log-x-1-x-x-dx-

Question Number 151501 by talminator2856791 last updated on 21/Aug/21

\int (\log x + 1) x^{x} d x

Answered by puissant last updated on 21/Aug/21

K = \int (1 + l n x) x^{x} d x

x^{x} = e^{x l n x} \frac{d}{d x} e^{x l n x} = (1 + l n x) x^{x}

\Rightarrow K = x^{x} + C

Commented by Olaf_Thorendsen last updated on 21/Aug/21

x^{x} = e^{x \ln x}

\frac{d}{d x} x^{x} = \frac{d}{d x} e^{x \ln x} = (1 + \ln x) e^{x \ln x} = (1 + \ln x) x^{x}

K = x^{x} + C

Commented by Tawa11 last updated on 22/Aug/21

Sir, help me check Q 151636

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