# Log Derivative Integral

Calculus Level pending

What is the sum of all the values of $$x$$ that satisfy $\displaystyle \log_{x^2} \left\{ \frac{d}{dx} \int_{x}^{x+1} \frac{1}{2}(t^2-t)\ dt \right\} = x^2-8x+\frac{15}{2} ?$

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