\( \lim _ { x \rightarrow a } ( m x + b ) = m a + b \)

5) \( \int \frac{24 x^{2}-8 x}{2 x^{3}-x^{2}} d x \)

4) \( \int \frac{3 x-1}{3 x^{2}-2 x} d x= \)

Ejercicio 3. Calcular \[ \begin{array}{ll}\text { i) } \int_{1}^{2}(4 x-2) e^{3 x+1} \mathrm{~d} x & \text { ii) } \int \frac{\cos (x)}{\operatorname{sen}(x)-\operatorname{sen}^{3}(x)} \mathrm{d} x\end{array} \quad \text { iii) } \int_{2}^{e} \frac{\sqrt{\ln (x)+2}}{x} \mathrm{~d} x \]

If \( z=x \cdot f\left(\frac{y}{x}\right)+y\left(\frac{y}{x}\right) \cdot S \cdot T \cdot \cdot x \frac{\partial z}{\partial x}+ \) \( y \cdot \frac{\partial z}{\partial y}=x \cdot f(y / x) \)

2) \( \lim _{x \rightarrow 0}\left(\frac{1}{x \sqrt{1+x}}-\frac{1}{x}\right)= \)