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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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