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Evaluate: int(ddx)/(sqrt(1+x^2)+sqrt((1+...

Evaluate: `int(ddx)/(sqrt(1+x^2)+sqrt((1+x^2)^3))`

Text Solution

Verified by Experts

The correct Answer is:
`1+sqrt(1+t^(2))+c`
`I=int(xdx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))))`
`=int(xdx)/(sqrt((1+x^(2))(1+sqrt(1+x^(2)))))`
` "Let " 1+sqrt(1+x^(2))=t^(2)`
` :. 2tdt =(x)/(sqrt(1+x^(2)))dx`
` :. I=int2t=t+c=1+sqrt(1+t^(2))+c`
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