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int({x+sqrt(x^(2)+1)})/(sqrt(x^(2)+1))dx...

`int({x+sqrt(x^(2)+1)})/(sqrt(x^(2)+1))dx` is equal to

A

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

B

`(1)/(n){x+sqrt(x^(2)+1)}^(n)+C`

C

`(1)/(n+1){x+sqrt(x^(2)+1)}^(n+1)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Let `I=int({x+sqrt(x^(2)+1)})/(sqrt(x^(2)+1))dx`
`rArr I=int{x+sqrt(x^(2)+1)}^(n-1)xx(x+sqrt(x^(2)+1))/(sqrt(x^(2)+1))dx`
`rArrI=int{x+sqrt(x^(2)+1)}^(n-1)d(x+sqrt(x^(2)+1))`
`rArrI=(1)/(n)(x+sqrt(x^(2)+1))^(n)+C`
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