Int ((2x)/(X+1)(X+2))dx?

Question

please show all work

Answer 1

ʃ(2x) / (x + 1)(x + 2) dx = ʃ(2x) / (x² + 3x + 2) dx

                                  = ʃ(2x + 3 ) - 3 / (x² + 3x + 2) dx

                                  = ʃ(2x + 3 )  / (x² + 3x + 2) dx + ʃ - 3 / (x + 1)(x + 2) dx

                                  = log|(x + 1)(x + 2)| -3ʃ(1 / (x + 1) (x + 2) dx

                                  = log|(x + 1)(x + 2)| -3[ʃ(1 / (x + 1) dx - ʃ1 / (x + 2) dx

                                  = log|(x + 1)(x + 2)| -3[log|x + 1| - log|x + 2| + C