Evaluate: (i) `int1/(sqrt(1+4x^2))\ dx` (ii) `int1/(sqrt(a^2+b^2\ x^2))\ dx`

Explanation

(i)
`int frac{d x}{sqrt{1+4 x^{2}}} `

`=int frac{d x}{sqrt{1+(2 x)^{2}}} `

`text { let } 2 x=t `

`Rightarrow 2 d x=d t `

`Rightarrow d x=frac{d t}{2} `

`text { Now, } int frac{d x}{sqrt{1+(2 x)^{2}}} `

`=frac{1}{2} int frac{d t}{sqrt{1+t^{2}}} `

...