Evaluate: (i) `int(e^x+1)/(e^x+x)\ dx` (ii) `int1/(xlogx)\ dx`

Explanation

(i)
`Let {I}=int frac{e^{x}+1}{e^{x}+x} d x`

Putting `e^{x}+x=t`

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

`Rightarrow(e^{x}+1) d x=d t`

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

`=ln |t|+C `

`=ln |e^{x}+x|+C[because t=e^{x}+x]`



...