Evaluate \( : \int \frac{x+3}{\sqrt{5-x^{2}-4 x}} \)

2. The rate of certain chemical reaction is given by \( r(x)=k x(a-x) \), \( 0 \leq x \leq a, a>0 \) and \( k>0 \). For what values of \( x \) does the rate of reaction increase? \( \begin{array}{llll}\text { A. } 0 \leq x \leq \frac{a}{2} & \text { B. } \frac{a}{2} \leq x \leq a & \text { C. }-\infty \leq x \leq \frac{a}{2} & \text { D. } \frac{a}{2} \leq x \leq \frac{3 a}{4}\end{array} \)

40. Let \( f(x)=x^{3}-12 x+1 \) be defined on \( [0,3] \). What is the range of \( f \) ? \( \begin{array}{llll}\text { A. }(-\infty, \infty) & \text { B. }(-\infty, 1] & \text { C. }[-15,1] & \text { D. }[-15,17]\end{array} \)

Integrate \( f(x)=\frac{1}{\left(x^{2}+4\right)\left(x^{2}+2\right)} \) use partia fraction

D': dyferent \( f(x)=\frac{3 x^{2}+2 x}{4 x^{2}+2 x} \)

To find the turning point and the degree of the polynomial \( P(x)=x^{99}-1 \), let's break it