45. \( \int \frac{x d x}{\left(3 x^{2}-4\right)^{4}} \)

25. \( N=\frac{p+q}{p+r}, \quad p=u+v w, \quad q=v+u w, \quad r=w+u v \) \( \frac{\partial N}{\partial u}, \frac{\partial N}{\partial v}, \frac{\partial N}{\partial w} \quad \) donde \( u=2, v=3, w=4 \)

INSTRUCCIONES: Resuelvi 1. \( \int_{1}^{4} x^{2} d x= \)

Tarea \( \int 5 d x= \) \( \int \frac{d x}{3}= \) \( \int x d x= \) \( \int 3 d u= \)

2. Sea \( f(x)=3 x^{2} \), continua en el intervalo \( [1,9] \) y \( x \) un punto dentro del intervalo. Determine \( F(x)= \)

Find the minimum value of \( f(t)=2 t^{3}-24 t^{2}+90, t \geq 0 \), and give the value of \( t \) where this minimum occurs. The minimum value occurs when \( t=\square \) with a value of \( \square \).