Integration by Parts Problem 8

This discussion sets the analysis but it needs to be completed. Please add the finishing touches.

The formatting uses “latex”. Add this to your text:  [ latexpage]  (no space before the “l”)

Here is my latex code for the first line: (Start and end with a Dollar Sign)

Solve:      latex \int ln(x^2 + 15x + 54) dx

Solve:      $latex \int ln(x^2 + 15x + 54) dx $

Factor:

$latex x^2 + 15x + 54   =(x+6)(x+9)

\int ln(x^2 + 15x + 54) dx =  \int ln(x+6) + ln(x+9)dx

Now take one of them: \int ln(x+6)dx

Set u = ln(x+6) and dv = dx

du = dx/(x+6) and v = x\\

Result using Integration by Parts:

\int ln(x+6)dx = xln(x+6) – \int x/(x+6)dx =

xln(x+6) – \int (1 – 1/(x+6) )dx = xln(x+6) -ln|x+6| + c

$