Solve u = e ^ ∫ frac{1{x wrt x}(int(lnx)e^-intfrac{dx{x}}+c_{1})

$$u = e ^ { \int \frac { 1 } { x } d x } ( \int ( \ln x ) e ^ { - \int \frac { d x } { x } } + c _ { 1 } )$$

Solve for c_1

$$c_{1}=\frac{-x\ln(x)+u}{x^{2}e^{С}}-\frac{С_{1}}{x}$$

$$x>0$$

Solve for u

$$u=\frac{x\left(2c_{1}xe^{С}+\ln(x)^{2}\right)}{2}+С_{1}xe^{С_{2}}$$

$$x>0$$