Is there any other solution to the integral equation $\int_{0}^{\infty}e^{kx}f(x) dx=\frac{k^2+k}{k^3},k<0$ except $f(x)=x-1$?

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Is there any other solution to the integral equation $$\displaystyle\int_{0}^{\infty}e^{kx}f(x) dx=\frac{k^2+k}{k^3},k<0$$ except $f(x)=x-1$?