1.

`int(dx)/((x+1)sqrt(4x+3))` is equal toA. `tan^(-1)sqrt(4x+3)+C`B. `3tan^(-1)sqrt(4x+3)+C`C. `2tan^(-1)sqrt(4x+3)+C`D. `4tan^(-1)sqrt(4x+3)+C`

Answer» Correct Answer - C
Let `l=int(dx)/((x+1)sqrt(4x+3))`
Put `4x+3=t^(2) rArr 4 dx = 2t dt`
`therefore" "l=(1)/(2)int(tdt)/(((t^(2)-3)/(4)+1)t)=2int(dt)/(1+t^(2))`
`=2tan^(-1)t+C=2tan^(-1)sqrt(4x+3)+C`


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