Using Fundamental Theorem of Calculus: Part One, find the following: 1. Given \( f(t)=\left(2+t^{4}\right)^{5} \) and \( g(x)=\int_{1}^{x}\left(2+t^{4}\right)^{5} d t \), what is \( g^{\prime}(x)= \) ?

5. El resultado de: A) \( 5 / 3 \operatorname{sen} 3 x+C \) B) \( -3 / 5 \operatorname{sen} 3 x+C \) C) \( 1 / 3 \operatorname{sen} 3 x+C \)

If \( f(x)=\frac{7}{x+5} \) and \( g(x)=\frac{x+73}{x^{2}-25} \), determine \( (f+g)(x) \) \( (f+g)(x)=\frac{\pi+32}{x^{2}-25} \) \( (f+g)(x)=\frac{x+32}{x+5} \) \( (f+g)(x)=\frac{8}{x^{2}-25} \) \( (f+g)(x)=\frac{8}{x-5} \)

The function \( P(x)=\frac{120}{1+372 e^{-0.133 x}} \) models the percentage, \( P(x) \), of Americans who are \( x \) years old and have some degree of heart disease. What is the percentage, to the nearest tenth, of 39 -year olds with some degree of heart disease?

Suppose that the functions \( u \) and \( w \) are defined as follows. \( \begin{array}{l}u(x)=-5 x+1 \\ w(x)=-x+5\end{array} \) Find the following. \( \begin{array}{l}(w \circ u)(1)=\square \\ (u \circ w)(1)=\square\end{array} \)

8.- Resolver por Integración por fracciones parciales \( \int \frac{1}{x^{2}-4} d x \) Opciones: a) \( \frac{1}{2} \ln |x-2|-\frac{1}{2} \ln |x+2|+C \) b) ln \( |x-2|-\ln |x+2|+C \) c) \( \frac{1}{2} \ln |x+2|-\frac{1}{2} \ln |x-2|+C \) d) \( \left.{ }^{\frac{1}{2}} \ln \left|x+2+\frac{1}{2} \ln \right| x-2 \right\rvert\,+C \)