If F(x) = int_{x^2}^{x^3} log t , dt (x 0), | vedclass

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(A) Given $F(x) = \int_{x^2}^{x^3} \log t \, dt$. Applying the Leibniz integral rule,which states that $\frac{d}{dx} \int_{g(x)}^{h(x)} f(t) \, dt = f

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$(9x^2 - 4x)\log x$

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(A) Given $F(x) = \int_{x^2}^{x^3} \log t \, dt$. Applying the Leibniz integral rule,which states that $\frac{d}{dx} \int_{g(x)}^{h(x)} f(t) \, dt = f(h(x)) \cdot h'(x) - f(g(x)) \cdot g'(x)$. Here,$f(t) = \log t$,$h(x) = x^3$,and $g(x) = x^2$. Thus,$F'(x) = \log(x^3) \cdot \frac{d}{dx}(x^3) - \log(x^2) \cdot \frac{d}{dx}(x^2)$. $F'(x) = (3 \log x) \cdot (3x^2) - (2 \log x) \cdot (2x)$. $F'(x) = 9x^2 \log x - 4x \log x$. $F'(x) = (9x^2 - 4x) \log x$.

If $F(x) = \int_{x^2}^{x^3} \log t \, dt$ $(x > 0)$,then $F'(x) = $

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