A) \[\log (x+1)+\frac{2}{x+1}+c\]
B) \[\log (x+1)-\frac{2}{x+1}+c\]
C) \[\frac{2}{x+1}-\log (x+1)+c\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\frac{x-1}{{{(x+1)}^{2}}}\,dx=\int_{{}}^{{}}{\frac{x+1-2}{{{(x+1)}^{2}}}}\,dx}\] \[=\int_{{}}^{{}}{\frac{1}{x+1}\,dx}-\int_{{}}^{{}}{\frac{2}{{{(x+1)}^{2}}}\,dx=\log (x+1)+\frac{2}{(x+1)}+c}\].
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