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Question Number 126710 by slahadjb last updated on 23/Dec/20

$$\int ln\left(x\right)e^{x^2}dx???$$

Answered by Dwaipayan Shikari last updated on 23/Dec/20

$$\int e^{x^2}log\left(x\right)dx{x}^2=u\Rightarrow 2x=\frac{du}{dx}$$$$=\frac{1}{2}\int u^{-\frac{1}{2}}{e}^{u}log\left(u\right)du$$$$Generally{\int }_0^x{t}^{s-1}{e}^{-t}dt=\mathrm{\Gamma }(s,x)\left(IncompleteGamma\right)$$$$Here\frac{1}{2}\int u^{-\frac{1}{2}}{e}^{u}log\left(u\right)du=\frac{1}{2}\stackrel{\bullet }{\mathrm{\Gamma }}(\frac{1}{2},;)$$

Commented by slahadjb last updated on 23/Dec/20

$$>whereislog\left(u\right)?$$

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