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Question
Integrate the function in (x2 + 1) log x.
Solution
Let `I = int (x^2 + 1) log x dx`
`= int log x. (x^2 + 1) dx`
Integrating piecewise by taking (log x) as the first function, we get
`I = (log x) int (x^2 + 1) dx - int [d/dx log x int (x^2 + 1) dx] dx`
`= log x. (x^3/3 + x) - int 1/x . (x^3/3 + 1) dx`
`= (x^3/3 + x) log x - int (x^3/3 + 1) dx`
`= (x^3/3 + x) log x - (x^3/9 + x) + C`
`= (x^3/3 + x) log x - x^3/9 - x + C`
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