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प्रश्न
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
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उत्तर
Let I = `int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Put f(x) = (log x)2
∴ f '(x) = `(2 log "x")/"x"`
∴ I = ∫ ex [f(x) + f '(x)] + dx
= ex f(x) + c
∴ I = ex (log x)2 + c
Notes
The answer in the textbook is incorrect.
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