Evaluate: `int1/(x^2sqrt(1+x^2))dx`

Answer

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

Explanation

Put `x=tan theta`
`implies dx=sec^(2) theta d theta`
` :. int (1)/(x^(2)sqrt(1+x^(2)))dx=int(sec^(2) theta d theta)/(tan^(2)theta sec theta)`
`=int "cosec" theta cot theta d theta`
`= -"cosec" theta +C`
`=(-sqrt(x^(2)+1))/(x)+C`