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Question
Integrate the function in x log 2x.
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Solution
Let `I = int x log 2x dx`
`= (log 2x) * x^2/2 - int d/dx (log 2x) (x^2)/2 dx`
`= log (2x)* x^2/2 - int 2/(2x) (x^2/2) dx + C`
`= x^2/2 log (2x) - 1/2 int x dx + C`
`= x^2/2 log (2x) - 1/2 * x^2/2 + C`
`= x^2/2 log (2x) - x^2/4 + C`
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