Evaluate the Integral

Question

Evaluate the Integral. Please show all steps. If possible please attach a video going through the problem.

Answer 1

integral of (x^2+x+1)/(x+2)(x+1)^2 dx evaluated from 0 to 2

use partial fraction

= integral of (3/(x+2) - 2/(x+1) + 1/(x+1)^2) dx

= 3integral(dx/(x+2)dx -2integral(dx/(x+1) + integral(dx/(x+1)^2

use u substitution on each and plug back for x equivalents

=3ln|x+2| -2ln|x+1} - 1/(x+1) evaluated from 0 to 2

= 3ln2 -2ln3 + 2/3