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Question
Evaluate the following.
∫ x log x dx
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Solution
Let I = ∫ x log x dx
`= log "x" int "x" "dx" - int["d"/"dx" (log "x") int "x dx"] "dx"`
`= log "x" * "x"^2/2 - int [1/"x" xx "x"^2/2]` dx
`= "x"^2/2 log "x" - 1/2 int "x dx"`
`= "x"^2/2 log "x" - 1/2 * "x"^2/2 + "c"`
∴ I = `"x"^2/2 log "x" - "x"^2/4 + "c"`
Notes
The answer in the textbook is incorrect.
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