Question

Evaluate : $\int e^{{\sin }^{-1}x}(\frac{\ell nx}{\sqrt{1-x^2}}+\frac{1}{x})dx$

Answer 1

$\int e^{{\text{sin}}^{-1}x}(\frac{\ln x}{\sqrt{1-x^2}}+\frac{1}{x})dx=\int e^{{\text{sin}}^{-1}x}\ln xd\left({\text{sin}}^{-1}x\right)+\int e^{{\text{sin}}^{-1}x}\frac{dx}{x}=e^{{\text{sin}}^{-1}x}\ln x-\int \frac{e^{{\text{sin}}^{-1}x}}{x}dx+\int \frac{e^{{\text{sin}}^{-1}x}}{x}dx=e^{{\text{sin}}^{-1}x}\ln x+c$