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Question Number 66048 by aliesam last updated on 08/Aug/19

$$\int \frac{x}{\sqrt{ln\left(1/x\right)}}dx$$

Commented by Prithwish sen last updated on 08/Aug/19

$$\int \frac{\mathrm{x}}{\sqrt{-\mathrm{lnx}}}\mathrm{dx}\mathrm{put}-\mathrm{lnx}={\mathrm{u}}^2\Rightarrow \mathrm{dx}=-{2\mathrm{ue}}^{-{\mathrm{u}}^2}$$$$=-2\int {\mathrm{e}}^{-{2\mathrm{u}}^2}\mathrm{du}\mathrm{and}\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{Gaussian}\mathrm{integral}.$$$$\mathrm{And}\mathrm{it}\mathrm{has}\mathrm{no}\mathrm{closed}\mathrm{form}.$$$$\mathrm{please}\mathrm{check}.$$

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