 + x}{1 + x} - \frac{1}{1 + x} \\ \\ = 1 - \frac{1}{1 + x}$
Now, Integrating it we get,

$= > x - log(1 + x) + c \\ \\ = x + log( \frac{1}{1 + x} ) + c$
Hope this is ur required answer

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