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Evaluate: int1/(sqrt(x)+x)dx...

Evaluate: `int1/(sqrt(x)+x)dx`

A

`log|1+sqrt(x)|+C`

B

`2log|1+sqrt(x)|+C`

C

`(1)/(sqrtx)tan^(-1)sqrt(x)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(dx)/(sqrt(x)(1+sqrt(x)))*"Put"(1+sqrtx)=t and(1)/(2sqrt(x))dx=dt`.
`:." "I=2*int(1)/(t)dt=2log|t|+C`.
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