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solve-x-x-1-ln-x-dx-




Question Number 97089 by Mathudent last updated on 06/Jun/20
solve  ∫x^x (1+ln x)dx .
$${solve}\:\:\int{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}\:. \\ $$
Answered by  M±th+et+s last updated on 06/Jun/20
let x^x =u    du=x^x (1+ln(x))dx  ∫du=u+c  ∫x^x (1+ln(x))dx=x^x +c
$${let}\:{x}^{{x}} ={u}\:\:\:\:{du}={x}^{{x}} \left(\mathrm{1}+{ln}\left({x}\right)\right){dx} \\ $$$$\int{du}={u}+{c} \\ $$$$\int{x}^{{x}} \left(\mathrm{1}+{ln}\left({x}\right)\right){dx}={x}^{{x}} +{c} \\ $$
Commented by Mathudent last updated on 06/Jun/20
thank you
Commented by  M±th+et+s last updated on 06/Jun/20
you are welcome
$${you}\:{are}\:{welcome} \\ $$

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