Evaluate $\displaystyle \int\frac{{{12}{x}+{12}}}{{{2}{x}^{{2}}+{4}{x}+{10}}}{\left.{d}{x}\right.}$ where $\displaystyle {2}{x}^{{2}}+{4}{x}+{10}>{0}$.
First substitute u = Preview Question 6 Part 1 of 4  
Then $\displaystyle \int\frac{{{12}{x}+{12}}}{{{2}{x}^{{2}}+{4}{x}+{10}}}{\left.{d}{x}\right.}=\int$ Preview Question 6 Part 2 of 4   du
Now integrate with respect to u to get Preview Question 6 Part 3 of 4   + C
So $\displaystyle \int\frac{{{12}{x}+{12}}}{{{2}{x}^{{2}}+{4}{x}+{10}}}{\left.{d}{x}\right.}$ = Preview Question 6 Part 4 of 4   + C