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Question Number 129060 by benjo_mathlover last updated on 12/Jan/21

φ = ∫ ((ln (x))/x^2 ) dx

ϕ=∫ln(x)x2dx

Answered by liberty last updated on 12/Jan/21

let ln (x)=h ⇒x = e^h φ = ∫ (h/e^(2h) ) (e^h dh )= ∫ h.e^(−h) dh ; [ by parts ] φ=−h.e^(−h) −e^(−h) + c φ = −((ln (x))/x)−(1/x) + c φ = ((−ln (x)−1)/x) + c

letln(x)=h⇒x=ehϕ=∫he2h(ehdh)=∫h.e−hdh;[byparts]ϕ=−h.e−h−e−h+cϕ=−ln(x)x−1x+cϕ=−ln(x)−1x+c

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