Integration following Multiple Derivations

Calculus Level 3

Using the following formulas: \[\begin{cases}f(x) = \dfrac{5^{\cos ^2(x)+\sin ^2(x)}}{e^x} \\ g(x) = f(x) - f'(x) \\ h(x) = \dfrac{f(x)f'(x)}{g(x)g'(x)}\end{cases}\]

Determine: \(\displaystyle \int_{0}^{100} h(x) dx\)

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