A cup of coffee is at a temperature of 90°C when it is placed in a room where the ambient temperature is 20°C. According to Newton's Law of Cooling, if the cooling constant k is 0.1, what will be the temperature of the coffee after 15 minutes?

5.- Realiza la siguiente derivada logaritmica con base diferente a) \( \log _{9}\left(9 x^{3}-5\right) \)

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

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

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

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