Consider the indefinite integral ∫x+8x2+16x dx\displaystyle \int\frac{{{x}+{8}}}{\sqrt{{{x}^{{2}}+{16}{x}}}}\ {\left.{d}{x}\right.}:

a) This can be transformed into a basic integral by letting

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}=   (Hint: You may need to use parentheses before your "dx").

b) Performing the substitution yields the integral

∫\displaystyle \int  

c) Once we integrate and substitute, the final answer in terms of x is:  

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