dy/dx=(1+Lnx)y and if y=1 when x=1, then y=?

i know i have to find the integral by multiplying dx to the other side and bringing y to left.

and i got Ln(y)+ C = x + 1/x + C
what do i do next.

ln(y)=x+1/x+c
e^(ln(y))=e^(x+1/x+c), so
y= e^(x+1/x+c)
y= Ce^(x+1/x)

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