Evaluate the following definite integral: `int_1^2x/((x+1)(x+2))dx`

Explanation

`=int_{1}^{2} frac{2 x+2-(x+1)}{(x+1)(x+2)} d x `
`
=int_{1}^{2} frac{2}{(x+2)} d x-int_{1}^{2} frac{1}{(x+1)} d x`


We know that derivative of `log x=frac{1}{x}`

According to that
`

=[-log (x+1)+2 log (x+2)]_{1}^{2}`


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