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

`int (x dx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3)))` is equal to

A

`(1)/(2)In (1+sqrt(1+x^(2)))+C`

B

`(-2)/(3(1+sqrt(1+x^(2)))^(3//2))+C`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
d
Let `1+x^(2)=t^(2)`. then x dx = t dt `thereforeI=int(x)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))))dx`
`rArr I=int(t)/(sqrt(t^(2)+t^(3)))dt=int(1)/(sqrt(1+t))dt=2sqrt(1+t)+C`
`rArr I=2sqrt(1+sqrt(1+x^(2)))+C`
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