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What is the value of int(sqrtx + x)^(-1)...

What is the value of `int(sqrtx + x)^(-1) dx`?

A

`(1)/(2)log(1+sqrtx)+C`

B

`2log (1+sqrtx)+C`

C

`(1)/(2)log(1+sqrtx)+C`

D

`3log(1+sqrtx)+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int(dx)/(x+sqrtx)=int(1)/(sqrtx(1+sqrtx))dx`
`"Put "1+sqrtx-t rArr (1)/(sqrtx)dx=2dt`
`therefore" "l=2 int(1)/(t)dt=2og t+C`
`" "=2 log(1+sqrtx)+C`
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