How can we find the integral of 1/x?

If y(x) is a definite integral of 1/x then we have

dy/dx = 1/x

Therefore

dx/dy = x

From which we we know

x = ce^y

(Why? It's the same as saying the solution to f’(y)=f is f(y)=ce^y)

Taking log of both sides

lnx = lnc + y

Which shows that the integral is lnx plus an arbitrary constant, y = lnx + k

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