Evaluate the following definite integral: `int_1^3(logx)dx`

Explanation

Taking `I =int_{1}^{3} log x cdot d x`
`
=int_{1}^{3} log x cdot 1 d x`
`
=[log x int_{1} cdot d x]_{1}^{3}[frac{d}{d x}(log x) int 1 cdot d x] cdot d x`
`
=[log x cdot(x)]_{1}^{3}-int_{1}^{3} frac{1}{x} x cdot d x`
`
=[x log x]_{1}^{3}-int_{1}^{3} 1 cdot d x`
`
=(3 log 3-1 log 1)-[x]_{1}^{3}`
`
=(3 log 3-0)-(3-1) `
`
=3 log 3-2`
`
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