Evaluate the integral $\displaystyle \int\frac{{{\left.{d}{x}\right.}}}{{{x}^{{2}}+{4}{x}+{10}}}$.

a. For this integral, the appropriate substitution that will yield an inverse trigonometric antiderivative is $\displaystyle {u}=$ .

b. Rewriting the integral in terms of $\displaystyle {u}$ gives $\displaystyle \int$ $\displaystyle {d}{u}$    Preview Question 6 Part 2 of 3  

c. $\displaystyle \int\frac{{{\left.{d}{x}\right.}}}{{{x}^{{2}}+{4}{x}+{10}}}=$ $\displaystyle +{C}$    Preview Question 6 Part 3 of 3       Write your final answer in terms of $\displaystyle {x}$.