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Evaluate: int(x+1)/(x\ (1+x\ e^x))\ dx...

Evaluate: `int(x+1)/(x\ (1+x\ e^x))\ dx`

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`I=int frac{x+1}{x(1+x e^{x})} d x `
`I=int frac{e^{x}(x+1)}{e^{x} x(1+x e^{x})} d x `
`text { Put } e^{x}=t `
`Rightarrow e^{x}(x+1) d x=d t `
`I=int frac{d t}{t(1+t)} ldots ldots(1) `
`text { Let, } `
`frac{1}{t(1+t)}=frac{A}{t}+frac{B}{1+t} `
`Rightarrow 1=A(t+1)+B t ldots(2) `
...
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