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

$$$$$$\int (\log x+1)x^{x}dx$$$$$$

Answered by puissant last updated on 21/Aug/21

$$K=\int (1+lnx)x^{x}dx$$$$x^x=e^{xlnx}\frac{d}{dx}{e}^{xlnx}=(1+lnx)x^x$$$$\Rightarrow K=x^x+C$$

Commented by Olaf_Thorendsen last updated on 21/Aug/21

$$x^x=e^{x\ln x}$$$$\frac{d}{dx}{x}^x=\frac{d}{dx}{e}^{x\ln x}=(1+\ln x)e^{x\ln x}=(1+\ln x)x^x$$$$\mathrm{K}=x^x+\mathrm{C}$$

Commented by Tawa11 last updated on 22/Aug/21

$$\mathrm{Sir},\mathrm{help}\mathrm{me}\mathrm{check}\mathrm{Q}151636$$

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