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Evaluate: int("log"(x+sqrt(1+x^2)))/(sqr...

Evaluate: `int("log"(x+sqrt(1+x^2)))/(sqrt(1+x^2))dxdot`

A

`2 log_(e)(x+sqrt(x^(2)+1))+C`

B

`{log_(e)(x+sqrt(x^(2)+1))}^(2)+C`

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
We hav, `I=int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx`
`rArr I=intlog_(e)(x+sqrt(x^(2)+1))d{log_(e)(x+sqrt(x^(2)+1))}`
`rArrI=(1)/(2){log_(e)(x+sqrt(x^(2)+1))}^(2)+C`
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