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Question Number 185959 by Michaelfaraday last updated on 30/Jan/23

$$solve:$$$$\int x^{Inx}dx$$

Answered by Frix last updated on 30/Jan/23

$$\int x^{\ln x}dx\stackrel{t=\frac{1}{2}+\ln x}{=}\frac{1}{\sqrt[4]{\mathrm{e}}}\int {\mathrm{e}}^{t^2}dt=\frac{\sqrt{\pi }}{2\sqrt[4]{\mathrm{e}}}\mathrm{erfi}\left(t\right)=$$$$=\frac{\sqrt{\pi }}{2\sqrt[4]{\mathrm{e}}}\mathrm{erfi}(\frac{1}{2}+\ln x)+C$$

Commented by Michaelfaraday last updated on 30/Jan/23

$$thankssir$$

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