`int1/(sqrt(x)+root(4)x)\ dx` (ii) `int1/(x^(1//3)(x^(1//3)-1))\ dx`

Explanation

(i)
Let `I=int frac{1}{sqrt{x}+root[4]x} d x`

Let `x=t^{4}`

On differentiating both sides, we get


`d x=4 t^{3} d t `

therefore `I=int frac{4 t^{3}}{sqrt{t^{4}}+root[4]{t^{4}}} d t `

`=int frac{4 t^{3}}{t^{2}+t} d t `

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