Evaluate: (i) `int(x+1)/(x\ (x+logx)\ dx` (ii) `int1/(sqrt(1-x^2)(2+3sin^(-1)x)\ dx`

Explanation

(i)

Note: Here, we are considering `log x` as `log _{e} x`

`Let {I}=int frac{x+1}{x(x+log x)} d x`

Putting `x+log x=t`

`Rightarrow 1+frac{1}{x}=frac{d t}{d x} `

`Rightarrow frac{x+1}{x} d x=d t `

`therefore I=int frac{1}{t} d t `

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