Resuelve el ejercicio aplicando las reglas de potencia de integrales. \[ \int\left(x^{4}-6 x^{2}-2 x+4\right) d x \] \( \frac{x^{5}}{5}-2 x^{3}-5 x^{2}-4 x+C \) a. \( \frac{x^{5}}{5}-2 x^{3}-x^{2}+4 x+C \) c. \( \frac{x^{5}}{5}-2 x^{3}-x^{2}-4 x-C \) d. \( \frac{x^{3}}{5}-2 x^{5}-x^{2}+4 x+C \)

If the slope of the tangent to the curve: \( y=f(x) \) at any point on it equals \( 6 x+a \), whe \( a \) is constant if the equation of the tangent to the curve at the point \( (1,-1) \) is \( y=4- \) \( 5 x \), then the equation of the curve is ... \( \begin{array}{llll}\text { a) } y=3 x^{2}-4 & \text { b) } y=3 x^{2}-11 x+7 & \text { c) } y=3 x^{2}-4 x & \text { d) } y=3 x^{2}-x-3\end{array} \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

If the slope of the tangent to the curve: \( y=f(x) \) at any point on it equals \( 6 x+a \), where \( a \) is constant if the equation of the tangent to the curve at the point \( (1,-1) \) is \( y=4- \) \( 5 x \), then the equation of the curve is ... \( \begin{array}{llll}\text { a) } y=3 x^{2}-4 & \text { b) } y=3 x^{2}-11 x+7 & \text { c) } y=3 x^{2}-4 x & \text { d) } y=3 x^{2}-x-3\end{array} \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

Show that \( \Gamma\left(\frac{1}{2}\right)=\sqrt{\pi} \)