If `int(dx)/((x+100)sqrt(x+99))=f(x)+C`, then `f(x)` isA. `2(x+100)^(1//2)`B. `3(x+100)^(1//2)`C. `2tan^(-1)(sqrt(x+99))`D. `2tan^(-1)(sqrt(x+100))`

If `int(dx)/((x+100)sqrt(x+99))=f(x)+C`, then `f(x)` isA. `2(x+100)^(1

1.	If `int(dx)/((x+100)sqrt(x+99))=f(x)+C`, then `f(x)` isA. `2(x+100)^(1//2)`B. `3(x+100)^(1//2)`C. `2tan^(-1)(sqrt(x+99))`D. `2tan^(-1)(sqrt(x+100))`
Answer» Correct Answer - C Let `l=int(dx)/([(sqrt(x+99))^(2)+1]sqrt(x+99))` Put`" "sqrt(x+99)= t rArr (1)/(sqrt(x+99))dx=2dt` `therefore" "=int(2dt)/(t^(2)+1)=2 tan^(-1)t+C` `=2tan^(-1)sqrt((x+99))+C` But`" "2tan^(-1)sqrt(x+99)+C=f(x)+C" [given]"` `therefore" "f(x)=2 tan^(-1)(sqrt(x+99))`